Pharmaceutical Calculations

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Pharmaceutical Calculations
15 h Edit ion

H war C. A sel, Phd
Professor and Dean Emeritus
College of Pharmacy
University of Georgia
Athens, Georgia
Shelly J. S ck , Phd, RPh
Professor
College of Pharmacy
Southwestern Oklahoma State University
Weatherford, Oklahoma
Pharmaceutical
Calculations
15 h Edit ion
Senior Acquisitions Editor: Tari Broderick
Product Development Editor: Stephanie Roulias
Production Project Manager: Priscilla Crater
Designer: H olly McLaughlin
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15th Edition
Copyright © 2017 Wolters Kluwer
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9 8 7 6 5 4 3 2 1
Printed in China
Library of Congress Cataloging-in-Publication D ata
N ames: Ansel, H oward C., 1933- , author. | Stockton, Shelly J., author.
T itle: Pharmaceutical calculations / H oward C. Ansel, Shelly J. Stockton.
Description: 15th edition. | Philadelphia : Wolters Kluwer, [2016] | Includes
bibliographical references and index.
Identifiers: LCCN 2015039620 | ISBN 9781496300713 (alk. paper)
Subjects: | MESH : Drug Dosage Calculations. | Pharmaceutical
Preparations—administration & dosage.
Classification: LCC RS57 | N LM Q V 748 | DDC 615.1/401513—dc23 LC record available at http://lccn.loc.
gov/2015039620
T his work is provided “as is,” and the publisher disclaims any and all warranties, express or implied, including any
warranties as to accuracy, comprehensiveness, or currency of the content of this work.
T his work is no substitute for individual patient assessment based upon healthcare professionals’ examination of
each patient and consideration of, among other things, age, weight, gender, current or prior medical conditions,
medication history, laboratory data and other factors unique to the patient. T he publisher does not provide medical advice or guidance and this work is merely a reference tool. H ealthcare professionals, and not the publisher,
are solely responsible for the use of this work including all medical judgments and for any resulting diagnosis and
treatments.
Given continuous, rapid advances in medical science and health information, independent professional verification of medical diagnoses, indications, appropriate pharmaceutical selections and dosages, and treatment options
should be made and healthcare professionals should consult a variety of sources. W hen prescribing medication,
healthcare professionals are advised to consult the product information sheet (the manufacturer’s package insert)
accompanying each drug to verify, among other things, conditions of use, warnings and side effects and identify
any changes in dosage schedule or contraindications, particularly if the medication to be administered is new,
infrequently used or has a narrow therapeutic range. To the maximum extent permitted under applicable law, no
responsibility is assumed by the publisher for any injury and/or damage to persons or property, as a matter of
products liability, negligence law or otherwise, or from any reference to or use by any person of this work.
LW W.com
v
Preface
T he 15th edition of Pharmaceutical Calculations marks the introduction of Professor Shelly
Stockton as co-author. Professor Stockton’s experience in pharmacy practice and her expertise in teaching pharmaceutics and pharmacy calculations are reflected in her substantial
contributions to this textbook. Combined with the many progressive changes recommended by a select review team of pharmacy students, practitioners, and educators, this new
edition maintains the standard for today’s academic and basic practice requirements in the
subject area of pharmaceutical calculations.
Each chapter has been thoroughly revised with the focus directed toward providing
basic pharmaceutical calculations along with supporting explanations of the pharmaceutical
or clinical purpose underpinning each type of calculation. H undreds of new problems have
been added to include many current products encountered in pharmacy practice. Relevance
is further demonstrated by the inclusion of select product labels directly linked to example
problems. N ew in this edition are Authors’ Extra Points that provide brief explanations of
select underlying subjects, as: pharmacopeias, electronic prescriptions, drug names, and the regulation of pharmacy compounding. A section on equianalgesic dosing for narcotic analgesics has
been added to Chapter 10 along with dosing tables related to the subject.
All of the valued features of the previous edition have been retained and enhanced,
including the following: in-chapter example problems with step-by-step solutions; end-ofchapter practice problems with answers; Case-in-Point features that provide clinical or pharmaceutical case studies; Calculations Capsules that provide boxed summaries of chapter
calculations; CalcQuiz sections that provide a limited number of unsolved problems, useful as
homework, quiz, or assessment exercises; and, the Comprehensive Review Problems at the end
of the book that provide multipart solved problems for student use as a final self-assessment.
T hroughout its history, this textbook has served as a valuable resource in meeting the
instructional needs of pharmacy students in the area of pharmaceutical calculations. T his
new edition is expected to continue to meet that need.
Compan on Web s te
Pharmaceutical Calculations, 15th edition, includes additional resources for both instructors and
students, available on the book’s companion Web site at http://thePoint.lww.com/Ansel15e.
Resources for Students
•  Interactive math calculations Q uiz Bank, with more than 400 review problems and
detailed solutions
Resources for instructors
•  CalcQ uiz Solutions
•  Searchable Full Text Online
See the inside front cover for more details, including the passcode you will need to gain
access to the Web site.

vii
Acknowledgments
T he author gratefully acknowledges the contributions to this revision by the following persons: Tom Schoenbachler, for insights into contemporary community pharmacy practice;
Deborah Elder, for contributions in the area of pharmacy compounding; Ken Duke, for
problems in the area of nuclear pharmacy; Warren Beach, for some Case-in-Point calculations; Flynn Warren, for a host of problems including many relating to institutional pharmacy practice; Michael Ansel and Catherine Chuter, for information on the verification and
data processing of electronic prescriptions; Les Ramos and Margaret Ramos, for their input
in various areas of clinical calculations; H ardeep Saluja and Sarai Flynn for contributions to
the chapter on bioavailability and pharmacokinetics; Patra Kositchaiwat and Ryan Varghese
for their input in the area of electrolyte solution calculations; and Loyd V. Allen, Jr. for
his continued courtesy in allowing use of formulas published in the International Journal of
Pharmaceutical Compounding.
Gratitude is expressed to the following reviewers, whose experience was drawn upon
during the planning process and whose thoughtful analysis and constructive comments led
to many of the changes in this revision: Stacy Cairns, Kimberly Daugherty, David Dubins,
H eather Gegenhuber, N ancy Kleiman, William Kolling, Kimberly N guyen, and T ien Phan.
Particular thanks are offered to Tari Broderick, Senior Acquisitions Editor, and
Stephanie Roulias, Product Development Editor, for their support and guidance during the
revision process and to the other exceptional people at Wolters Kluwer H ealth | Lippincott
Williams & Wilkins for their work in the design, preparation, and production of this revision. Finally, special appreciation is extended to Tom Conville for his expertise in copyediting and assistance in resource development.
Howard C. Ansel
Athens, Georgia
Shelly J. Stockton
Weatherford, Oklahoma

ix
Preface v
Acknowledgments vii
Introduction xi
1 Fundamentals of Pharmaceutical Calculations …………………………………………………1
2 International System of Units ………………………………………………………………………17
3 Pharmaceutical Measurement …………………………………………………………………….35
4 Interpretation of Prescriptions and Medication Orders ……………………………………..52
5 Density and Specific Gravity ……………………………………………………………………….77
6 Percent Strength, Ratio Strength, and Other Expressions of Concentration ………….88
7 Calculation of Doses: General Considerations ……………………………………………….110
8 Calculation of Doses: Patient Parameters …………………………………………………….129
9 Calculations Involving Units of Activity and Other Measures of Potency …………….157
10 Selected Clinical Calculations ……………………………………………………………………167
11 Isotonic and Buffer Solutions …………………………………………………………………….189
12 Electrolyte Solutions: Milliequivalents, Millimoles, and Milliosmoles ………………….214
13 Intravenous Infusions, Parenteral Admixtures, Rate-of-Flow Calculations ………….239
14 Assessment of Nutritional Status, Enteral and Parenteral Nutrition,
and the Food Nutrition Label …………………………………………………………………….270
15 Altering Product Strength, Use of Stock Solutions, and Problem Solving
by Alligation …………………………………………………………………………………………..296
16 Reducing and Enlarging Formulas ……………………………………………………………..316
17 Selected Calculations in Contemporary Compounding ……………………………………323
18 Selected Calculations Involving Veterinary Pharmaceuticals ……………………………353
19 Selected Calculations Associated with Plant Extractives …………………………………362
20 Calculation of Active Drug Moiety ………………………………………………………………369
21 Selected Calculations Involving Radiopharmaceuticals …………………………………..374
Contents
x Contents
22 Selected Bioavailability and Pharmacokinetic Calculations ……………………………..386
23 Cost Differential Calculations in Drug Therapy ……………………………………………..399
Appendix A Common Systems of Measurement and Intersystem
Conversion ……………………………………………………………………………405
Appendix B Glossary of Pharmaceutical Dosage Forms and Drug
Delivery Systems …………………………………………………………………….412
Comprehensive Review Problems ………………………………………………………………417
Index…………………………………………………………………………………………………….445
Table of Atomic Weights …………………………………………………………………………..453
xi
Introduction
Scope of Pharmaceutical Calculations
T he use of calculations in pharmacy is varied and broad-based. It encompasses calculations
performed by pharmacists in traditional as well as in specialized practice settings and within
operational and research areas in industry, academia, and government. In the broad context,
the scope of pharmaceutical calculations includes computations related to:
•  chemical and physical properties of drug substances and pharmaceutical ingredients;
•  biological activity and rates of drug absorption, bodily distribution, metabolism, and
excretion (pharmacokinetics);
•  statistical data from basic research and clinical drug studies;
•  pharmaceutical product development and formulation;
•  prescriptions and medication orders including drug dosage, dosage regimens, and
patient adherence to medication treatment plans;
•  pharmacoeconomics; and other areas.
For each of these areas, there is a unique body of knowledge. Some areas are foundational, whereas others are more specialized, constituting a distinct field of study. T his
textbook is foundational, providing the basic underpinnings of calculations applicable to
pharmacy practice in community, institutional, and industrial settings.
In community pharmacies, pharmacists receive, fill, and dispense prescriptions and provide relevant drug information to ensure their safe and effective use. Prescriptions may call
for prefabricated pharmaceutical products manufactured in industry, or, they may call for
individual components to be weighed or measured by the pharmacist and compounded into a
finished product. In hospitals and other institutional settings, medication orders are entered
into a patient’s medical chart, becoming part of the electronic medical record.
In the preparation of pharmaceuticals, both medicinal and nonmedicinal materials are
used. T he medicinal components (active therapeutic ingredients or ATIs) provide the benefit
desired. T he nonmedicinal ingredients (pharmaceutical excipients) are included in a formulation to produce the desired pharmaceutical qualities, as physical form, chemical and physical
stability, rate of drug release, appearance, and taste, when desired.
W hether a pharmaceutical product is produced in the industrial setting or prepared in
a community or institutional pharmacy, pharmacists engage in calculations to achieve standards of quality. T he difference is one of scale. In pharmacies, relatively small quantities of
medications are prepared and dispensed for specific patients. In industry, large-scale production is designed to meet the requirements of pharmacies and their patients on a national and
even international basis. T he latter may involve the production of hundreds of thousands
of dosage units of a specific drug product during a single production cycle. T he preparation
of the various dosage forms and drug delivery systems (defined in Appendix B), containing
carefully calculated, measured, verified, and labeled quantities of ingredients, enables accurate dosage administration.
xii Introduction
A Step-Wise Approach toward Pharmaceutical Calculations
Success in performing pharmaceutical calculations is based on:
•  An understanding of the purpose or goal of the problem
•  An assessment of the arithmetic process required to reach the goal
•  An implementation of the correct arithmetic manipulations
For many pharmacy students, particularly those without pharmacy experience, difficulty arises when the purpose or goal of a problem is not completely understood. T he
background information provided in each chapter is intended to assist the student in understanding the purpose of each area of calculations. Additionally, the following steps are suggested in addressing the calculation problems in this textbook as well as those encountered
in pharmacy practice.
St e p 1. Take the time necessary to carefully read and thoughtfully consider the problem prior to engaging in computations. An understanding of the purpose or goal of
the problem and the types of calculations that are required will provide the needed
direction and confidence.
St e p 2. Estimate the dimension of the answer in both quantity and units of measure
(e.g., milligrams) to satisfy the requirements of the problem. A section in Chapter 1
provides techniques for estimation.
St e p 3. Perform the necessary calculations using the appropriate method both for
efficiency and understanding. For some, this might require a step-wise approach,
whereas others may be capable of combining several arithmetic steps into one.
Mathematical equations should be used only after the underlying principles of the
equation are understood.
St e p 4. Before assuming that an answer is correct, the problem should be read again
and all calculations checked. In pharmacy practice, pharmacists are encouraged to
have a professional colleague check all calculations prior to completing and dispensing a prescription or medication order. Further, if the process involves components
to be weighed or measured, these procedures should be double-checked as well.
St e p 5. Finally, consider the reasonableness of the answer in terms of the numerical
value, including the proper position of a decimal point, and the units of measure.
1
Pharmaceutical calculationsis the area o study that applies the basic principles o mathematics
to the preparation and e icacious use o pharmaceutical preparations. It includes calculations rom initial product ormulation through clinical administration and outcomes
assessment.
Mathematically, pharmacy students beginning use o this textbook are well prepared.
T he basic units o measurement and problem-solving methods have been previously learned
and are amiliar. T he newness lies in the terminology used and in the understanding o the
pharmaceutical/clinical purpose and goal o each computation. Of vital importance is an
appreciation of the need for accuracy, as each calculation must be understood to be directly applicable
to the health outcomes and safety of patients.
T his initial chapter introduces some basic aspects and methods o pharmaceutical
calculations.
Units of Measurement
Pharmacy and all other health pro essions utilize the International Systems of Units
(SI), commonly re erred to as the metric system. T his amiliar system, with its base units
(meter, liter, kilogram) and corresponding subdivisions, is presented in detail in Chapter 2.
Pharmaceutical calculations o ten require the accurate conversion o quantities rom a given
or calculated unit to another (e.g., milligrams to micrograms). Prof ciency in operating within
this system is undamental to the practice o pharmacy.
Two other systems o measurement are presented in Appendix A. T he avoirdupois system is the common system o commerce, which has not ully been replaced in the United
States by the International System o Units. Many product designations are dual scale; that
is, equivalent SI and common system measures. It is in the common system that goods are
packaged and sold by the ounce, pound, pint, quart, and gallon or linearly measured by the
inch, oot, yard, and mile. T he apothecaries’ system of measurement is the traditional system o
pharmaceutical measurement, which is now largely o historic signi icance. Intersystem conversion remains an exercise in pharmaceutical calculations and is a component o Appendix A.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:
D mon ra h u of percent n pharma u al al ula on .
Apply h m hod of ratio and proportion n pro l m ol ng.
Apply h m hod of dimensional analysis n pro l m ol ng.
D mon ra an und r and ng of gn f an f gur .
Apply and al da h m hod of estimation n pharma u al al ula on .
1
Fundamentals of Pharmaceutical
Calculations
2 Pharma euti al c al ulations
Percent
T he term percent and its corresponding sign, %, mean “in a hundred.” So, 50 percent (50%)
means 50 parts in each one hundred of the same item.
In pharmacy, percent most often is used to: (a) define the concentration or strength of
a pharmaceutical preparation (e.g., a 10% ointment), (b) describe the accuracy of a method
or procedure (e.g., a 5% error in a measurement or weighing), and (c) quantify a parameter
in a clinical study (e.g., 15% of subjects exhibited a particular effect). Calculations relating
to subject area (a) are presented in Chapter 6, and those of subject area (b) are presented
in Chapter 3.
T he following examples demonstrate the use of percent to define a clinical result.
(1) During a clinical study involving 2430 subjects, 2% of the subjects developed a headache.
How many patients experienced this adverse effect?
NOTE: In performing a pharmaceutical calculation, a given percent may be used
directly (as when using a calculator), or it may be converted to a ratio or decimal
fraction (e.g., 2% = 2/100 = 0.02).
2430 × 2% = 48.6 or 48 patients,
or, 2430 × 2/100 = 48.6 or 48 patients,
or, 2430 × 0.02 = 48.6 or 48 patients.
(2) During a clinical study, 48 out of a total of 2430 patients developed a headache. Calculate
the percent of patients who experienced this adverse effect.
48
2430
× 100 1 975 = % . or ≈ 2%
Pr a Ct iCe Pr o b l e ms
1. In a clinical study of niacin as a lipid-altering agent, 60% of the 90 patients in
the study group developed flushing. Calculate the number of patients having this
reaction.
2. In a clinical study of divalproex sodium (DEPAKOT E) in patients prone to
migraine headaches, nausea occurred in 62 of 202 patients whereas the use of a
placebo resulted in nausea in 8 of 81 patients. Compare these data in terms of
percent of subjects reporting nausea in each study group.
3. If a clinical study of a new drug demonstrated that the drug met the effectiveness
criteria in 646 patients of the 942 patients enrolled in the study, express these
results as a decimal fraction and as a percent.
4. Ritonavir (N ORVIR) oral solution contains, in addition to ritonavir, 43.2% alcohol and 26.57% propylene glycol. Calculate the quantities of each of these two
ingredients in a 240-mL bottle of the oral solution.
5. If a 60-gram tube of an ointment contains 2.5 grams of active ingredient, calculate
the percent concentration of active ingredient in the ointment.
6. T he literature for a pharmaceutical product states that 26 patients of the 2103
enrolled in a clinical study reported headache after taking the product. Calculate
(a) the decimal fraction and (b) the percentage of patients reporting this adverse
response.
1 • Fundamentals of Pharma euti al c al ulations 3
Ratio and Proportion
Ratio
T he relative amount o two quantities (one to the other), is called their ratio. A ratio
resembles a common raction except in the manner in which it is presented. For example,
the raction ½ may be expressed as the ratio, 1:2, and is not read as “one hal ,” but rather
as “one is to two.” Rules governing common ractions apply to ratios. For example, i the
two terms o a ratio are either multiplied or divided by the same number, the value remains
unchanged. T he value is the quotient o the f rst term divided by the second term. For
instance, the value o the ratio 20:4 is 5. I the ratio is multiplied by 4, becoming 80:16, or
divided by 4, becoming 5:1, the value remains 5. W hen two ratios have the same value, they
are termed equivalent ratios, as is the case with the ratios 20:4, 80:16, and 5:1.
As described next, equivalent ratios provide the basis or problem solving by the ratio
and proportion method.
Proportion
A proportion is the expression o the equality o two ratios. It may be written in any one o
three standard orms:
( ) : :
( ) : :: :
( )
1 2 3
a b c d
a b c d
ab
= cd
=
Each o these expressions is read: a is to b as c is to d, and a and d are called the extremes
(meaning “outer members”) and b and c the means (“middle members”).
In any proportion, the product of the extremes is equal to the product of the means. T his
principle allows us to ind the missing term o any proportion when the other three terms
are known. I the missing term is a mean, it will be the product of the extremes divided by the
given mean, and i it is an extreme, it will be the product of the means divided by the given extreme.
Using this in ormation, we may derive the ollowing ractional equations:
If then
and
ab
cd
a
bc
d
b ad
c
c
ad
b
d bc
a
=
= = = =
,
, , , .
In a proportion that is properly set up, the position o the unknown term does not matter. H owever, some persons pre er to place the unknown term in the ourth position—that
is, in the denominator o the second ratio. It important to label the units in each position (e.g.,
mL, mg) to ensure the proper relationship between the ratios of a proportion.
T he application o ratio and proportion enables the solution to many o the pharmaceutical calculation problems in this text and in pharmacy practice.
(1) If 3 tablets contain 975 milligrams of aspirin, how many milligrams should be contained
in 12 tablets?
3
12

( ) ( ) tablets tablets

975 ( ) ( ) milligrams x milligrams

(
x millig
=
rrams
tablets milligrams
tablets
) ( ) ( )
( )
=
×
=
12 975
3
3900 milligrams
4 Pharma euti al c al ulations
(2) If 3 tablets contain 975 milligrams of aspirin, how many tablets should contain 3900
milligrams?
3 975
3900
( )
( )
( )
( )
(
tablets
x tablets
milligrams
milligrams
x tabl
=
eets
tablets milligrams
milligrams
)
( )
( )
=
( ) ×
=
3 3900
975
12 tablets
(3) If 12 tablets contain 3900 milligrams of aspirin, how many milligrams should 3 tablets contain?
12
3
( ) 3900
( )
( )
( )
(
tablets
tablets
milligrams
x milligrams
x milli
=
ggrams
tablets milligrams
tablets
) ( ) ( )
( )
=
×
=
3 3900
12
975 milligrams
(4) If 12 tablets contain 3900 milligrams of aspirin, how many tablets should contain
975 milligrams?
12 3900
975
( )
( )
( )
( )
(
tablets
x tablets
milligrams
milligrams
x tab
=
llets tablets milligrams
milligrams
) ( ) ( )
( )
=
×
=
12 975
3900
3 tablets
Proportions need not contain whole numbers. If common or decimal fractions are
supplied in the data, they may be included in the proportion without changing the method.
For ease of calculation, it is recommended that common fractions be converted to decimal
fractions prior to setting up the proportion.
(5) If 30 milliliters (mL) represent 1/6 of the volume of a prescription, how many milliliters
will represent ¼ of the volume?
1
6

1 0 167 0 25 30 . ( ) . ( ) volume volume

( ) ( ) mL x mL

0 167 0 25 4
4
= =
=
=
. .
and
x 491 . or ≈ 45 mL
Ca l Cu l at io n s Ca Ps u l e
Ratio and Proportion
• A ratio expresses the relative magnitude of two like quantities (e.g., 1:2, expressed as
“1 to 2.”)
• A proportion expresses the equality of two ratios (e.g., 1:2 = 2:4).
• The four terms of a proportion are stated as:
a b c d a b c a
b
cd
: : : :: : = = , or, d, or
and expressed as “a is to b as c is to d.”
• Given three of the four terms of a proportion, the value of the fourth, or missing, term
may be calculated by cross multiplication and solution.
• The ratio-and-proportion method is a useful tool in solving many pharmaceutical
calculation problems
1 • Fundamentals of Pharma euti al c al ulations 5
Dimensional Analysis
W hen performing pharmaceutical calculations, some students prefer to use a method termed
dimensional analysis (also known as factor analysis, factor-label method, or unit-factor
method). T his method involves the logical sequencing and placement of a series of ratios
(termed factors) into an equation. T he ratios are prepared from the given data as well as
from selected conversion actorsand contain both arithmetic quantities and their units of measurement. Some terms are inverted (to their reciprocals) to permit the cancellation of like
units in the numerator(s) and denominator(s) and leave only the desired terms of the answer.
One advantage of using dimensional analysis is the consolidation of several arithmetic steps
into a single equation.
In solving problems by dimensional analysis, the student unfamiliar with the process
should consider the following steps1,2:
St ep 1. Identify the wanted unit of the answer (e.g., mL, mg, etc.) and place it at the
beginning of the equation. Some persons prefer to place a question mark next to it.
St ep 2. Identify the given quantity(ies) and its (their) unit(s) of measurement.
St ep 3. Identify the conversion factor(s) that is (are) needed for the “unit path” to
arrive at the arithmetic answer in the unit wanted.
St ep 4. Set up the ratios such that the cancellation of the units of measurement in the
numerators and denominators will retain only the wanted unit as identified in Step 1.
St ep 5. Perform the arithmetic computation by multiplying the numerators, multiplying the denominators, and dividing the product of the numerators by the product
of the denominators.
T he general scheme shown here and in the “Calculations Capsule: Dimensional
Analysis” may be helpful in using the method.
Unit Path
Given Quantity
Conversion Factor
as Needed
Conversion Factor
as Needed
Conversion
Computation
Wanted Quantity
and Unit
(Wanted Unit) = =
Example Calculations Using Dimensional Analysis
(1) How many f uidounces (f . oz.) are there in 2.5 liters (L)?
St ep 1. T he wanted unit for the answer is luidounces.
St ep 2. T he given quantity is 2.5 L.
St ep 3. T he conversion factors needed are those that will take us from liters to
fluidounces.
As the student will later learn, these conversion factors are as follows:
1 liter = 1000 mL (to convert the given 2.5 L to milliliters)
1 luidounce = 29.57 mL (to convert milliliters to fluidounces)
St ep 4. Set up the ratios in the unit path
Unit Path
Given Quantity
Conversion
Computation
=
2.5 L 1000 mL 1 fl. oz.
1 L 29.57 mL
fl.oz. (Wanted Unit) =
Conversion Factor
as Needed
Conversion Factor
as Needed
Wanted Quantity
and Unit
6 Pharma euti al c al ulations
NOTE: T he unit path is set up such that all units of measurement will cancel
out except for the unit wanted in the answer, fluidounces, which is placed in the
numerator.
St ep 5. Perform the computation:
Unit Path
Given Quantity
Conversion Factor
as Needed
Conversion Factor
as Needed
Conversion
Computation
Wanted Quantity
and Unit
1 fl. oz. 2.5 × 1000 × 1 = 2500 = 84.55 fl. oz.
1 × 29.57 29.57
2.5 L
1 L
1000 mL
29.57 mL
fl.oz. (Wanted Unit) =
or
2 5
1000
1
1
29 57
2 5 1000 1
1 29 57
2500
29 57
.
. .
.
.
. .
L
mL
L
fl oz
mL
× × =
× ×
×
= = 8455 fl oz . . .
NOTE: T he student may wish to see the problem solved by ratio and proportion:
St ep 1.
1
2 5
L 1000
L
mL
x mL
x
( )
( ) =
( )
. ( ) ; = 2500 mL
St ep 2.
29 57
2500
. . . 1
. .
. .
mL
mL
fl oz
x fl oz
x .
( )
( ) =
( )
( )
= 84 55 fl oz
Ca l Cu l at io n s Ca Ps u l e
Dimensional Analysis
• An alternative method to ratio and proportion in solving pharmaceutical calculation
problems.
• The method involves the logical sequencing and placement of a series of ratios to
consolidate multiple arithmetic steps into a single equation.
• By applying select conversion factors in the equation—some as reciprocals—unwanted
units of measure cancel out, leaving the arithmetic result and desired unit.
• Dimensional analysis scheme:
Unit Path
Given Quantity
Conversion
Computation
=
Conversion Factor
as Needed
Conversion Factor
as Needed
Wanted Quantity
and Unit
(Wanted Unit) =
1 • Fundamen als of Pharma eu al c al ula ons 7
Ca s e in Po in t 1.1 A pharma s onsul s w h a paren on he use of a ough
syrup for her 5-year-old h ld. t he nonpres r p on ough syrup on a ns, n ea h
5-mL (m ll l ers), 10 mg (m ll grams) of dex rome horphan Hb r, a ough suppressan , and 100 mg of gua fenes n, an expe oran . t he pa kage la el nd a es ha
he dose for a h ld 2 o 6 years of age s 1/4 of he adul dose of wo easpoonfuls.
t he pharma s sugges s us ng an oral syr nge al ra ed n 0.25-mL un s for dos ng.
if a s andard easpoonful s equ valen o 5 mL, (a) how many m ll l ers should e
adm n s ered o he h ld, and ( ) how many m ll grams of ea h of he wo herapeungred en s would e adm n s ered per h ld’s dose?
(2) A medication order calls for 1000 milliliters of a dextrose intravenous infusion to be
administered over an 8-hour period. Using an intravenous administration set that delivers
10 drops/milliliter, how many drops per minute should be delivered to the patient?
Solving by dimensional analysis:
8 hours 480 minutes (min) =
? drops 1000 mL 10 drops
1 mL
1
480 min
= × × = 20.8 or 21 drops per minute
NOTE: “drops” was placed in the numerator and “minutes” in the denominator to
arrive at the answer in the desired term, drops per minute.
T he student may wish to see this problem solved by ratio and proportion:
St ep 1.
480 (min)
1 (min)
1000 (mL)
x (mL)
= = ; x 2.08 mL
St ep 2.
1 (mL)
2.08 (mL)
10 (drops)
x (drops)
= = ; x 2.08 mL or 21 drops per minute
T he following problem is often used to demonstrate the process of dimensional analysis.
(3) Calculate the number of seconds in a day.
? s 1 day 24 h
1 day
60 min
1 h
60 s
1 min
1
24 60 60
1 1 1
= × × = × ×
× ×
× ×
= 86, 400 s
8 Pharma euti al c al ulations
Pr a Ct iCe Pr o b l e ms
1. If an insulin injection contains 100 units of insulin in each milliliter, how many
milliliters should be injected to receive 40 units of insulin?
2. An injection contains 2 mg of medication in each milliliter (mL). If a physician
prescribes a dose of 0.5 mg to be administered to a hospital patient three times
daily, how many milliliters of injection will be required over a 5-day period?
3. In a clinical study, a drug produced drowsiness in 30 of the 1500 patients studied.
H ow many patients of a certain pharmacy could expect similar effects, based on
a patient count of 100?
4. A formula for 1250 tablets contains 6.25 grams of diazepam. H ow many grams of
diazepam should be used in preparing 550 tablets?
5. If 100 capsules contain 400 mg of an active ingredient, how many milligrams of
the ingredient will 48 capsules contain?
6. Each tablet of T YLEN OL W IT H CODEIN E contains 30 mg of codeine phosphate and 300 mg of acetaminophen. By taking 2 tablets daily for a week, how
many milligrams of each drug would the patient take?
7. A cough syrup contains 10 mg of dextromethorphan hydrobromide per 5 mL. H ow
many milligrams of the drug are contained in a 120-mL container of the syrup?
8. If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient per
hour, how many milligrams of medication are delivered per half minute?
9. T he biotechnology drug filgrastim (N EUPOGEN ) is available in syringes
containing 480 micrograms (mcg) of filgrastim per 0.8 mL. H ow many micrograms of the drug would be administered by each 0.5 mL injection?
10. An oral solution contains, in each milliliter, 80 mg of lopinavir and 20 mg of
ritonavir. H ow many milligrams of each drug would be contained in a calculated
dose of 0.4 mL?
11. Aripiprazole (ABILIFY) injection is available in single-dose vials containing
9.75 mg of aripiprazole in each 1.3 mL of injection. Calculate the volume of injection that would provide a dose of 5.25 mg of aripiprazole.
12. Acyclovir (ZOVIRAX) suspension contains 200 mg of acyclovir in each 5 mL.
H ow many milligrams of acyclovir are contained in a pint (473 mL) of suspension?
13. A metered dose inhaler contains 225 mg of metaproterenol sulfate, which is
sufficient for 100 inhalations. H ow many micrograms (mcg) of metaproterenol
sulfate would be administered with each inhalation if there are 1000 micrograms
in each milligram?
14. A pediatric vitamin drug product contains the equivalent of 0.25 mg of fluoride
ion in each milliliter. H ow many milligrams of fluoride ion would be provided by
a dropper that delivers 0.6 mL?
15. If a pediatric vitamin contains 1500 units of vitamin A per milliliter of solution,
how many units of vitamin A would be administered to a child given 2 drops of the
solution from a dropper calibrated to deliver 20 drops per milliliter of solution?
16. An elixir contains 25 mg of drug in each 5 mL. H ow many milligrams of the drug
would be used in preparing 4000 mL of the elixir?
17. An elixir of ferrous sulfate contains 220 mg of ferrous sulfate in each 5 mL. If
each milligram of ferrous sulfate contains the equivalent of 0.2 mg of elemental
iron, how many milligrams of elemental iron would be represented in each 5 mL
of the elixir?
18. An estradiol transdermal patch is available in various patch sizes. T he patch size
is closely proportional to the amount of drug contained in the patch. If the patch
1 • Fundamentals of Pharma euti al c al ulations 9
containing 0.025 mg of estradiol is 6.5 cm2 in size, calculate the approximate size
of the patch containing 0.1 mg of estradiol.
19. If an ophthalmic solution contains 1 mg of dexamethasone phosphate in each
milliliter of solution, how many milligrams of dexamethasone phosphate would
be contained in 2 drops if the eyedropper used delivered 20 drops per milliliter?
20. A 15-mL package of nasal spray delivers 20 sprays per milliliter of solution, with each
spray containing 1.5 mg of drug. (a) H ow many total sprays will the package deliver?
(b) H ow many milligrams of drug are contained in the 15-mL package of the spray?
21. A penicillin V potassium preparation provides 400,000 units of activity in each
250-mg tablet. H ow many total units of activity would a patient receive from taking 4 tablets a day for 10 days?
22. If a 5-g packet of a potassium supplement provides 20 milliequivalents of potassium ion and 3.34 milliequivalents of chloride ion, (a) how many grams of the
powder would provide 6 milliequivalents of potassium ion, and (b) how many
milliequivalents of chloride ion would be provided by this amount of powder?
23. If a potassium chloride elixir contains 20 milliequivalents of potassium ion in each
15 mL of elixir, how many milliliters will provide 25 milliequivalents of potassium
ion to the patient?
24. T he blood serum concentration of the antibacterial drug ciprofloxacin increases
proportionately with the dose of drug administered. If a 250-mg dose of the
drug results in a serum concentration of 1.2 micrograms of drug per milliliter of
serum, how many micrograms of drug would be expected per milliliter of serum
following a dose of 500 mg of drug?
25. T he dosage of the drug thiabendazole (MIN T EZOL) is determined in direct
proportion to a patient’s weight. If the dose of the drug for a patient weighing 150
pounds is 1.5 grams, what would be the dose for a patient weighing 110 pounds?
26. If 0.5 mL of a mumps virus vaccine contains 5000 units of antigen, how many
units would be present in each milliliter if the 0.5 mL of vaccine was diluted to
2 mL with water for injection?
27. A sample of O riental ginseng contains 0.4 mg of active constituents in each
100 mg of powdered plant. H ow many milligrams of active constituents would
be present in 15 mg of powdered plant?
N OT E: Solve problems 28 to 32 by dimensional analysis, using the following
equivalencies as needed:
1 gram (g) = 1000 milligrams (mg)
1 mg = 1000 micrograms (mcg)
1 kilogram (kg) = 2.2 pounds (lb)
28. If 120 mL of a syrup contains 1.2 g of rimantadine H Cl, and if a 2.5-mL dose of the
syrup is administered, how many milligrams of rimantadine H Cl would be given?
29. H ow many milliliters of an injection containing 0.25 mg of drug in each milliliter
should be administered to provide a dose of 10 mcg?
30. An injection intended for pediatric use contains 100 mcg of digoxin per milliliter.
W hat volume of injection should be administered to provide a dose of 0.04 mg?
31. A patient is to receive 2 mg of drug from an injection labeled to contain 150 mcg/mL.
Calculate the milliliters of injection to administer.
32. T he dose of a drug is 0.05 mg for each kilogram of a patient’s weight. T he drug
is available as an oral liquid containing 50 mcg/0.1 mL. Calculate the dose of the
oral liquid, in milliliters, for a patient who weighs 132 lb.
10 Pharma euti al c al ulations
Alligation
Alligation is an arithmetic method o solving problems relating mixtures o components o
di erent strengths. T here are two types o alligation: alligation medial and alligation alternate.
Alligation medial may be used to determine the strength o a common ingredient in a
mixture o two or more preparations. For example, i a pharmacist mixed together known
volumes o two or more solutions containing known amounts o a common ingredient, the
strength o that ingredient in the resulting mixture can be determined by alligation medial.
Alligation alternate may be used to determine the proportion or quantities o two or
more components to combine in order to prepare a mixture o a desired strength. For
example, i a pharmacist wished to prepare a solution o a speci ied strength by combining
two or more other solutions o di ering concentrations o the same ingredient, the proportion or volumes o each solution to use may be determined by alligation alternate.
Alligation medial and alligation alternate may be used as options in solving a number
o pharmaceutical calculations problems. T he methods and problem examples are presented
in Chapter 15.
Significant Figures
W hen we count objects accurately, every f gure in the numeral expressing the total number
o objects must be taken at its ace value. Such f gures may be said to be absolute. W hen we
record a measurement, the last f gure to the right must be taken to be an approximation, an
admission that the limit o possible precision or o necessary accuracy has been reached and
that any urther f gures to the right would not be signif cant—that is, either meaningless or,
or a given purpose, needless.
A denominate number, like 325 grams, is interpreted as ollows: T he 3 means 300 grams,
neither more nor less, and the 2 means exactly 20 grams more; but the inal 5 means approximately
5 grams more, that is, 5 grams plus or minus some raction o a gram. W hether this raction is, or
a given purpose, negligible depends on how precisely the quantity was (or is to be) weighed.
Significant figures, then, are consecutive igures that express the value o a denominate number accurately enough or a given purpose. T he accuracy varies with the number
o signi icant igures, which are all absolute in value except the last, and this is properly
called uncertain.
W hether zero is signi icant, however, depends on its position or on known acts about
a given number. T he interpretation o zero may be summed up as ollows:
(1) Any zero between digits is signif cant.
(2) Initial zeros to the le t o the f rst digit are never signif cant; they are included
merely to show the location o the decimal point and thus give place value to the
digits that ollow.
(3) One or more f nal zeros to the right o the decimal point may be taken to be
signif cant.
Examples:
Assuming that the ollowing numbers are all denominate:
(1) In 12.5, there are three signif cant f gures; in 1.256, our signif cant f gures; and in
102.56, f ve signif cant f gures.
(2) In 0.5, there is one signif cant f gure. T he digit 5 tells us how many tenths we have.
T he nonsignif cant 0 simply calls attention to the decimal point.
(3) In 0.05, there is still only one signif cant f gure, as there is in 0.005.
1 • Fundamentals of Pharma euti al c al ulations 11
(4) In 0.65, there are two signi cant gures, and likewise two in 0.065 and 0.0065.
(5) In 0.0605, there are three signi cant gures. T he rst 0 calls attention to the decimal point, the second 0 shows the number o places to the right o the decimal
point occupied by the remaining gures, and the third 0 signi cantly contributes to
the value o the number. In 0.06050, there are four signi cant gures, because the
nal 0 also contributes to the value o the number. [It should be noted, however, that in
pharmacy practice “trailing zeros” are not retained as a result of a calculation as they may
lead to misinterpretation and error.]
Ca l Cu l at io n s Ca Ps u l e
Significant Figures
• Digits other than zero are significant.
• A zero between digits is significant.
• Zeros used only to show the location of the decimal point are not significant.
• The United States Pharmacopeia states that in performing pharmaceutical calculations, all figures are to be utilized until the calculations are completed and then only the
significant figures retained in the final result.3
Rules for Rounding
(1) W hen rounding a measurement, retain as many gures as will give only one
uncertain gure. For example, in using a ruler calibrated only in ull centimeter
units, it would be correct to record a measurement o 11.3 centimeters but not
11.32 centimeters, because the 3 (tenths) is uncertain and no gure should ollow it.
(2) W hen eliminating superf uous gures ollowing a calculation, add 1 to the last gure retained in a calculation i it is 5 or more. For example, 2.43 may be rounded
o to 2.4, but 2.46 should be rounded o to 2.5.
(3) W hen adding or subtracting approximate numbers, include only as many decimal
places as are in the number with the fewest decimal places. For example, when adding
162.4 grams + 0.489 gram + 0.1875 gram + 120.78 grams, the sum is 283.8565 grams,
but the rounded sum is 283.9 grams. H owever, when an instrument has the capability to weigh precisely all the quantities in such a calculation, rounding may be
deemed inappropriate.
One o the actors determining the degree o approximation to per ect measurement
is the precision o the instrument used. It would be incorrect to claim that 7. 76 milliliters
had been measured in a graduate calibrated in units o 1 milliliter, or that 25.562 grams had
been weighed on a balance sensitive to 0.01 gram.
We must clearly distinguish significant figures rom decimal places. W hen recording a
measurement, the number o decimal places we include indicates the degree of precision with
which the measurement has been made, whereas the number o signi icant igures retained
indicates the degree of accuracy that is su icient or a given purpose.
Sometimes we are asked to record a value “correct to (so many) decimal places.” We
should never con use this amiliar expression with the expression “correct to (so many) signi icant igures.” For example, i the value 27.625918 is rounded to five decimal places, it is
written 27.62592; but when this value is rounded to five significant figures, it is written 27.626.
12 Pharma euti al c al ulations
In this regard, there is an assumption made in pharmaceutical calculations that all
measurements in the filling of a prescription or in compounding a formula are performed
with equal precision by the pharmacist. T hus, or example, i the quantities 5.5 grams,
0.01 gram, and 0.005 gram are speci ied in a ormula, they may be added as i they
are precise weights, with a sum o 5.515 grams.
(4) W hen multiplying or dividing two approximate numbers, retain no more signif –
cant f gures than the number having the ewest signif cant f gures. For example, i
multiplying 1.6437 grams by 0.26, the answer may be rounded rom the calculated
0.427362 gram to 0.43 gram.
(5) W hen multiplying or dividing an approximate number by an absolute number,
the result should be rounded to the same number o signif cant f gures as in the
approximate number. T hus, i 1.54 milligrams is multiplied by 96, the product,
243.84 milligrams, may be rounded to 244 milligrams, or to three signif cant f gures.
(6) O tentimes, logic plays a role. For example, when a calculation is per ormed to
determine the number of doses available rom a medication or the number of drops to
be administered to a patient, it is both logical and practical to express the answer
in whole units.
Pr a Ct iCe Pr o b l e ms
1. State the number o signi icant igures in each o the italicized quantities:
(a) One luidounce equals 29.57 milliliters.
(b) One liter equals 1000 milliliters.
(c) One inch equals 2.54 centimeters.
(d) T he chemical costs $1.05 per pound.
(e) One gram equals 1,000,000 micrograms.
( ) One microgram equals 0.001 milligram.
2. Round each o the ollowing to three signi icant igures:
(a) 32.75
(b) 200.39
(c) 0.03629
(d) 21.635
(e) 0.00944
3. Round each o the ollowing to three decimal places:
(a) 0.00083
(b) 34.79502
(c) 0.00494
(d) 6.12963
4. I a mixture o seven ingredients contains the ollowing approximate weights,
what can you validly record as the approximate total combined weight o the
ingredients?
26.83 grams, 275.3 grams, 2.752 grams, 4.04 grams, 5.197 grams, 16.64 grams,
and 0.085 gram.
5. Per orm the ollowing computations, and retain only signi icant igures in the results:
(a) 6.39 – 0.008
(b) 7.01 – 6.0
(c) 5.0 × 48.3 grams
(d) 24 × 0.25 gram
(e) 56.824 ÷ 0.0905
( ) 250 ÷ 1.109
1 • Fundamentals of Pharma euti al c al ulations 13
Estimation
It is important for pharmacy students and pharmacists to recognize the reasonableness of
the result of a calculation. By performing an estimation of the answer prior to calculation,
the approximate result may be predetermined. T his helps assure the correct dimension
of the answer including the critical placement of a decimal point.
T he technique of estimation is demonstrated by the examples that follow. Rounding of
numbers is a component of this process.
Add the following numbers: 7428, 3652, 1327, 4605, 2791, and 4490.
Estimation:
T he figures in the thousands column add up to 21,000, and with each number on the
average contributing 500 more, or every pair 1000 more, we get 21,000 + 3000 = 24,000,
estimated answer (actual answer, 24,293).
In multiplication, the product of the two leftmost digits plus a sufficient number of zeros
to give the right place value serves as a fair estimate. T he number of zeros supplied must equal
the total number of all discarded figures to the left of the decimal point. Approximation to the
correct answer is closer if the discarded figures are used to round the value of those retained.
Multiply 612 by 413.
Estimation:
4 × 6 = 24, and because we discarded four figures, we must supply four zeros, giving
240,000, estimated answer (actual answer, 252,756).
In division, the given numbers may be rounded off to convenient approximations, but
again, care is needed to preserve the correct place values.
Divide 2456 by 5.91.
Estimation:
T he numbers may be rounded off to 2400 and 6. We may divide 24 by 6 mentally,
but we must remember the two zeros substituted for the given 56 in 2456. T he estimated
answer is 400 (actual answer, 416).
Pr a Ct iCe Pr o b l e ms
1. Estimate the sums:
(a) 5641 (b) 3298 (c) $75.82
2177 368 37.92
294 5192 14.69
8266 627 45.98
3503 4835 28.91
49.87
2. Estimate the products:
(a) 42 × 39 =
(b) 596 × 204 =
(c) 8431 × 9760 =
(d) 0.0726 × 6951 =
(e) 6.1 × 67.39 =
3. Estimate the quotients:
(a) 171 ÷ 19 =
(b) 184 ÷ 2300 =
(c) 98,000 ÷ 49 =
(d) 1.0745 ÷ 500 =
(e) 458.4 ÷ 8 =
14 Pharma euti al c al ulations
Ca l Cq u iz
1.A. Digoxin (LANOXIN) pediatric elixir contains 0.05 mg (milligram) of digoxin in each
milliliter (mL) of elixir. If there are 1000 µg (micrograms) in each milligram, how many
micrograms of digoxin would be delivered in each dose of 0.6 mL?
1.B. A probiotic colon health product contains, in each capsule, 3 billion viable cells
of Lactobacillus acidophilus and Bifidobacterium longum. Express, by exponential
notation, the number of viable cells in a container of 30 capsules.
1.C. A liquid dietary supplement is packaged in 10-mL dropper containers to deliver
2000 international units of vitamin D3 in each drop (0.027 mL). Calculate the number
of drops delivered per milliliter.
1.D. The drug pramlintide (SYMLIN) is an antihyperglycemic agent for use in patients with
diabetes treated with insulin. A 5-mL vial contains 600 µg of pramlintide per milliliter.
A 0.05-mL dose measures 5 insulin units on the syringe used for injection and provides 30 µg of pramlintide. Calculate the number of micrograms of pramlintide and
the corresponding measurement of insulin units on the syringe with the administration of 0.075 mL of injection.
1.E. A physician prescribed mometasone furoate monohydrate (NASONEX) nasal spray
for a patient, with directions to administer two sprays into each nostril once daily. If
each spray contains 50 µg of drug and the container can deliver a total of 120 sprays,
how many micrograms of drug would the patient receive daily, and how many days
of use will the prescription last the patient?
a n s w e r s t o “Ca s e in Po in t ” a n d Pr a Ct iCe Pr o b l e ms
Case in Point 1.1
1 teaspoonful = 5 mL
Adult dose = 2 teaspoonfuls = 10 mL
(a) Child’s dose = 1/4 × 10 mL (2 teaspoonfuls) = 2.5 mL
(b) ? mg dextromethorphan HBr =
×
=
10 2 5
5
5
mg mL
mL
mg
.
dextromethorphan H Br
and
?
.
mg guaifenesin mg mL
mL
mg guaifenesin
=
×
=
100 2 5
5
50
Proof of calculations: child’s dose is ¼ of adult dose:
Child’s calculated dose of cough syrup/adult dose = 2.5 mL/10 mL = ¼ √
Child’s calculated dose of dextromethorphan H Br/adult dose = 5 mg/20 mg = ¼ √
Child’s calculated dose of guaifenesin/adult dose = 50 mg/200 mg = ¼ √
1 • Fundamentals of Pharma euti al c al ulations 15
Percent
1. 54 patients
2. 30.7% DEPAKOT E subjects
9.9% placebo subjects
3. 0.69 or 69%
4. 103.68 mL alcohol
63.77 mL propylene glycol
5. 4.17%
6. 0.012 or 1.2% of patients
Ratio, Proportion, and Dimensional
Analysis
1. 0.4 mL insulin injection
2. 3.75 mL
3. 2 patients
4. 2.75 g diazepam
5. 192 mg
6. 420 mg codeine phosphate
4200 mg acetaminophen
7. 240 mg dextromethorphan hydrobromide
8. 0.125 mg
9. 300 mcg filgrastim
10. 32 mg lopinavir and 8 mg ritonavir
11. 0.7 mL aripiprazole injection
12. 18,920 mg acyclovir
13. 2250 mcg metaproterenol sulfate
14. 0.15 mg fluoride ion
15. 150 units vitamin A
16. 20,000 mg
17. 44 mg elemental iron
18. 26 cm2
19. 0.1 mg dexamethasone phosphate
20. (a) 300 sprays
(b) 450 mg
21. 16,000,000 units
22. (a) 1.5 g
(b) 1 milliequivalent chloride ion
23. 18.75 mL
24. 2.4 mcg ciprofloxacin
25. 1.1 g thiabendazole
26. 2500 units antigen
27. 0.06 mg
28. 25 mg rimantadine H Cl
29. 0.04 mL injection
30. 0.4 mL injection
31. 13.3 mL injection
32. 6 mL oral liquid
Significant Figures
1. (a) four
(b) four
(c) three
(d) three
(e) seven
(f) one
2. (a) 32.8
(b) 200
(c) 0.0363
(d) 21.6
(e) 0.00944
3. (a) 0.001
(b) 34.795
(c) 0.005
(d) 6.130
4. 330.8 g
5. (a) 6.38
(b) 1.0
(c) 240 g
(d) 6.0 g
(e) 628
(f) 225
Estimation
1. (a) 20,500 (19,881)
(b) 14,500 (14,320)
(c) $240.00 ($253.19)
2. (a) 40 × 40 = 1600 (1638)
(b) 600 × 200 = 120,000 (121,584)
(c) 8000 × 10,000 = 80,000,000
(82,286,560)
(d) (7 × 70) = 490 (504.6426)
(e) 6 × 70 = 420 (411.079)
3. (a) 170 ÷ 20 = 8.5 (9.0)
(b) 180 ÷ 2000 = 0.09 (0.08)
(c) 9800 ÷ 5 = 1960 (2000)
(d) 0.01 ÷ 5 = 0.002 (0.002149)
(e) 460 ÷ 8 = 57.5 (57.3)
16 Pharma euti al c al ulations
References
1. D imensional Analysis–Tripod.com. Available at: http://susanp3.tripod.com/snurse/id28.htm. Accessed
October 16, 2015.
2. Craig GP. Clinical Calculations Made Easy. 4th Ed. Baltimore, MD: Lippincott Williams & Wilkins, 2008.
3. T he United States Pharmacopeial Convention. United States Pharmacopeia 32 National Formulary 27. Rockville,
MD: T he United States Pharmacopeial Convention, 2009;1:675.
17
T he International System of Units (SI), formerly called the metric system, is the
internationally recognized decimal system of weights and measures. T he system was formulated in France in the late 18th century. Over the years, effort has been made in the United
States to transition from use of the common systems of weights and measures (e.g., pounds,
feet, gallons) to the international system. Today, the pharmaceutical research and manufacturing industry, the United States Pharmacopeia–National Formulary,a and all the health
professions reflect conversion to the SI system. T he advantages include the simplicity of the
decimal system, the clarity provided by the base units and prefixes, and the ease of scientific
and professional communications provided through the use of a universally accepted system.
T he base units of the SI are the meter (for length), the kilogram (for weight), and the
liter (for volume).b Subdivisions and multiples of these base units, their relative values, and
their corresponding prefixes are shown in Table 2.1.
Guidelines for the Correct Use of the SI
T he following are select guidelines for the correct use of the SI from the U.S. Metric
Association, with additional considerations relevant to the practice of pharmacy1,2:
•  Unit names and symbols are not capitalized except when used at the beginning of a
sentence or in headings. H owever, the symbol for liter (L, l) may be capitalized or
not. For example, for four grams, use 4 g and not 4 G; for 4 millimeters, use 4 mm and
not 4 MM; but, for 4 liters, 4 L or 4 l are acceptable.
•  In the United States, the decimal marker (or decimal point) is placed on the line with
the number; however, in some countries, a comma or a raised dot is used, for example,
4.5 mL (United States) and 4,5 mL or 4 ·5 mL (non-United States).
aT he United States Pharmacopeia—National Formulary (USP–N F) establishes standards for the quality, purity, and
strength of prescription and nonprescription medicines. T hese standards, which are recognized and used by
over 140 countries, are published in printed volumes and electronically. The Authors’ Extra Point at the end of this
chapter further describes the USP–NF and other national, regional, and international pharmacopeias.
bAlthough not included in this text, the SI includes measures of force, viscosity, electricity, luminance, and many
others in a variety of disciplines.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:
D mon ra an und r and ng of h in rna onal s y m of Un .
c on r m a ur w h n h in rna onal s y m of Un .

c on r m a ur	w n h in rna onal s y m of Un	and o h r y m of
m a ur u d n pharma y. Apply h in rna onal s y m of Un
n pharma u al al ula on .

2
International System
of Units
18 Pharma euti al c al ulations
•  Periods are not used ollowing SI symbols except at the end o a sentence, for example,
4 mL and 4 g, not 4 mL. and 4 g.
•  A compound unit that is a ratio or quotient o two units is indicated by a solidus
(/) or a negative exponent, for example, 5 mL/h or 5 mL·h-1.
•  Symbols should not be combined with spelled-out terms in the same expression, for
example, 3 mg/mL, not 3 mg/milliliter.
•  Plurals o unit names, when spelled out, have an added “s.” Symbols or units, however,
are the same in singular and plural, for example, 5 milliliters or 5 mL, not 5 mLs.
•  Two symbols exist or microgram: mcg (o ten used in pharmacy practice) and mg (SI).
•  T he symbol or square meter is m2; or cubic centimeter, cm3; and so orth. In
pharmacy practice, a cubic centimeter (cm3) is considered equivalent to a milliliter.2
T he symbol “cc,” or cubic centimeter, is not an accepted SI symbol.
•  Decimal ractions are used, not common ractions, for example, 5.25 g, not 5¼ g.
•  A zero always should be placed in ront o a leading decimal point to prevent
medication errors caused by uncertain decimal points, for example, 0.5 g, not .5 g.
It is critically important for pharmacists to recognize that a misplaced or misread
decimal point can lead to an error in calculation of a minimum of one-tenth or
10 times the desired quantity.
•  To prevent misreadings and medication errors, “trailing” zeros should not be placed
ollowing a whole number on prescriptions and medication orders, for example, 5 mg,
not 5.0 mg. H owever, in some tables (such as those o the SI in this chapter), pharmaceutical ormulas, and quantitative results, trailing zeros o ten are used to indicate
exactness to a specif c number o decimal places.
•  In selecting symbols o unit dimensions, the choice generally is based on selecting
the unit that will result in a numeric value between 1 and 1000, for example, 500 g,
rather than 0.5 kg; 1.96 kg, rather than 1960 g; and 750 mL, rather than 0.75 L.
T b 2.1 •  Pr e f Ixe S a n d r e l aTIve va l Ue S o f Th e In Te r n aTIo n a l SySTe m (SI)

P i	m	i g
Sub i isi s atto- femto- pico- nano- micro- milli- centi- deci- mu tip s deca- hecto- kilo- myria- mega- giga- tera- peta- exa-
one-quintillionth (10-18) of the basic unit one-quadrillionth (10-15) of the basic unit one-trillionth (10-12) of the basic unit one-billionth (10-9) of the basic unit one-millionth (10-6) of the basic unit one-thousandth (10-3) of the basic unit one-hundredth (10-2) of the basic unit one-tenth (10-1) of the basic unit
10 times the basic unit 100 times (102) the basic unit 1000 times (103) the basic unit 10,000 times (104) the basic unit 1 million times (106) the basic unit 1 billion times (109) the basic unit 1 trillion times (1012) the basic unit 1 quadrillion times (1015) the basic unit 1 quintillion times (1018) the basic unit

2 • internat onal s y tem of Un t 19
Special Considerations of the SI in Pharmacy
Although some remnants o the common systems o measurement (see Appendix A) in
pharmacy remain, the use o the SI is nearly total. T he system is used to manu acture and
label pharmaceutical products (Fig. 2.1); write, f ll, and compound prescriptions and institutional medication orders; dose patients; express clinical laboratory test results; and communicate both verbally and through scientif c and pro essional literature.
In the large-scale manu acture o dosage orms, pharmaceutical ingredients are
measured in kilogram and kiloliter quantities. In the community and institutional pharmacy, compounding and dispensing in milligram, gram, and milliliter quantities are more
common. Drug doses are typically administered in milligram or microgram amounts and
prepared in solid dosage orms, such as tablets or capsules, or in a stated volume o a liquid
preparation, such as an oral solution (e.g., 30 mg/5 mL) or injection (e.g., 2 mg/mL). Doses
or certain drugs are calculated on the basis o body weight and expressed as mg/kg, meaning a certain number o milligrams of drug per kilogram of body weight. Clinical laboratory
values are in metric units and expressed, or example, as mg/dL, meaning milligrams of drug
per deciliter of body fluid (such as blood).
Particle Size and Nanotechnology
Drug particle size has long been an important consideration in pharmaceutical technology.
T hrough the milling and reduction o drug materials to micron size, the sur ace area o
particles is increased (Fig. 2.2) and pharmaceutical and clinical benef ts o ten accrue. T hese
benef ts may include the ollowing3:
•  Increased aqueous dissolution rates or poorly soluble substances
•  Improved bioavailability, with increased rates o absorption o orally administered
drugs
•  Lower oral dosage possibilities with enhanced drug absorption
•  Expanded ormulation options in the preparation o stable and predictable pharmaceutical suspensions and colloidal dispersions or all routes o administration,
including oral, parenteral, respiratory, ophthalmic, and nasal.
f IGUr e 2.1 •  Example of a pharmaceutical product with the label indicating
the strength and quantity (50 mg/10 mL) in SI or metric units. (Reprinted with
permission from Lacher BE. Pharmaceutical Calculations for the Pharmacy
Technician. Philadelphia, PA: Lippincott Williams & Wilkins; 2007.)
20 Pharma euti al c al ulations
An area of technology with great potential is nanotechnology. Nanotechnology centers
on the understanding and control of matter between approximately 1 and 100 nanometers
(nm) in size, referred to as the nanoscale range.4 For perspective, a nanometer is onebillionth of a meter; about 25,400,000 nm equals 1 inch; the helix of DN A has a diameter
of about 2 nm; and a typical bond between two atoms is about 0.15 nm.5 N anotechnology
has applications for many potential products, including those that integrate chemistry, the
biological sciences, medicine, and computer technology.
Measure of Length
T he meter is the primary unit of length in the SI.
T he table of metric length:
1 kilometer (km) = 1,000,000 meters
1 hectometer (hm) = 100,000 meters
1 decameter (dam) = 10,000 meters
1 meter (m)
1 decimeter (dm) = 0.100 meter
1 centimeter (cm) = 0.010 meter
1 millimeter (mm) = 0.001 meter
1 micrometer (mm) = 0.000,001 meter
1 nanometer (nm) = 0.000,000,001 meter
T he table may also be written:
1 meter = 0.001 kilometer
0.01 hectometer
0.1 decameter
10 decimeters
100 centimeters
1000 millimeters
1,000,000 micrometers
1,000,000,000 nanometers
Examples of the use of linear measurement in pharmacy include the dimensions of
transdermal skin patches, expressed in cm2; the use of a patient’s height and weight in
calculating the doses of certain drugs; and the clinical reference to the size of a patient’s
physical structure, as a tumor, usually measured in mm or cm. As a point of reference,
1 inch is equivalent to 2.54 centimeters or 25.4 millimeters (Fig. 2.3).
Total surface area
6 cm2
Total surface area
12 cm2
Total surface area
24 cm2
f IGUr e 2.2 •  Depiction of increased surface area by particle size reduction. (Adapted from company literature, Nanocrystal, Elan Drug Delivery, Inc.)
2 • internat onal s y tem of Un t 21
Another application of linear measurement is in distance exercise, undertaken as a component
of maintaining good health status. T hese programs are typically measured by both time and distance in miles or kilometers, the relationship of which is demonstrated in Table 2.2.
Measure of Volume
T he liter is the primary unit of volume. It represents the volume of the cube of one-tenth of
a meter, that is, of 1 dm3.
T he table of metric volume:
1 kiloliter (kL) = 1000,000 liters
1 hectoliter (hL) = 100,000 liters
1 decaliter (daL) = 10,000 liters
1 liter (L)
1 deciliter (dL) = 0.100 liter
1 centiliter (cL) = 0.010 liter
1 milliliter (mL) = 0.001 liter
1 microliter (mL) = 0.000,001 liter
T his table may also be written:
1 liter = 0.001 kiloliter
0.010 hectoliter
0.100 decaliter
10 deciliters
100 centiliters
1000 milliliters
1,000,000 microliters
Although not precisely equivalent, the milliliter is so nearly the same volume as the
cubic centimeter (cm3, cc), the United States Pharmacopeia–National Formulary states: “One
milliliter (mL) is used herein as the equivalent of 1 cubic centimeter (cc).”2
Measurement of volume is commonplace for the pharmacist in preparing and dispensing liquid medications and for the patient in measuring dosage. Examples of pharmaceutical
graduates for measuring volume are shown in Figure 2.4.
f IGUr e 2.3 •  Ruler calibrated in millimeter, centimeter, and inch units. (Courtesy of Schlenker Enterprise, Ltd.)
T b 2.2 •  d e mo n STr aTIo n S o f l In e a r r e l aTIo n Sh IPS

f t 5280	y	s	mi s 1	m t s 1609.3	Ki 1.6093	t s	1 mile
1760

1 kilometer 3280.8 1093.6 0.62137 1000 1
22 Pharma euti al c al ulations
Measure of Weight
T he primary unit of weight in the SI is the gram, which is the weight of 1 cm3 of water at 4°C,
its temperature of greatest density. For practical purposes, 1 cm3 of water ≈ 1 mL ≈ 1 g
of weight.
T he table of metric weight:
1 kilogram (kg) = 1,000,000 grams
1 hectogram (hg) = 100,000 grams
1 dekagram (dag) = 10,000 grams
1 gram (g)
1 decigram (dg) = 0.100 gram
1 centigram (cg) = 0.010 gram
1 milligram (mg) = 0.001 gram
1 microgram (mg or mcg) = 0.000,001 gram
1 nanogram (ng) = 0.000,000,001 gram
1 picogram (pg) = 0.000,000,000,001 gram
1 femtogram (fg) = 0.000,000,000,000,001 gram
T his table may also be written:
1 gram = 0.001 kilogram
0.010 hectogram
0.100 decagram
10 decigrams
100 centigrams
1000 milligrams
1,000,000 micrograms
1,000,000,000 nanograms
1,000,000,000,000 picograms
1,000,000,000,000,000 femtograms
f IGUr e 2.4 •  Examples of metric-scale cylindrical (A) and
conical pharmaceutical graduates (B). (Courtesy of Kimble/
Kontes Glass.)
2 • internat onal s y tem of Un t 23
T he weighing of components in the manufacture of a pharmaceutical product and in
the compounding of a prescription or medication order is a usual function of a pharmacist.
And, since most therapeutic agents are solid substances (i.e., powders), their doses are determined and expressed in units of weight, most often in milligrams. An example of a metric
set of weights is shown in Chapter 3.
Prescription Writing Style Using the SI
Prescriptions written in the SI use Arabic numerals before the abbreviations for the denominations (e.g., 6 g). Q uantities of weight are usually written as grams and decimals of a gram,
and volumes as milliliters and decimals of a milliliter:

Dextromethorphan H Br Guaifenesin Cherry syrup, to make

320 mg 3.2 g 240 mL

Fundamental Computations
Reducing SI Units to Lower or Higher Denominations by Using a Unit
Position Scale
T he metric system is based on the decimal system; therefore, conversion from one denomination to another can be done simply by moving the decimal point as demonstrated in
Figure 2.5.
To change a metric denomination to the next smaller denomination, move the decimal point one place to the right.
To change a metric denomination to the next larger denomination, move the decimal
point one place to the left.
Decimal Movement
To Convert From Larger to Smaller Units
To Convert From Smaller to Larger Units
1.23 kg
12.3 hg
123.0 dag
1230.0 g
9.876 g
98.76 dg
987.6 cg
9876.0 mg
kg hg dag g dg cg mg (0.1 mg) (0.01 mg) mg
f IGUr e 2.5 •  Position scale of units of weight.
24 Pharma euti al c al ulations
(1) Reduce 1.23 kilograms to grams.
1.23 kg = 1230 g
(2) Reduce 9876 milligrams to grams.
9876 mg = 9.876 g
In the first example, 1.23 kg is to be converted to grams. On the scale, the
gram position is three decimal positions from the kilogram position. T hus, the
decimal point is moved three places toward the right. In the second example, the
conversion from milligrams also requires the movement of the decimal point three
places, but this time to the left.
(3) Reduce 85 micrometers to centimeters.
85 mm = 0.085 mm = 0.0085 cm
(4) Reduce 2.525 liters to microliters.
2.525 L = 2525 mL = 2,525,000 mL
The 3-Decimal Point Shift
In pharmacy practice, and health care in general, the denominations most used differ by
1000 or by a factor of 3 decimal places. T hus, on the decimal scale (Fig. 2.5), a 3-place decimal point shift, left to right or right to left, will yield most commonly used denominations.
3-Place Shift for Common Weight Denominations:
kilograms (kg) _ _ _ grams (g) _ _ _ milligrams (mg) _ _ _ micrograms (mcg)
3-Place Shift for Common Volume Denominations:
liters (L) _ _ _ milliliters (mL)
Reducing SI Units to Lower or Higher Denominations by Ratio and Proportion
or by Dimensional Analysis
(5) Reduce 1.23 kilograms to grams.
From the table: 1 kg = 1000 g
By ratio and proportion:
1
1000
kg 1 23
g
kg
x g
.x= =;
1230 g
By dimensional analysis:
1 23
1000
1
. kg g
kg
× = 1230 g
(6) Reduce 62,500 mcg to g.
From the table: 1 g = 1,000,000 mcg
By ratio and proportion:
1 000 000
1
, , , 62 500
; .
mcg
g
mcg
x g
= = x 0 0625 g
By dimensional analysis:
62 500
1
1 000 000
,
, ,
mcg .
g
mcg
× = 0 0625 g
2 • internat onal s y tem of Un t 25
Ca l CUl aTIo n S Ca PSUl e
International System of Units (SI)
•   The SI or decimal system of measurement is used in the practice of pharmacy and
throughout the pharmaceutical industry.
•   The primary SI units for calculating mass or weight (gram), volume (liter), and length
(meter) are used along with prefixes to indicate multiples or subdivisions of the primary
units.
•   To change an SI denomination to the next smaller denomination, the decimal point is
moved one place to the right:
gram(g) > d ecigram(dg > c entigram(cg > milligram(mg)
5.555 g = 55.55 dg = 555.5 cg = 5555 mg
Each value is equivalent.
•   To change an SI denomination to the next larger denomination, the decimal point is
moved one place to the left:
5.555 kg = 55.55 hg = 555.5 dag = 5555 g
kilogram(kg) > hectogram(hg) > dekagram(d ag) > gram(g)
Each value is equivalent.
•   A unit position scale (e.g., see Fig. 2.5), ratio and proportion, or dimensional analysis
may be used to change denominations.
•   Only numbers of the same denomination may be added to or subtracted from one
another.
Recognizing Equivalent Expressions
On occasion, it may be necessary to recognize, or prove by calculation, equivalent expressions. For example, a given quantity expressed in terms of “mg/100 mL” is equivalent to
“mg/dL.”
Practice problems (#47 to #50) at the conclusion of this chapter provide exercises to
determine equivalent expressions.
Addition and Subtraction
To add or subtract quantities in the SI, reduce them to a common denomination, preferably
a base unit, and arrange their denominate numbers for addition or subtraction as ordinary
decimals.
(1) Add 1 kg, 250 mg, and 7.5 g. Express the total in grams.
1 1000

250 7 5 mg g .

0 25 7 5 1007 75 g g g or . . 1008 g

kg g
===
..

26 Pharma eu i al c al ula ions
(2) Add 4 L, 375 mL, and 0.75 L. Express the total in milliliters.
4 4000
375 375
0 75 750
L mL
mL mL
L mL
==
=.
5125 mL
(3) A capsule contains the following amounts of medicinal substances: 0.075 g, 20 mg, 0.0005 g,
4 mg, and 500 mg. W hat is the total weight of the substances in the capsule?

0 075 20 0 0005 . . g mg g

0 075 0 02 0 0005 . . . g g g

4 0 004
500 0 00
..
mg g
====
g =m 005
0 1000
g
. g or 100 mg
(4) Subtract 2.5 mg from 4.85 g.

4 85 2 5 . . g mg	4 85 0 0025 . . g g
4 8475 . . g or 4 848 g
(5) A prescription calls for 0.06 g of one ingredient, 2.5 mg of another, and enough of a third to make 0.5 g. How many milligrams of the third ingredient should be used?
1 0 06 2 2 5 st ingredient g nd ingredient mg : . : .	0 06 .	g
0 0025 0 0625 g . . gg

=
= –
==

T otal weight W eight of st and nd W eight of rd : : : 1 2 3

. . . 0 5 0 0625 0 43

–
775 g or 437 5 mg .
Multiplication and Division
Because every measurement in the SI is expressed in a single given denomination, problems involving multiplication and division are solved by the methods used for any decimal
numbers.
(1) Multiply 820 mL by 12.5 and express the result in liters.
820 mL × 12.5 = 10250 mL = 10.25 L
(2) Divide 0.465 g by 15 and express the result in milligrams.
0.465 g ÷ 15 = 0.031 g = 31 mg
Ca Se In Po In T 2.1 A nurse elephones a pharma y regarding he proper quani y of an inje ion o adminis er o a pedia ri pa ien from a 1-mL vial on aining
0.1 mg of digoxin. t he a ending physi ian had pres ribed a dose of 25 m g. How
many millili ers should be he pharma is ’s response?
2 • internat onal s y tem of Un t 27
Relation of the SI to Other Systems of Measurement
In addition to the International System of Units, the pharmacy student should be aware of
two other systems of measurement: the avoirdupois and apothecaries’ systems. T he avoirdupois system, widely used in the United States in measuring body weight and in selling goods
by the ounce or pound, is slowly giving way to the international system. T he apothecaries’
system, once the predominant pharmacist’s system of volumetric and weight measure, has
also largely been replaced by the SI. T he pharmacist must still appreciate the relationship
between the various systems of measurement, however, and deal effectively with them as the
need arises.
T he avoirdupois and apothecaries’ systems of measurement, including all necessary
equivalents and methods for intersystem conversion, are presented in Appendix A. T he
example equivalents presented in Table 2.3 are useful in gaining perspective and in solving certain problems in the text—for example, when there is need to convert fluid ounces
to milliliters or kilograms to pounds. T hese equivalents should be committed to memory.
T b 2.3 •  So me USe f Ul e q UIva l e n TS
e ui ts gth
1 inch = 2.54 cm
1 meter (m) = 39.37 in
e ui ts u
1 fluid ounce (fl. oz.) = 29.57 mL
1 pint (16 fl. oz.) = 473 mL
1 quart (32 fl. oz.) = 946 mL
1 gallon, United States (128 fl. oz.) = 3785 mL
1 gallon, United Kingdom = 4545 mL
e ui ts w ight
1 pound (lb, avoirdupois) = 454 g
1 ounce (oz, avoirdupois) = 28.35 g
1 kilogram (kg) = 2.2 lb
Example Problems
(1) An injection contains 5 mg of drug in each 10-mL vial. If the dose of the drug for a patient
is determined to be 150 mg, how many milliliters should be administered?

150 m g × × = 0 3 mL .
m g	mg
mL	mg

10
5
1
1000
W hen quantities in units of the apothecaries’ or avoirdupois
systems of measurement (see Appendix A) are encountered, it is
suggested that they be converted to equivalent quantities in SI
units and the required calculation then solved in the usual manner.
28 Pharma eu i al c al ula ions
(2) A patient is determined to have a total serum cholesterol level of 240 mg/dL. W hat is the
equivalent value in mg/100 mL?
1 dL = 100 mL; thus, 240 mg/dL = 240 mg/100 mL
(3) The dose of a drug is 0.5 mg/kg of body weight/day. W hat is the equivalent dose in mg/lb/
day?
0.5 mg = 500 mg
1 kg = 2.2 lb
T hus, 0.5 mg/kg/day = 500 mg/2.2 lb/day = 227.3 mg/lb/day
(4) An oral suspension contains 1.5 g of the therapeutic agent in a pint of the suspension.
Calculate the quantity of therapeutic agent, in milligrams, present in each 5-mL dose.

? mg mL . . = ´ ´ ´ = 5 or 15 86 15 9 mg
. 1 5	mg 1000	pt
g 1	mL	1

g pt
1
473
Or, by ratio and proportion:
1.5 g = 1500 mg
1 pint = 473 mL
1500
473 5
mg 15 86
mL
x mg
mL
= = ; . . x or 15 9 mg
Pr a CTICe Pr o b l e mS
1. W hat is the weight, in milligrams, of 100 tablets, each containing 20 mcg of a
therapeutic agent?
2. Add 7.25 L and 875 cL. Reduce the result to milliliters.
3. Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 mg, and express the answer in grams.
4. Reduce 1.256 g to micrograms, to milligrams, and to kilograms.
5. Are the terms mcg/mL and mg/L equivalent or not equivalent?
6. A low-strength aspirin tablet contains 81 mg of aspirin per tablet. H ow many
tablets may a manufacturer prepare from 0.5 kg of aspirin?
7. Adhesive tape made from fabric has a tensile strength of not less than
20.41 kg/2.54 cm of width. Reduce these quantities to grams and millimeters.
8. In a clinical study, the drug methotrexate produced a blood level of 6.6 mg of
methotrexate in each milliliter of blood (6.6 mg/mL). Express the methotrexate
blood level in terms of mg/dL.
Ca Se In Po In T 2.2 A hospi al pharma is is asked o prepare an in ravenous
infusion of dopamine. b ased on he pa ien ’s weigh , he pharma is al ula es a dose
of 500 m g/min for on inuous infusion. t he on en ra ion of a premixed dopamine
infusion is 400 mg/250 mL. Wha is he on en ra ion of he infusion on a m g/mL
asis? How many milligrams of dopamine is he pa ien o re eive in he firs hour of
rea men ? How long will he infusion las ?
2 • internat onal s y tem of Un t 29
9. An inhalation aerosol contains 225 mg of metaproterenol sulfate, which is
sufficient for 300 inhalations. H ow many micrograms of metaproterenol sulfate
would be contained in each inhalation?
10. T RIPH ASIL-28 birth control tablets are taken sequentially, 1 tablet per day for
28 days, with the tablets containing the following:
Phase 1—6 tablets, each containing 0.05 mg levonorgestrel and 0.03 mg ethinyl
estradiol
Phase 2—5 tablets, each containing 0.075 mg levonorgestrel and 0.04 mg ethinyl
estradiol
Phase 3—10 tablets, each containing 0.125 mg levonorgestrel and 0.03 mg ethinyl
estradiol; then, 7 inert tablets (no drug).
H ow many total milligrams each of levonorgestrel and ethinyl estradiol are
taken during the 28-day period?
11. COLCRYS scored tablets each contain 0.6 mg of colchicine. H ow many micrograms of colchicine would a patient take by administering one-half tablet?
12. T he following clinical laboratory data are within normal values for an adult.
Convert each value to mcg/mL:
(a) Ammonia, 30 mcg/dL
(b) Folate, 18 pg/mL
(c) Serum creatinine, 1.0 mg/dL
(d) Prostate-specific antigen (PSA), 3 ng/mL
(e) Cholesterol, total, 150 mg/dL
13. T he package insert for DON N ATAL EXT EN TABS indicates the amount of
phenobarbital present in each tablet, in milligrams and in the equivalent weight
(3/4 grains) in the apothecary system. Refer to Appendix A and calculate the milligrams of phenobarbital present in each tablet.
14. Levothyroxine sodium tablets (SYN T H ROID) are available in 12 different
strengths ranging from 25 to 300 mg. Express this range in milligrams.
15. N orgestrel and ethinyl estradiol tablets are available containing 0.5 mg of norgestrel and 50 mg of ethinyl estradiol. H ow many grams of each ingredient would
be used in making 10,000 tablets?
16. Approximately 0.02% of a 100-mg dose of the drug miglitol (GLYSET ) has been
shown to appear in human breast milk. Calculate the quantity of drug detected,
in milligrams, following a single dose.
17. H ow many grams of digoxin (LAN OXIN ) would be required to make 25,000
tablets each containing 250 mcg of digoxin?
18. Adalimumab (H UMIRA), a recombinant human monoclonal antibody, is available in a prefilled syringe containing 40 mg/0.8 mL of injection. Calculate the
concentration of drug on a mg/mL basis.
19. If an injectable solution contains 25 mg of a drug substance in each 0.5 mL, how
many milliliters would be required to provide a patient with 0.25 mg of the drug
substance?
20. A patient is instructed to take one 50 mg tablet of pergolide mesylate (PERMAX)
a day for the first two days of treatment; 150 mg/day on the third, fourth, and fifth
days of treatment; 250 mg/day on the sixth, seventh, and eighth days; and 350 mg
on the ninth day and return to the physician for assessment. During this treatment period, how many milligrams of drug were taken?
21. Treatment with the drug carvedilol for heart failure is initiated with a dose of
3.125 mg twice daily and then increased every two weeks with twice daily doses of
30 Pharma euti al c al ulations
6.25 mg, 12.5 mg, and 25 mg. H ow many of each of these tablet strengths should
be dispensed for this protocol?
22. Digoxin (LAN OXIN ) is available for parenteral pediatric use in a concentration
of 0.05 mg/mL. H ow many milliliters would provide a dose of 40 mg?
23. ROXAN OL oral solution contains 0.6 g of morphine sulfate in each 30-mL
bottle affixed with a calibrated dropper. Calculate (a) the concentration of
morphine sulfate on a mg/mL basis and (b) the milligrams of morphine sulfate
delivered by a 0.6-mL dose.
24. T he starting dose of sodium oxybate oral solution (XYREM) is 4.5 g/night
divided into two equal doses and administered 2.5 to 4 hours apart. H ow many
milliliters of the oral solution containing sodium oxybate, 500 mg/mL, should be
administered in each divided dose?
25. An intravenous solution contains 500 mg of a drug substance in each milliliter.
H ow many milligrams of the drug would a patient receive from the intravenous
infusion of a liter of the solution?
26. If an intravenous solution containing 123 mg of a drug substance in each 250-mL
bottle is to be administered at the rate of 200 mg of drug per minute, how many
milliliters of the solution would be given per hour?
27. An oral inhalation (DULERA) to treat asthma provides, in each inhalation,
100 mg of mometasone furoate and 5 mg of formoterol fumarate. T he recommended dose is “two inhalations twice daily (morning and evening).” Calculate
the quantity of each drug inhaled daily and express the answers in milligrams.
28. An injection contains 50 mcg/0.5 mL of drug. H ow many mL of the injection
should be administered to deliver 0.04 mg of drug?
29. An injection containing 7.5 mg of leuprolide acetate is administered to a patient
weighing 25 kg. Calculate the dose on a mcg/lb basis if 1 kg = 2.2 lb.
30. A gas chromatograph column measures 1.8 m in length and 3 mm in internal
diameter. Convert these measurements to inches.
31. A prefilled syringe contains 20 mg of drug in 2 mL of solution. H ow many
micrograms of drug would be administered by an injection of 0.5 mL of the solution?
32. A vial contains 80 mg of drug in 2 mL of injection. H ow many milliliters of the
injection should be administered to obtain 0.02 g of drug?
33. One-half liter of solution for intravenous infusion contains 2 g of drug. H ow
many milliliters of the solution would contain 0.5 mg of drug?
34. A 125-mL container of amoxicillin contains 600 mg/5 mL. H ow many milliliters
would be used to administer 400 mg of amoxicillin?
35. An effervescent tablet has the following formula:
Acetaminophen 325 mg

Calcium carbonate	280 mg
Citric acid Potassium bicarbonate Sodium bicarbonate	900 mg 300 mg 465 mg

(a) Calculate the total weight, in grams, of the ingredients in each tablet.
(b) H ow many tablets could be made with a supply of 5 kg of acetaminophen?
36. A new analytic instrument is capable of detecting picogram quantities of a chemical substance. H ow many times more capable is this instrument than one that can
detect nanogram quantities of the same chemical?
37. T he rate of drug delivered to the skin by fentanyl transdermal patches is directly
proportional to the dimension of the patch. If a patch size of 5.25 cm2 delivers
2 • internat onal s y tem of Un t 31
12 mcg/hour of fentanyl, calculate the delivery rate of drug expected from a
31.5-cm2 patch.
38. If an albuterol inhaler contains 18 mg of albuterol, how many inhalation doses
can be delivered if each inhalation dose contains 90 mg?
39. Acetaminophen, in amounts greater than 4 g per day, has been associated with
liver toxicity. W hat is the maximum number of 500-mg tablets of acetaminophen
that a person may take daily and not reach the toxic level?
40. A lung tumor measuring 2.1 cm was detected in a patient. W hat are the equivalent dimensions in millimeters and in inches?
41. T he recommended dose for a brand of nicotine patch is one 21-mg dose per day
for 6 weeks, followed by 14 mg per day for 2 weeks, and then 7 mg per day for
2 more weeks. W hat total quantity, in grams, would a patient receive during this
course of treatment?
42. A medical device is sterilized by gamma radiation at 2.5 megarads (Mrad). Express
the equivalent quantity in rads.
43. A round transdermal patch measures 4.3 cm in diameter. Convert this dimension
to inches and millimeters.
44. A solution for direct IV bolus injection contains 125 mg of drug in each 25 mL of
injection. W hat is the concentration of drug in terms of mg/mL?
45. T he total number of human genomic characters is 3.5 billion. Express this
quantity numerically without using a decimal point.
46. Conjugated estrogen tablets (PREMARIN ) are available in strengths of 0.3 mg,
0.45 mg, 0.625 mg, 0.9 mg, and 1.25 mg. If patient “A” took one tablet daily of
the lowest dose and patient “B” took one tablet daily of the highest dose, what is
the difference in the total quantities taken between patients “A” and “B” over a
period of 30 days?
(a) 2.85 mg
(b) 2850 mcg
(c) 2.85 cg
(d) 2.85 dg
47. Teratogenic studies of insulin glargine were undertaken in rats at doses up to
0.36 mg/kg/day. T his is equivalent to which of the following?
(a) 360 cg/lb/day
(b) 792 mcg/lb/day
(c) 360 mg/lb/day
(d) 163.6 mcg/lb/day
48. Pharmacy students, traveling to attend a national pharmacy meeting, were on
an airplane with an average air speed of 414 miles per hour. W hich is the closest
equivalent air speed?
(a) 6 mi/min
(b) 257 km/h
(c) 666 km/h
(d) 180 m/s
49. T he product of biotechnology, filgrastim (N EUPOGEN ), is available in vials
containing 0.3 mg of drug in each milliliter. W hich choice is equivalent in
concentration?
(a) 0.03 mg/0.1 dL
(b) 300 mcg/0.01 dL
(c) 3 mcg/0.01 cL
(d) 300 mcg/10 cL
32 Pharma euti al c al ulations
50. In a clinical study of finasteride (PROSCAR), a single oral dose of 5 mg resulted
in an average blood concentration of 37 ng of drug per milliliter (37 ng/mL) of
blood plasma. T his is equivalent to which of the following?
(a) 37,000 mcg/mL
(b) 0.037 mcg/mL
(c) 0.000037 mg/cL
(d) 0.0037 mcg/dL
Ca l Cq UIz
2.A. A health news story that received widespread attention in recent years involved the
successful premature birth of octuplets. The eight babies ranged in weight from
1 lb 8 oz to 3 lb 4 oz. Using the equivalents for the avoirdupois system given in this
chapter, calculate the babies’ range in weight, in grams and in kilograms.
2.B. Levothyroxine sodium tablets are available in 11 different strengths, ranging from
0.025 mg to 200 µg. Calculate the difference, in micrograms, between these two
strengths.
2.C. An inhalation aerosol contains 0.03 g of albuterol sulfate per canister and is labeled
to deliver 200 full inhalations. If each inhalation contains 108 µg of albuterol sulfate,
how many milligrams of drug would remain in the canister?
2.D. A 0.5-mL container of an investigational ophthalmic solution contains a drug in a
concentration of 0.01 mg/mL. How many micrograms of drug would be administered
in a 50-µL drop?
2.E. A long-acting formulation of leuprolide acetate requires injection only once every
3 months. Clinical studies revealed that 4 hours following a single injection, the mean
blood plasma level of leuprolide was 36.3 ng/mL and dropped over the next month
to a steady level of 23.9 ng/mL. Express the difference between these the two values
in µg/dL.
a n Sw e r S To “Ca Se In Po In T” a n d Pr a CTICe Pr o b l e mS
Case in Point 2.1
0. / / 1 100 mg mL mcg mL =
25
1
100
1 4
0 25
mcg
mL
mcg
mL
or mL
× = /
.
Case in Point 2.2
Concentration of infusion, mcg/mL:
400
250
400 000
250
1600
mg
mL
mcg
mL
mcg mL
= =
,
/
2 • internat onal s y tem of Un t 33
mg, dopamine, first hour:
500
1
60

1 h	30 mg h min / =

1
1000
mcg
mg
mcg
min
× ×
Infusion duration:
400 1
500
1000
1
800 13 20
mg
mcg
mcg
mg
h
´ ´
= =
min
min , min
Practice Problems
1. T his is a bit of a trick question. T he weight of the therapeutic agent in the 100
tablets may easily be calculated as 2 mg; however, the question asks for the weight
of the 100 tablets, which cannot be calculated without the known weight of all of
the tablets’ components, both therapeutic and nontherapeutic (as tablet fillers,
binders, etc.) or by actually weighing the tablets.
2. 16,000 mL
3. 7.325 g
4. 1,256,000 mcg

1256 mg 0.001256 kg

25. 500 mg 26. 24.39 mL

5. Equivalent
6. 6,172 aspirin tablets
7. 20,410 g/25.4 mm
8. 0.66 mg/dL
9. 750 mcg metaproterenol sulfate
10. 1.925 mg levonorgestrel
0.68 mg ethinyl estradiol
11. 300 mcg colchicine

12. (a) Ammonia, 0.3 mcg/mL (b) Folate, 0.000018 mcg/mL (c) Serum creatinine, 10 mcg/mL (d) Prostate-specific antigen (PSA), 0.003 mcg/mL

33. 0.125 mL 34. 3.33 mL 35. (a) 2.27 g (b) 15,384 tablets 36. 1000 times

 

(e) Cholesterol, 1500 mcg/mL 13. 48.75 mg phenobarbital

37. 72 mcg/h 38. 200 doses

 

14. 0.025 to 0.3 mg levothyroxine sodium

39. 8 tablets 40. 21 mm and 0.83 inches.

15. 5 g norgestrel
0.5 g ethinyl estradiol
16. 0.02 mg miglitol
17. 6.25 g digoxin
18. 50 mg/mL
19. 5 mL
20. 1.65 mg pergolide mesylate

21. 28 carvedilol tablets of each strength

48. (c) 666 km/h 49. (b) 300 mcg/0.01 dL

22. 0.8 mL
23. (a) 20 mg/mL morphine sulfate
(b) 12 mg morphine sulfate
24. 4.5 mL oxybate oral solution
27. 0.4 mg mometasone furoate and
0.02 mg formoterol fumarate
28. 400 mL
29. 136.4 mcg/lb
30. 70.866 or 70.9 inches
0.118 or 0.12 inches
31. 5000 mcg
32. 0.5 mL
41. 1.176 g nicotine
42. 2,500,000 rads
43. 1.69 inches and 43 mm
44. 5 mg/mL
45. 3,500,000,000 or 35 × 108
46. (c) 2.85 cg
47. (d) 163.6 mcg/lb/day
50. (b) 0.037 mcg/mL
34 Pharma euti al c al ulations
AUTHORS’ ExTRA POIn T
Ph a r ma Co Pe Ia S
The United States Pharmacopeia a d the National Formulary (USP-n F) is a combi atio of two books of
sta dards, desig ated u der the U.S. Federal Food, Drug, a d Cosmetics Act as the official compe dia
for drugs marketed i the U ited States.a,b The United States Pharmacopeia (USP) co tai s mo ographs
for drug substa ces, dosage forms, compou ded preparatio s, a d dietary suppleme ts whereas National
Formulary (NF) co tai s mo ographs for pharmaceutical e cipie ts. The combi ed volume is published
a ually i hard copy a d o li e with the sta dards u der co ti ual revisio through the issua ce of
suppleme ts, bulleti s, a d a ou ceme ts.
The USP-n F is published by the United States Pharmaceutical Convention, comprised of represe tatives
of over 400 member orga izatio s represe ti g academic i stitutio s, health practitio ers, scie tific associatio s, co sumer groups, ma ufacturers, gover me tal bodies, a d other i terested groups. The established
sta dards are e forced i the U ited States u der the authority of the federal Food a d Drug Admi istratio .
Although the USP-n F sta dards are used i more tha 140 cou tries, there are a umber of other
pharmacopeias published arou d the world. Amo g the cou tries issui g atio al pharmacopeias are
Arge ti a, Brazil, Chi a, Egypt, Fra ce, Germa y, I dia, I do esia, Japa , Me ico, Philippi es, Russia,
Spai , Switzerla d, a d the U ited Ki gdom (British Pharmacopoeia). I additio , there are regio al pharmacopeias, amely, the European Pharmacopoeia a d the African Pharmacopoeia. A d i ter atio ally,
there is The International Pharmacopoeia, published by the World Health Orga izatio .c
Ca ada, u der its “Food a d Drugs Act,” utilizes a umber of pharmacopeias, i cludi g the USP-NF,
European Pharmacopoeia (Ph.Eur), Pharmacopée française (Ph.F), the British Pharmacopoeia (BP), and
The International Pharmacopoeia (Ph. Int.).
ahttp://www.usp.org/usp- f
bThe term “pharmacopeia” comes from the Greek pharmakon, mea i g “drug,” a d poiein, mea i g “make,” the combi atio
i dicati g a y recipe, formula, or sta dard required to make a drug or drug product.
chttp://www.who.i t/medici es/publicatio s/pharmacopoeia/WHOPSMQSM2006_2_I de PharmacopoeiasUpdated.pdf
References
1. U.S. Metric Association. Correct SI-metric usage. Available at: http://lamar.colostate.edu/~hillger/correct.htm.
Accessed July 11, 2014.
2. United States Pharmacopeia 32 National Formulary 27. Vol. 1. Rockville, MD: United States Pharmacopeial
Convention, 2009; 9.
3. Junghanns J-UAH , Müller H . N anocrystal technology, drug delivery and clinical applications. International
Journal of N anomedicine 2008;3(3):295–310. Available at: http://www.ncbi.nlm.nih.gov/ pmc/ articles/
PMC2626933/. Accessed April 11, 2014.
4. N ational N anotechnology Initiative. W hat is nanotechnology. Available at: http://www.nano.gov/html/facts/
whatIsN ano/html. Accessed March 6, 2011.
5. Seeman N C. N anotechnology and the double helix. Scientific American 2004;290:64–75.
35
Pharmaceutical measurement is an important part of pharmacy practice. It is employed in
community and institutional pharmacies, in pharmaceutical research, in the development
and manufacture of pharmaceuticals, in chemical and product analysis, and in quality control. T his chapter focuses on the equipment and methods used in the accurate measurement
of therapeutic and pharmaceutical materials in the community and institutional practice of
pharmacy.
T he expertise of pharmacists in accurately weighing and measuring materials is
a historical and unique skill, acquired through professional education and training.
Moreover, this capability is an expectation of other health professionals and the patient
community being served. It is not an overstatement to say that patients’ lives depend
on it.
T he role of the pharmacist in providing pharmaceutical care includes the ability and
responsibility to compound—that is, to accurately weigh, measure volume, and combine
individual therapeutic and pharmaceutical components in the formulation and preparation
of prescriptions and medication orders.
Measurement of Volume
Common instruments for the pharmaceutical measurement of volume range from micropipettes and burettes used in analytic procedures to large, industrial-size calibrated vessels.
T he selection of measuring instrument should be based on the level of precision required. In
pharmacy practice, the most common instruments for measuring volume are cylindric and
conical (cone-shaped) graduates (Fig. 3.1). For the measurement of small volumes, however,
the pharmacist often uses a calibrated syringe or, when required, a pipette.
W hereas cylindric graduates are calibrated in SI or metric units, conical graduates are
usually dual scale, that is, calibrated in both metric and apothecary units of volume. Both
glass and plastic graduates are commercially available in a number of capacities, ranging
from 5 to 1000 mL and greater.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

D	r	n rum n for olum r m a ur m n and hara	r z h r d ff r n	n
appl a on and a ura y.
D	r	h	orr	pro dur wh n u ng a pharma u al alan .
D f n sensitivity requirement and apply	n al ula on .
P rform al ula on	y h al quo m hod.

D mon ra an und r and ng of percentage of error n pharma u al m a ur m n .
3
Pharmaceutical Measurement
36 Pharma euti al c al ulations
FIGURE 3.1 •  Examples of conical and cylindric graduates, a pipette, and a pipette-filling bulb for volumetric
measurement.
Volume
error
Re ading
error
A B
C
FIGURE 3.2 •  Volume error differentials due to instrument diameters. (A) Volumetric pipette; (B) cylindric
graduate; and (C) conical graduate.
3 • Pharmaceutical Measurement 37
As a general rule, it is best to select the graduate with a capacity equal to or just exceeding the volume to be measured. Measurement o small volumes in large graduates increases
the potential or error. T he design o a volumetric apparatus is an important actor in
measurement accuracy; the narrower the bore or chamber, the lesser the error in reading
the meniscus and the more accurate the measurement (Fig. 3.2). According to the United
States Pharmacopeia, a deviation o ±1 mm in the reading o the meniscus when using a
100-mL cylindrical graduate results in an error o approximately 0.5 mL and 1.8 mL at the
100-mL mark when using a 125-mL conical graduate.1
It is essential or the pharmacist to select the proper type and capacity o instrument
or volumetric measure and to care ully observe the meniscus at eye level to achieve the
desired measurement.
Measurement of Weight
T here is a wide range o weights, balances, and scales available or pharmaceutical measurement. T he proper selection depends upon the particular task at hand. Standard prescription
balances and highly sensitive electronic balances generally su f ce in traditional pharmaceutical compounding, whereas large-capacity scales are used in the industrial manu acture o
pharmaceutical products. W hichever instrument is used, however, it must meet established
standards or sensitivity, accuracy, and capacity.
A di erentiation may be made between a scale and a balance. A scale measures a single
object’s weight (think o a bathroom scale). A scale reading will di er i the gravity is
di erent, that is, less at higher elevations and greater at sea level. A balance uses a lever and
ulcrum, or a pivoting point, to compare the masses o two di erent objects. A weight o
known mass is used to measure the substance being weighed. A balance is more precise than
a scale. Analytical balances are characterized by a precision/capacity ratio o 1/500,000 or better and a readability o 0.1 mg or better. Microbalances have readabilities as low as 0.001 mg,
and ultramicrobalances have readabilities as low as 0.0001 mg.a
Some terminology associated with balances and scales is presented in Table 3.1.
Class A prescription balances (Fig. 3.3) are designed or the weighing o medicinal or
pharmaceutical substances required in the illing o prescriptions or in small-scale compounding. Some prescription balances have a weighbeam and rider, and others a dial, to add
up to 1 g o weight. As required, additional external weights may be added to the right-hand
balance pan. T he material to be weighed is placed on the le t-hand pan. Powder papers
are added to each pan be ore any additions, and the balance is leveled by leveling eet or
balancing screws. Weighings are per ormed through the care ul portion-wise (by spatula)
addition and removal o the material being weighed, with the balance being arrested (pans
locked in place by the control knob) during each addition and removal o material and unarrested with the lid closed or determinations o balance rest points. W hen the unarrested
pans neither ascend nor descend, and the index plate shows the needle is in the center, the
material and balance weights are considered equivalent. T he student may wish to re er to
other sources, such as the United States Pharmacopeia, or more detailed in ormation on the
proper use and testing o the prescription balance.1
aBalances o all types are available rom several manu acturers including OH AUS Corporation (http://us.ohaus.
com/us/en/home/products.aspx), Sartorius Corporation (http://www.sartorius.us/us/products/laboratory/
laboratory-balances/), and A&D Weighing (http://www.andonline.com/weighing/).
38 Pharma euti al c al ulations
Minimally, a Class A prescription balance should be used in all prescription compounding procedures. Balances of this type have a sensitivity requirement (SR) of 6 mg or less
with no load and with a load of 10 g in each pan. To avoid errors of greater than 5% when using
this balance, the pharmacist should not weigh less than 120 mg of material (i.e., a 5% error in a
weighing of 120 mg = 6 mg). Most commercially available Class A balances have a maximum
capacity of 120 g.
T he term sensitivity requirement is defined as the load that will cause a change of one
division on the index plate of the balance. It may be determined by the following procedure:
(1) Level the balance.
(2) Determine the rest point of the balance.
(3) Determine the smallest weight that causes the rest point to shift one division on
the index plate.
Tab e 3.1 •  So ME TERMIn o l o Gy ASSo c IATEd wITh BAl An c ES An d Sc Al ESa

Term	Mea i g
Accuracy	The degree of agreement between the value displayed on a balance and the true value of the quantity measured. Adjusting a measuring device to a reference point or standard unit of measure. Calibration is critical to accuracy, and although most balances are calibrated during manufacture, calibration should be verified at installation and per formed periodically to maintain accuracy. Some balances are self-calibrating. The maximum weight measurable by the balance or scale.
Calibration
Capacity
Load Precision Readability Sensitivity requirement	The weight applied to the receiving balance or scale. The degree of agreement between repeated measurements of the same quantity. The smallest fraction of a division to which a balance or scale can be read. The load (weight) that will cause a change of one division on the index plate on a balance. The degree of constancy of measurement of an instrument when subject to variation in external factors such as time, temperature, and supply voltage.
Stability

aSources: http://www.scalesonline.com/t/ScaleTerminology and http://www.ohaus.com/us/en/home/support/glossary.aspx
FIGURE 3.3 •  Torbal torsion balance and Ohaus electronic balance. (Courtesy of Torbal and Ohaus.)
3 • Pharmaceutical Measurement 39
For greater accuracy than a Class A prescription balance allows, many pharmacies utilize high-precision electronic analytical balances to weigh very small quantities (Fig. 3.4).
Many of these balances are capable of weighing accurately 0.1 mg, are self-calibrating, and
are equipped with convenient digital readout features. T he usual maximum capacities for
balances of this precision range from about 60 to 210 g depending upon the model. A set of
metric weights that may be used to weigh materials on a prescription balance and/or used
to calibrate an analytical balance is shown in Figure 3.5.
FIGURE 3.5 •  Set of metric weights.
(Courtesy of Mettler-Toledo, Inc.)
FIGURE 3.4 •  Sartorius BasicLite analytical balance. (Courtesy of Sartorius Corporation.)
40 Pharma euti al c al ulations
Aliquot Method of Weighing and Measuring
W hen a degree of precision in measurement that is beyond the capacity of the instrument at
hand is required, the pharmacist may achieve the desired precision by calculating and measuring in terms of aliquot parts. An aliquot is a fraction, portion, or part that is contained an
exact number of times in another.
Weighing by the Aliquot Method
T he aliquot method of weighing is a method by which small quantities of a substance may
be obtained within the desired degree of accuracy by weighing a larger-than-needed portion
of the substance, diluting it with an inert material, and then weighing a portion (aliquot) of
the mixture calculated to contain the desired amount of the needed substance. A stepwise
description of the procedure is depicted in Figure 3.6 and is described as follows:
Preliminar y Step. Calculate the smallest quantity of a substance that can be
weighed on the balance with the desired precision.
T he equation used:
100 Sensitivity Requirement (mg)
Acceptable Error (%)
% × = Smallestt Q uantity (mg)
On a balance with an SR of 6 mg, and with an acceptable error of no greater than 5%,
a quantity of not less than 120 mg must be weighed.
100 6
5
120
%
× %
=
mg
mg
St e p 1. Select a multiple of the desired quantity that can be weighed with the
required precision.
•  If the quantity of a required substance is less than the minimum weighable amount,
select a “multiple” of the required quantity that will yield an amount equal to or
greater than the minimum weighable amount. (A larger-than-necessary multiple may
be used to exceed the minimum accuracy desired.)
•  Example:
If the balance in the example in the preliminary step is used, and if 5 mg of a drug substance
is required on a prescription, then a quantity at least 25 times (the multiple) the desired
amount, or 125 mg (5 mg × 25), must be weighed for the desired accuracy. (If a larger
multiple is used, say 30, and 150 mg of the substance is weighed [5 mg × 30], then a
weighing error of only 4% would result.)
Step 1 Step 2 Step 3
5 mg
[drug
needed]
25

[multiple factor]

[quantity actually weighed]

125 mg
Add 2875 mg
[diluent]
3000 mg mixture
[125 mg drug +
2875 mg diluent]
Weigh 1/25 of 3000 mg =
120 mg
[5 mg drug + 115 mg diluent]
X = =
FIGURE 3.6 •  Depiction of the aliquot method of weighing using the example described in the text.
3 • Pharmaceutical Measurement 41
St e p 2. D ilute the multiple quantity with an inert substance.
•  The amount of inert diluent to use is determined by the fact that the aliquot portion
of the drug–diluent mixture weighed in Step 3 must be equal to or greater than the
minimum weighable quantity previously determined.
•  By multiplying the amount of the aliquot portion to weigh in Step 3 by the multiple
selected in Step 1, the total quantity of the mixture to prepare is determined.
•  Example:
According to the preliminary step, 120 mg or more must be weighed for the desired accuracy.
If we decide on 120 mg for the aliquot portion in Step 3, and multiply it by the multiple
selected in Step 1 (i.e., 25), we arrive at 3000 mg for the total quantity of the drug–diluent mixture to prepare. Subtracting the 125 mg of drug weighed in Step 1, we must add
2875 mg of diluent to prepare the 3000 mg of drug–diluent mixture.
St e p 3. Weigh the aliquot portion of the dilution that contains the desired quantity.
•  Since 25 times the needed amount of drug substance was weighed (Step 1), an aliquot
part equal to 1/25 of the 3000-mg drug–diluent mixture, or 120 mg, will contain the
required quantity of drug substance.
•  Proof: 125
1
25
125 5
2875
× =
×
mg in
mg dilu
( )
(
drug substance weighed mg S ep t 1
eent weighed in mg
mg aliquot part
S ep t 2) = 115
120
Example Problems
(1) A torsion prescription balance has a sensitivity requirement of 6 mg. Explain how you
would weigh 4 mg of atropine sulfate with an accuracy of ±5%, using lactose as the
diluent.
Because 6 mg is the potential balance error, 120 mg is the smallest amount that
should be weighed to achieve the required precision.
If 120 mg, or 30 times the desired amount of atropine sulfate, is chosen as the
multiple quantity to be weighed in Step 1, and if 150 mg is set as the aliquot to be
weighed in Step 3, then:
1. Weigh 30 × 4 mg 120 mg of atropine sulfate

2. Dilute with to make

4380 mg of lactose 4500 mg of dilution

3. Weigh 1/30 of dilution, or 150 mg of dilution, which will contain 4 mg of
atropine sulfate
Proof: 4500
150
mg dilution 120
mg dilution
mg atropine sulfate
x mg
( )
( )
( )
(
=
aatropine sulfate)
= 4 mg
In this example, the weight of the aliquot was arbitrarily set as 150 mg, which
exceeds the weight of the multiple quantity, as it preferably should. If 120 mg
had been set as the aliquot, the multiple quantity should have been diluted with
3480 mg of lactose to get 3600 mg of dilution, and the aliquot of 120 mg would
have contained 4 mg of atropine sulfate.
(2) A torsion prescription balance has a sensitivity requirement of 6.5 mg. Explain how you
would weigh 15 mg of atropine sulfate with an accuracy of ±5%, using lactose as the
diluent.
Because 6.5 mg is the potential balance error, 130 mg (20 × 6.5 mg) is the smallest amount that should be weighed to achieve the required accuracy.
42 Pharma euti al c al ulations
If 10 is chosen as the multiple, and if 130 mg is set as the weight of the aliquot,
then:
1. Weigh 10 × 15 mg 150 mg of atropine sulfate
2. Dilute with
to make
1150 mg of lactose
1300 mg of dilution
3. Weigh 110 of dilution, or 130 mg, which will contain 15 mg of atropine sulfate
Measuring Volume by the Aliquot Method
The aliquot method of measuring volume, which is identical in principle to the aliquot method
of weighing, may be used when relatively small volumes must be measured with great
precision:
St ep 1. Select a multiple of the desired quantity that can be measured with the required
precision.
St ep 2. D ilute the multiple quantity with a compatible diluent (usually a solvent for
the liquid to be measured) to an amount evenly divisible by the multiple selected.
St ep 3. Measure the aliquot of the dilution that contains the quantity originally desired.
Example Problems
(1) A formula calls for 0.5 mL of hydrochloric acid. Using a 10-mL graduate calibrated from
2 to 10 mL in 1-mL divisions, explain how you would obtain the desired quantity of hydrochloric acid by the aliquot method.
If 4 is chosen as the multiple, and if 2 mL is set as the volume of the aliquot,
then:
1. Measure 4 × 0.5 mL 2 mL of the acid
2. Dilute with 6 mL of water
to make 8 mL of dilution
3. Measure 1
4 of dilution, or 2 mL of dilution, which will contain 0.5 mL of
hydrochloric acid.
(2) A prescription calls for 0.2 mL of clove oil. Using a 5-mL graduate calibrated in units of
0.5 mL, how would you obtain the required amount of clove oil using the aliquot method
and alcohol as the diluent?
If 5 is chosen as the multiple, then:
1. Measure 5 × 0.2 mL 1 mL of clove oil
2. Dilute with 4 mL of alcohol
to make 5 mL of dilution
3. Measure 1
5 of the dilution, or 1 mL, which contains 0.2 mL of clove oil.
Least Weighable Quantity Method of Weighing
T his method may be used as an alternative to the aliquot method of weighing to obtain small
quantities of a drug substance.
NOTE: It is important for the student to recognize that
answers to aliquot calculations may vary, but still be correct,
depending upon the multiple factors arbitrarily chosen for use.
3 • Pharmaceutical Measurement 43
After determining the quantity of drug substance that is desired and the smallest quantity that can be weighed on the balance with the desired degree of accuracy, the procedure
is as follows:
St ep 1. Weigh an amount of the drug substance that is equal to or greater than the least
weighable quantity.
St ep 2. Dilute the drug substance with a calculated quantity of inert diluent such
that a predetermined quantity of the drug–diluent mixture will contain the desired
quantity of the drug.
If 20 mg of a drug substance is needed to fill a prescription, explain how you would obtain
this amount of drug with an accuracy of ±5% using a balance with an SR of 6 mg. Use lactose as
the diluent.
In this problem, 20 mg is the amount of drug substance needed. T he least weighable
quantity would be 120 mg. T he amount of drug substance to be weighed, therefore, must
be equal to or greater than 120 mg. In solving the problem, 120 mg of drug substance is
weighed. In calculating the amount of diluent to use, a predetermined quantity of drug–
diluent mixture must be selected to contain the desired 20 mg of drug substance. T he
quantity selected must be greater than 120 mg because the drug–diluent mixture must be
obtained accurately through weighing on the balance. An amount of 150 mg may be arbitrarily selected. T he total amount of diluent to use may then be determined through the
calculation of the following proportion:
20
150
mg drug needed for R 1
mg drug diluent mixture
to use in R
/
/
( )
(
)
–
=
220 mg total drug substance weighed
x mg total amount of drug dilu
( )
( – eent
mixture prepared)
x = 900 mg of the drug–diluent mixture to prepare
H ence, 900 mg – 120 mg = 780 mg of diluent (lactose) to use
It should be noted that in this procedure, each weighing, including that of the drug
substance, the diluent, and the drug–diluent mixture, must be determined to be equal to or
greater than the least weighable quantity as determined for the balance used and accuracy
desired.
c Al c Ul ATIo n S c APSUl E
Weighing Accuracy
•   The sensitivity requirement (SR) of a balance must be known or determined. An SR of
6 mg is usual.
•   An error in weighing of ±5% or less is acceptable.
•   The smallest quantity that should be weighed on a prescription balance is determined
by the equation:
100% Sensitivity Requirement (mg)
Acceptable Error (%)
Smalles
×
= tQuantity (mg)
That quantity is usually about 120 mg.
•   To weigh smaller quantities, an electronic balance or the aliquot method of weighing
should be used.
44 Pharma euti al c al ulations
Percentage of Error
Because measurements in the community pharmacy are never absolutely accurate, it
is important or the pharmacist to recognize the limitations o the instruments used
and the magnitude o the errors that may be incurred. W hen a pharmacist measures a
volume o liquid or weighs a material, two quantities become important: (1) the apparent weight or volume measured and (2) the possible excess or def ciency in the actual
quantity obtained.
Percentage of error may be de ined as the maximum potential error multiplied by 100 and
divided by the quantity desired. T he calculation may be ormulated as ollows:
Error
Q uantity desired
× 100% = Percentage of error
Calculating Percentage of Error in Volumetric Measurement
T he percentage o error in a measurement o volume may be calculated rom the above
equation, relating the volume in error (determined through devices o greater precision) to
the volume desired (or apparently measured).
Using a graduated cylinder, a pharmacist measured 30 mL o a liquid. On subsequent examination, using a narrow-gauge burette, it was determined that the pharmacist had actually measured
32 mL. W hat was the percentage o error in the original measurement?
32 30 2 mL mL mL the volume of error – = ,
2 100
30
mL
mL
× %
6 7% .=
Calculating Percentage of Error in Weighing
T he various scales and balances used in pharmaceutical weighing have ascribed to them
di erent degrees o precision. As described previously in this chapter, knowledge o the sensitivity requirement o the balance being used is critical in weighing to a specif ed degree o
accuracy. T he sensitivity requirement o a balance may be used to determine the percentage
o error in a given weighing.
(1) W hen the maximum potential error is ±4 mg in a total o 100 mg, what is the percentage
o error?
4 100
100
mg
mg
× %
= 4%
(2) A prescription calls or 800 mg o a substance. A ter weighing this amount on a balance, the
pharmacist decides to check by weighing it again on a more sensitive balance, which registers
only 750 mg. Because the f rst weighing was 50 mg short o the desired amount, what was
the percentage o error?
50 100
800
mg
mg
×
=
%
6 25% .
3 • Pharmaceutical Measurement 45
Examples of Measurement Applications in Pharmaceutical
Compounding
T he following are examples of the calculations applied in weighing and measuring in the
compounding of pharmaceutical formulas or medication orders. Many additional problems
are found in Chapter 17, Selected Calculations in Contemporary Compounding.

(1)2 Misoprostol Polyethylene oxide H ydroxypropyl methylcellulose Compounding Instructions:

400 µg 200 mg 15 g

(1) Accurately weigh each of the ingredients.
(2) Place the misoprostol in a mixing vessel, and add the polyethylene oxide in
equal portions until thoroughly blended.
(3) Add the hydroxypropyl methylcellulose in portions until all ingredients are
thoroughly blended.
(4) Label and dispense.
(a) Would a torsion prescription balance allow the accurate direct weighing of each
ingredient? Explain.
(b) Explain how the misoprostol might be accurately obtained using a torsion prescription balance and the aliquot method of weighing.
(c) How many misoprostol tablets, each containing 0.2 mg, could be used in compounding this order? How would they be combined?
Answers:
(a) N ot for the misoprostol. T he least weighable quantity using a torsion balance is 120 mg (with an SR of 6 mg and an acceptable error of ±5%), and the
misoprostol required is 400 µg or 0.4 mg. An analytical balance could be used.
(b) T he pharmacist could weigh 300 times the required amount of misoprostol,
120 mg (300 × 0.4 mg = 120 mg); then, mix that with 35,880 mg of polyethylene oxide to make 36,000 mg of mixture from which a 120-mg aliquot portion
could be taken to provide the 0.4 mg of misoprostol (and 119.6 mg of polyethylene oxide). H owever, this would be very wasteful of the ingredients, so the
better option is provided by (c).
(c) Two misoprostol tablets each containing 0.2 mg (200 µg) would provide the
400 µg required. T he tablets would be pulverized using a mortar and pestle
and the other ingredients combined in portions as described in the compounding instructions as stated above.

(2)2 Fentanyl citrate Methylparaben Propylparaben Propylene glycol N ormal saline solution Compounding Instructions:

2.5 mg 10 mg 10 mg 0.2 mL 10 mL

(1) Accurately weigh and measure each of the ingredients.
(2) Dissolve the methylparaben and the propylparaben in the polyethylene glycol.
46 Pharma eu i al c al ula ion
(3) Dissolve the entanyl citrate in the normal saline solution.
(4) Slowly add the solution o the parabens to the entanyl citrate solution and
mix well.
(5) Sterilize by f ltering through a sterile 0.2-µm f lter into a sterile metered spray
bottle.
(6) Label and dispense.
(a) W hat type of balance should be used to weigh the fentanyl citrate and the parabens?
(b) W hat are the best options in measuring the propylene glycol?
Answers:
(a) An analytical balance should be used.
(b) A graduated pipette or a graduated syringe.
c ASE In Po In T 3.1 A pharma i i a ked o ompound he following formula for
he prepara ion of 100 ap ule 3:

Estriol Estrone Estradiol Methocel E4M Lactose

200 mg 25 mg 25 mg 10 g 23.75 g

U ing a balan e ha ha an s R of 6 mg, he aliquo me hod of weighing, la o e
a he diluen , and an error in weighing of 4% how, by al ula ion , how he orre
quan i y of e rone an be ob ained o a ura ely ompound he formula.
c ASE In Po In T 3.2 A phy i ian pre ribed 25 4-mg ap ule of a drug for a peial need pa ien , knowing ha he do e pre ribed wa on idered “ ub herapeui .” t he lowe reng h ommer ially available able on ain 25 mg.
t he pharma i de ided o ele he minimum required number of 25-mg able (4 able ), redu e hem o a powder wi h a mor ar and pe le, weigh he powder
(280 mg), and on inue he pro e u ing he aliquo me hod. s he alled upon her
pharma y uden in ern o al ula e (a) he minimum quan i y of la o e (diluen )
o u e in preparing he ru hed able –diluen mix ure and (b) he quan i y of he
mix ure o u e o fill ea h ap ule.
t he pre rip ion balan e had an s R of 6 mg, and a weighing error of 5% wa
a ep able.
s how your al ula ion for (a) and (b), and ( ) prove ha your an wer o (b) i
orre by demon ra ing ha ea h ap ule would indeed on ain 4 mg of drug.
3 • Pharmaceutical Measurement 47
PRAc TIc E PRo Bl EMS
Calculations of Aliquot Parts by Weighing
1. A prescription calls for 50 mg of chlorpheniramine maleate. Using a prescription balance with a sensitivity requirement of 6 mg, explain how you would
obtain the required amount of chlorpheniramine maleate with an error not
greater than 5%.
2. A prescription balance has a sensitivity requirement of 0.006 g. Explain how you
would weigh 0.012 g of a drug with an error not greater than 5%, using lactose
as the diluent.
3. A torsion prescription balance has a sensitivity requirement of 4 mg. Explain
how you would weigh 5 mg of hydromorphone hydrochloride with an error not
greater than 5%. Use lactose as the diluent.
4. A torsion prescription balance has a sensitivity requirement of 0.004 g.
Explain how you would weigh 0.008 g of a substance with an error not greater
than 5% .
5. A prescription balance has a sensitivity requirement of 6.5 mg. Explain how you
would weigh 20 mg of a substance with an error not greater than 2%.
Calculations of Aliquot Parts by Measuring Volume
6.
Using a balance with a sensitivity of 4 mg, an acceptable weighing error of 5%
and cherry syrup as the solvent for tartar emetic, how could you obtain the correct
quantity of tartar emetic to fill the prescription?
7. A formula calls for 0.6 mL of a coloring solution. U sing a 10-mL graduate
calibrated from 2 to 10 mL in 1-mL units, how could you obtain the desired
quantity of the coloring solution by the aliquot method? U se water as the
diluent.
8. U sing a 10-mL graduate calibrated in 1-mL units, explain how you would
measure 1.25 mL of a dye solution by the aliquot method. U se water as the
diluent.
9. T he formula for 100 mL of pentobarbital sodium elixir calls for 0.75 mL of
orange oil. Using alcohol as a diluent and a 10-mL graduate calibrated in 1-mL
units, how could you obtain the desired quantity of orange oil?
Calculations of Percentage of Error
10. A pharmacist attempts to weigh 120 mg of codeine sulfate on a balance with a
sensitivity requirement of 6 mg. Calculate the maximum potential error in terms
of percentage.
11. In compounding a prescription, a pharmacist weighed 0.05 g of a substance on
a balance insensitive to quantities smaller than 0.004 g. W hat was the maximum
potential error in terms of percentage?
12. A pharmacist weighed 475 mg of a substance on a balance of dubious accuracy.
W hen checked on a balance of high accuracy, the weight was found to be 445 mg.
Calculate the percentage of error in the first weighing.

Sodium citrate Tartar emetic Cherry syrup ad

5 g 0.015 g 120 mL

48 Pharma euti al c al ulations
c Al c q UIz
3.A. A pharmacist receives a prescription for ear drops, calling for 0.05 mL of glacial
acetic acid, 2 mL of glycerin, and 8 mL of purified water. Using a 10-mL graduated
cylinder calibrated in 0.5-mL units, explain how the required quantity of glacial acetic
acid could be obtained.
3.B. A pharmacist quizzes a pharmacy intern on the aliquot method in the preparation
of 12 capsules each to contain 80 mg of morphine sulfate and 3.2 mg of naltrexone hydrochloride. Lactose is to be used as a diluent, a prescription balance with a
sensitivity of 6 mg is proposed, and a 4% error is acceptable. Provide the relevant
calculations.
3.C. The aliquot method was used to obtain 8 mg of a drug with a prescription balance
having a sensitivity of 6 mg. A weighing error of 5% was accepted. If 140 mg of the
drug was weighed, added to 2.1 g of lactose, and 120 mg of the mixture used to
provide the required quantity of drug, were the calculations correct or incorrect?
3.D. In preparing a zinc oxide ointment, 28.35 g of zinc oxide was used rather than the
correct quantity, 31.1 g. What percentage error was incurred?
13. A 10-mL graduate weighs 42.745 g. W hen 5 mL o distilled water is measured
in it, the combined weight o the graduate and water is 47.675 g. By de inition,
5 mL o water should weigh 5 g. Calculate the weight o the measured water and
express any deviation rom 5 g as percentage o error.
14. A graduate weighs 35.825 g. W hen 10 mL o water is measured in it, the weight
o the graduate and water is 45.835 g. Calculate the weight o the water, and
express any deviation rom 10 g as percentage o error.
15. A pharmacist attempts to weigh 0.375 g o morphine sul ate on a balance o dubious accuracy. W hen checked on a highly accurate balance, the weight is ound to
be 0.400 g. Calculate the percentage o error in the irst weighing.
Measurement Applications in Compounding

16.4 Carvedilol Water, purif ed Ora-Blend SF suspension Compounding Instructions:

100 mg 10 mL 90 mL

(1) Weigh carvedilol.
(2) Grind carvedilol powder in a mortar with the puri ied water until a smooth
paste results.
(3) Add the Ora-Blend SF (sugar- ree) suspension slowly with mixing in the
mortar until a smooth, uni orm suspension results.
(4) Pour into amber glass bottle or labeling and dispensing.
(a) Describe the type of balance to best use to weigh the carvedilol.
(b) If a torsion prescription balance is used to weigh the carvedilol, describe the aliquot method that may be used.
(c) If 12.5-mg carvedilol tablets are used as the source of the drug, describe the
compounding procedure to use.
3 • Pharmaceutical Measurement 49
An SwERS To “c ASE In Po In T” An d PRAc TIc E PRo Bl EMS
Case in Point 3.1
T he smallest quantity that should be weighed on the balance:
100 6
4
150
%
×%
=
mg
mg
Q uantity desired (estrone): 25 mg
Multiple factor selected: 6
Aliquot portion selected: 150 mg

Estrone (25 × 6) Lactose Aliquot mixture Aliquot portion (900 mg ÷ 6)

150 mg 750 mg 900 mg 150 mg of mixture will provide 25 mg estrone

Case in Point 3.2
T he smallest quantity that should be weighed on the balance:
100 6
5
120
%
×%
=
mg
mg
(a) Q uantity of mixture required to prepare 25 capsules each containing the weighable quantity of 120 mg:
120 mg × 25 (capsules) = 3000 mg
Q uantity of lactose required equals the quantity of mixture required less the
weight of the crushed tablets:
300 mg – 280 mg = 2720 mg or 2.72 g of lactose required
(b) Q uantity of mixture to fill each capsule:
3000 mg ÷ 25 (capsules) = 120 mg
(c) Proof of 4 mg of drug per capsule:
Amount of drug in mixture:
25 mg (per tablet) × 4 (tablets) = 100 mg
Amount of drug per capsule:
100 mg ÷ 25 (capsules) = 4 mg
or,
100
3000 120
mg
mg
x
mg
( )
( ) ( )
drug
mixture mixture
=
= 4 mg
50 Pharma uti al c al ulations
Practice Problems
Aliquot Parts by W ighing

1. Weigh Dilute with to make

150 mg chlorpheniramine maleate 450 mg lactose 600 mg mixture

 

Weigh/use 2. Weigh

200 mg mixture 120 mg drug

 

Dilute with to make Weigh/use 3. Weigh Dilute with to make Weigh/use

1380 mg inert powder 1500 mg mixture 150 mg mixture 80 mg hydromorphone hydrochloride 1520 mg lactose 1600 mg mixture 100 mg mixture

 

4. Weigh Dilute with to make

160 mg substance 3840 mg inert powder 4000 mg mixture

 

Weigh/use 5. Weigh

200 mg mixture 400 mg substance

 

Dilute with to make Weigh/use	7600 mg inert powder 8000 mg mixture 400 mg mixture
Aliquot Parts by M asuring volum
6. Weigh Dilute to Measure/use	90 mg tartar emetic 12 mL cherry syrup 2 mL mixture

 

7. Measure Dilute to

3 mL coloring agent 10 mL water

 

Measure/use 8. Measure

2 mL solution 5 mL dye

 

Dilute to Measure/use 9. Measure Dilute to Measure/use P r ntag of e rror

8 mL water 2 mL solution 3 mL orange oil 8 mL alcohol 2 mL solution

10. 5%
11. 8%
12. 6.32%
13. 1.4%
14. 0.1%
15. 6.67%
3 • Pharmaceutical Measurement 51
References
1. Prescription balances and volumetric apparatus. United States Pharmacopeia 32 National Formulary 27. Rockville,
MD: United States Pharmacopeial Convention, 2009;1:691–692.
2. Young L, Allen LV Jr, eds. The Art, Science, and Technology of Pharmaceutical Compounding. 2nd Ed. Washington,
DC: American Pharmaceutical Association; 2002.
3. H ormone replacement therapy. Secundum Artem 8(1):4. Available at: http://www.paddocklabs.com. Accessed
June 6, 2012.
4. Pharmaceutical Service Division, Ministry of H ealth Malaysia. Extemporaneous Formulary. Putrajaya, Malaysia.
Available at: http://www.moh-extemporaneous-formulary-2011.pdf. Accessed April 15, 2014.
16. (a) An analytical balance
(b) Weigh 200 mg carvedilol and mix with 20 mL of purified water. Measure
10 mL of the mixture to provide 100 mg of carvedilol.
(c) Eight 12.5-mg carvedilol tablets may be pulverized in a mortar with the
purified water and a portion of Ora-Blend SF suspension, as needed, until
smooth. T he remaining portion of the suspension vehicle may then be added
and blended until a uniform product results.
52
By def nition, a prescription is an order or medication issued by a physician, dentist, or
other properly licensed medical practitioner. A prescription designates a specif c medication
and dosage to be prepared and dispensed by a pharmacist and administered to a particular
patient.
A prescription may be written on preprinted prescription orms (traditional prescriptions) or transmitted to a pharmacy by computer (e-prescription), telephone, or acsimile
(FAX). As shown in Figure 4.1, a typical preprinted prescription orm contains the traditional symbol (meaning “recipe,” “take thou,” or “you take”), name, address, telephone
number, and other pertinent in ormation regarding the prescriber. Blank areas are used by
the prescriber to provide patient in ormation, the medication desired, and directions or
use. A prescription written by a veterinarian generally includes the animal species and/or
the pet’s name and the name o the owner.
In hospitals and other institutions, the orms are somewhat di erent and are re erred
to as medication orders. A medication order may be written (paper) or transmitted electronically. A typical paper medication order sheet is shown in Figure 4.2.
A prescription or medication order or an in ant, child, or an elderly person may
include the age, weight, and/or body sur ace area (BSA) o the patient. T his in ormation is
applicable in dose calculation (as discussed in Chapter 8). An example o a prescription or
a pediatric patient is shown in Figure 4.3.
A prescription may call or a pre abricated dosage orm (e.g., tablet) or it may call
or multiple components and require compounding by a pharmacist.a A medication may
aT he extemporaneous compounding o prescriptions is an activity or which pharmacists are uniquely quali ied by
virtue o their education, training, and experience. “Traditional” pharmacy compounding involves the mixing,
packaging, labeling, and dispensing o a medication upon receipt o a prescription or medication order or a
speci ic patient. Extended compounding activities involve the outsourcing o compounded medications to other
health care providers. Pharmaceutical manufacturing is the large-scale production o product or the marketplace.
A distinction between these di erent activities is provided by legislation, guidelines, and regulations o state
boards o pharmacy and the ederal Food and Drug Administration.1,2
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

D mon ra	an und r and ng of h forma and ompon n of rad onal pr	r p
on and -pr	r p on .
D mon ra an und r and ng of h forma and ompon n of a yp al n	u onal
m d a on ord r.
in rpr	ommon a r a on and ym ol u d on pr	r p on and m d a on
ord r and apply h m orr	ly n pharma u al al ula on .

Apply al ula on o nd a m d a on adh r n .
4
Interpretation of Prescriptions
and Medication Orders
4 • interpretat on of Prescr pt ons and Med cat on Orders 53
be prescribed by its brand name or by the nonproprietary (generic) name.b In some cases,
the product selection may be affected by pharmacy regulations and/or by provider–payer
options.
Prescriptions requiring compounding include the name and quantities of each ingredient, the form into which they are to be prepared (e.g., syrup, capsules), and directions for
patient use. Definitions and descriptions of dosage forms and drug delivery systems are
presented in Appendix B.
bA brief overview of the designation of nonproprietary and brand names may be found in Authors’ Extra Point A
at the end of this chapter.
(1)
(2) (3)
(1)
(4)
(5)
(6)
(7)
(8)
John M. Brown, M.D.
100 Main Street
Libertyville, Maryland
Phone 123-4567
Name Date
Address

Refill Label: Yes	times	No
Generic if available: Yes	No

DEA No. 1234563
State License No. 65432
FIGURE 4.1 •  Components of a typical prescription. Parts labeled are as follows:
(1) Prescriber information and signature.
(2) Patient information.
(3) Date prescription was written.
(4) symbol (the Superscription), meaning “take thou,” “you take,” or “recipe.”
(5) Medication prescribed (the Inscription).
(6) Dispensing instructions to the pharmacist (the Subscription).
(7) Directions to the patient (the Signa).
(8) Special instructions. It is important to note that for any Medicaid or Medicare prescription and according to
individual state laws, a handwritten language by the prescriber, such as “Brand necessary,” may be required
to disallow generic substitution.
NOTE: When filling the prescription, the pharmacist adds a prescription number for identification.
54 Pharma euti al c al ulations
CITY HOSPITAL
Athens, GA 30600
PHYSICIAN’S ORDER
Unless “No substitution permitted” is clearly written after the order, a generic or therapeutic
equivalent drug may be dispensed according to the Formulary policies of this hospital.
DATE TIME ORDERS
02/01/yy 1200 1. Propranolol 40 mg po QID
2. Furos emide 20 mg po q AM
3. Flurazepam 30 mg at HS prn s leep
4. D-5-W + 20 mEq KCl/L at 84 mL/hr
Hardmer, MD
PATIENT NAME:
ADDRESS:
CITY, STATE:
AGE/SEX:
PHYSICIAN:
HOSP.NO:
SERVICE:
ROOM:
Thompson, Linda
2345 Oak Circle
Athens, GA
35y/Female
J. Hardmer
900612345
Medicine
220 East
FIGURE 4.2 •  Typical hospital medication order sheet.
Mary M. Brown, M.D.
Pediatric Clinic
110 Main Stre et
Libe rtyville , Maryland
Phone 456-1234

Name Address Suzie Smith 123 Broad Street	Age 5	Weight lb 39.4
Date Jan 9, 20yy

 

Refill times Label: Yes Sig: 0	tsp q 12 h
No
Generic if available: Yes	No

DEA No. MB5555555
State Licens e No. 23456
Mary Brown, M.D .
Omnicef Oral Suspension
125 mg/ 5 mL
Disp. 100 mL
Give 14 mg/ kg/ day x 10 days
FIGURE 4.3 •  Example of a prescription for
a pediatric patient.
4 • interpretat on of Prescr pt ons and Med cat on Orders 55
Examples are shown or prescriptions calling or trade name products (Figs. 4.1
and 4.3), a generic drug (Fig. 4.4A), and compounding (Fig. 4.5). Figure 4.4B shows the
label o a product that may be used by the pharmacist in illing the medication order as
prescribed in Figure 4.4A.
Tamper-Resistant Prescription Pads
To prevent the unauthorized copying, modif cation, or counter eiting o prescriptions,
tamper-resistant prescription pads have been developed. T he tamper-resistant qualities o
these prescription orms are accomplished through the use o security paper, erase-resistant
paper, thermochromatic ink (which results in the appearance o the word “VOID” on photocopies), and/or imbedded holograms.
FIGURE 4.4 •  A. Example of a prescription written for a generic drug. B. Label of product which may be
used by a pharmacist in filling the prescription called for in Figure 4.4A. (Source: http://dailymed.nlm.nih.gov/
dailymed/about.cfm. Courtesy of Teva Pharmaceuticals.)
John M. Brown, M.D.
100 Main Stre et
Libe rtyville, Maryland
Phone 123-4567

Name Address Brad Smith 123 Broad Street

Date Jan 9, 20yy

Refill times

Label: Yes	No
Generic if available: Yes	No

DEA No. CB1234563
State Licens e No. 65432
RX 1234576
JM Brown, M.D.
Amoxicillin 250 mg/ 5 mL
Disp. 100 mL
Sig: two tsp. every 12 hours
until gone
0
A
56 Pharma euti al c al ulations
Electronic Health Record
An electronic health record (EH R) is a digital version of a patient’s paper chart. EH Rs
are real-time, patient-centered records that make information available instantly and
securely to authorized users. An EH R can contain a patient’s medical history, diagnoses, medications, treatment plans, immunization dates, allergies, radiology images,
and laboratory and test results. Integrated electronic health information systems allow
doctors, nurses, pharmacists, and other health care providers to appropriately access
and securely share a patient’s vital medical information electronically—with the intent
of improving the speed, quality, safety, and cost of patient care. In the hospital and
in other institutional settings, these systems include computerized physician order entry
(CPO E) by which a physician can order medications and provide other instructions for
a patient’s care.
e-Prescribing/e-Prescriptions
Electronic prescribing (e-prescribing) is the computer-to-computer transfer of prescription
information between authorized prescribers, pharmacies, intermediaries, and payers under
nationally accepted standards.3 In the inpatient or outpatient setting, a medication order for
John M. Brown, M.D.
100 Main Street
Libertyville, Maryland
Phone 123-4567

Name Address N eil Smith 123 Broad Street

Date Jan 9, 20yy

Refill times

Label: Yes	No
Generic if available: Yes	No

DEA No. CB1234563
State License No. 65432
JM Brown, M.D.
Metoclopramide H CL
Methylparaben
Propylparaben
Sodium Chloride
Purified Water, qs ad
M. ft. nasal spray
Sig: N asal spray for chemotherapyinduced emesis. U se as directed.
Discard after 60 days.
10 g
50 mg
20 mg
800 mg
100 mL
0
FIGURE 4.5 •  Example of a prescription requiring compounding.
4 • interpretat on of Prescr pt ons and Med cat on Orders 57
a patient is entered into an automated data entry system as a personal computer or a handheld device loaded with e-prescribing software and sent to a pharmacy as an e-prescription.
Some e-prescribing operational functions within EH R software programs are displayed in
Table 4.1. W hen an e-prescription is received in the pharmacy, it is printed out as the illustration shown in Figure 4.6.
T e 4.1 •  SOME E-PRESc RIb In G OPERaTIOn a l FUn c TIOn S WITh In El Ec TROn Ic
h Ea l Th REc ORd (Eh R) SOFTWa RE PROGRa MS
View Medication History
Update Medication History
Order Prescription During Patient Visit
•  Select Diagnosis Associated with the Prescription
•  Review Patient Coverage Information
•  Select Medication & Dosage
•  Enter Sig (Directions for Medication Use)
•  Review Clinical Decision Support Information & Alerts
•  Patient Medication Education Information Available
•  Search for and Select Patient’s Preferred Pharmacy
•  Submit Prescription Electronically
Approve Prescription Requests/Renewals
XYZ PHARMACY SYSTEM
Ele ctronically Transmitted to Smith Pharma cy
1234 Broad Stre et
Anytown, State, Zip
Date: 10/20/20yy

Rx # 9876543	ID # 11223344
Patient Information
Last Name: Jones First Name: Mary
DOB: Sex: Address:	10/18/YY Phone: (XXX)-888-7777
F
567 King Stre et Anytown, State, Zip Drug, SIG, and Re ll Information
Drug Name: Gabapentin
Strength: Quantity: SIG: Re lls: Label:	100 mg 60
Dose Form: capsules
Take 1 capsule at bedtime
6 yes
Prescriber Information
Last Name: Brown
First Name: J ames M
Address:	100 Main Stre et Anytown, State, Zip CB1234XXX 9876543XXX
DEA: NPI:

FIGURE 4.6 •  Illustration of an electronically transmitted prescription as received by a pharmacy. (DEA, Drug
Enforcement Administration; NPI, National Provider Identifier.)
58 Pharma euti al c al ulations
Among the advantages cited or e-prescriptions over traditional paper prescriptions are
reduced errors due to prescription legibility, concurrent so tware screens or drug allergies
and drug interactions, integrated in ormation exchange between health care providers,
reduced incidence o altered or orged prescriptions, e iciency or both prescriber and
pharmacist, and convenience to the patient, whose prescription would likely be ready or
pickup upon arrival at the pharmacy.4,5
Additional e-prescribing images are displayed in Authors’ Extra Point B at the end o
this chapter.
Hospital and Other Institutional Medication Order Forms
As noted previously, a typical paper medication order form used in the hospital setting is shown
in Figure 4.2. In addition, other orms may be used within a hospital by specialized units
such as in ectious disease, cardiac care, pediatrics, obstetrics, orthopedics, and others.6 Drugspecif c orms also may be used, as or heparin dosing, electrolyte in usions, and morphine
sul ate in patient-controlled anesthesia. An example o the latter is shown in Figure 4.7.
Other types o patient care acilities, such as outpatient clinics, intermediate- and
long-term care acilities (Fig. 4.8), cancer treatment centers, and others, utilize institutionspeci ic orms or medication orders.
City Hospital
Patient Controlled Anesthesia (PCA) Orders
MORPHINE SULFATE INJECTION, 1 mg/mL
Patient Information (Label)
Physician:
Date:
1. Mode (check)
2. PCA Dose
3. Period between Injections
4. Basal (Continuous) Rate
5. One-Hour Limit
6. Initial Loading Dose
7. Additional Instructions:
Physician’s Signature _______________________________________________
= __________ mL (mg)
= __________ minutes
= __________ mL (mg)/hr
= __________ mL (mg)
= __________ mL (mg)
DOSING GUIDELINES
1 mL (1 mg)
10 minutes
1 mL (1 mg)/hr
7 mL (7 mg)
2-5 mL (2-5 mg)
PCA Continuous PCA & Continuous
Time:
FIGURE 4.7 •  Example of a hospital form for prescribing a specific drug treatment: patient-controlled anesthesia.
(Adapted from www.hospital-forms.com. Ref.6)
4 • interpretat on of Prescr pt ons and Med cat on Orders 59
Paper medication forms in most health care institutions have been largely replaced
by computerized physician order entry (CPOE) as a part of the transition to EH R systems
(EH Rs).
Military Time
Militar y time is used not only in the military but in civilian life as well, such as in
hospitals, law enforcement, and emergency services. Its use provides an unambiguous
expression of time. In health care institutions, military time may be used to record the
time of a patient’s admission, when a medication was administered, the time of surgery,
and so forth.
Table 4.2 compares the expressions of military time and regular time. Military time is
verbalized, as for example, “twenty-three hundred hours.” Colons may be used to separate
hours and minutes, as 1331 or 13:31 hours (31 minutes past 1 o’clock in the afternoon), and
when desired seconds, as 1331:42 or 13:31:42.
Form of Compounded Prescriptions
T he quantities of ingredients designated on prescriptions to be compounded are written
using SI metric units as illustrated in the examples below.
In prescription writing, the decimal point may be replaced by a vertical line to designate whole or decimal fractions of grams or milliliters. If the designations “g” or “mL”
are absent, as in the second illustration, they are presumed. Unless otherwise noted, solid
materials are presumed to be grams and liquids, milliliters.
MEDICATION ORDER FORM
CITY NURSING HOME
Phys ician’s Orders
Attending Physician:
Resident’s Name:
1.
2.
3.
4.
____AM ____PM
____AM ____PM
____AM ____PM
____AM ____PM
____AM ____PM
____AM ____PM
____AM ____PM
____AM ____PM
DRUG DIAGNOSIS
ADMINISTRATION
TIMES
Order Number: (preprinted)
Room Number:
QUANTITY FREQUENCY
DOSE AND
ROUTE
Physician’s Signature:
Signature of Nurse
Receiving Order:
Ordered from
Pharmacy, Time/Date:
Time/Date Ordered:
Time/Date Ordered:
Received from
Pharmacy, Time/Date:
FIGURE 4.8 •  Example of a nursing home medication order form.
60 Pharma euti al c al ulations
T b e 4.2 •  c OMPa RaTIvE ExPRESSIOn S OF REGUl a R a n d MIl ITa Ry TIME

Regu r Time	Mi it r Time	Regu r Time	Mi it r Time
Midnight 1:00 a m	0000 0100	Noon 1:00 pm	1200 1300
2:00 a m	0200	2:00 pm	1400
3:00 a m	0300	3:00 pm	1500
4:00 a m	0400	4:00 pm	1600
5:00 a m	0500	5:00 pm	1700
6:00 a m	0600	6:00 pm	1800
7:00 a m	0700	7:00 pm	1900
8:00 a m	0800	8:00 pm	2000
9:00 a m	0900	9:00 pm	2100
10:00 a m	1000	10:00 pm	2200
11:00 a m	1100	11:00 pm	2300

Prescription and Medication Order Accuracy and Verification
It is the responsibility o the pharmacist to ensure that each prescription and medication
order received is correct in its orm and content, is appropriate or the patient being treated,
and is subsequently f lled, labeled, dispensed, and administered accurately. In essence, each
medication should be:
•  T herapeutically appropriate or the patient
•  Prescribed at the correct dose
•  Dispensed in the correct strength and dosage orm
•  Correctly labeled with complete instructions or the patient or caregiver
•  For the patient in a hospital or other health care acility, each medication must be
administered to the correct patient, at the correct time, and by the correct rate and
route o administration
M edication verification is the term used when there is a process in place to assure
the above bullet points. It is per ormed initially through the care ul reading, illing
(including calculations), checking, and dispensing o the prescription or medication
order. T he process o ten is enhanced by technologies, as the computer matching o a
drug package bar code with the prescription order and/or by matching the drug’s bar
code to a patient’s coded wrist band in a patient care acility (termed bedside medication
verification).
Acetylsalicylic acid 4 g
Phenacetin 0.8 g
Codeine sul ate 0.5 g
Mix and make capsules no. 20
Sig. one capsule every 4 hours
Dextromethorphan 0 18
Guai enesin syrup 1 2
Alcohol 2 1
Flavored syrup ad 60
Sig. 5 mL as needed or cough
Illustration of prescriptions written in SI metric units:
4 • interpretat on of Prescr pt ons and Med cat on Orders 61
Errors and Omissions
To ensure such accuracy, the pharmacist is obliged to review each prescription (both traditional and e-prescription) and medication order in a step-by-step manner to detect errors
and omissions. I there is any question regarding a prescription or medication order, the pharmacist
must seek clarif cation rom the prescriber.
Among the items that the pharmacist should check or the correct reading and interpretation o a prescription or medication order are as ollows:
•  Prescriber in ormation, including address and telephone number, Drug En orcement
Administration (DEA) number ( or authority to prescribe schedule drugs including
narcotics), state license number and/or the N ational Provider Identif er (N PI), an
identif cation number or participating health care providers, and signature
•  Date o the order and its currency to the request or f lling
•  Patient identif cation in ormation and, i pertinent to dose determination, the
patient’s age, weight, and/or other parameters
•  Drug prescribed, including dose, preparation strength, dosage orm, and quantity
•  Clarity o any abbreviations, symbols, and/or units o measure
•  Clarity and completeness o directions or use by the patient or caregiver
•  Ref ll and/or generic substitution authorization
•  N eed or special labeling, such as expiration date, conditions or storage, and oods
and/or other medications not to take concomitantly
•  A listing o the ingredients and quantities or orders to be compounded
Once the prescription or medication order is illed and the label prepared, be ore
dispensing, the pharmacist should make certain o the ollowing:
•  T he f lled prescription or medication order contains the correct drug, strength, dosage orm, and quantity. Placing a medication’s indication (use) on the prescription
label has been shown to be o benef t in understanding o the use o their medication
or some patients, particularly older patients and those taking multiple medications.7
T he bar coding o pharmaceutical products used in hospital settings is required by
the ederal Food and Drug Administration (FDA) as an added protection to ensure
accurate product dispensing and administration (Fig. 4.9).
•  T he pharmacy-imprinted serial number on the label matches that on the order.
•  T he label has the name o the correct patient and physician; the correct drug name, quantity,
and strength; the name or initials o the pharmacist who f lled the order; and the number
o ref lls remaining. Additional label in ormation and/or auxiliary labels may be required.
It is important that the instructions or use by the patient be clearly understood. This may require
that the pharmacist add words o clarity to the labeled instructions. For example, instead o “Take two
tablets daily,” the directions might indicate whether the two tablets are to be taken at once or at separate
and speci ied times. In addition, i the patient or caregiver has di iculty with the language, verbal reinorcement may be required.
Re er to the prescription shown in Figure 4.4A to identi y any errors and/or omissions in the
ollowing prescription label.
Main Street Pharmacy
150 Main Street
Libertyville, Maryland
Phone 456-1432

1234576	Jan 10, 20yy
Brad Smith	Dr. J. M. Brown
Take 2 teaspoon uls every 12 hours.
Ampicillin 250 mg/5 mL	100 mL Pharmacist: AB
Ref lls: 0

62 Pharma euti al c al ulations
Error: Drug name incorrect.
Omission: Directions incomplete.
N OT E: T here would be a serious question of whether the patient received the correct
medication.
Additional examples of errors and omissions are presented in the practice problems at
the end of the chapter.
Use of Roman Numerals on Prescriptions
Roman numerals commonly are used in prescription writing to designate quantities, as the
(1) quantity of medication to be dispensed and/or (2) quantity of medication to be taken by
the patient per dose.
T he student may recall the eight letters of fixed values used in the Roman system:
ss = ½ L or l = 50
i or j = 1 C or c = 100
V or v = 5 D or d = 500
X or x = 10 M or m = 1000
T he student also may recall that the following rules apply in the use of Roman numerals:
(1) A letter repeated once or more repeats its value (e.g., xx = 20; xxx = 30).
(2) One or more letters placed after a letter of greater value increases the value of the
greater letter (e.g., vi = 6; xij = 12; lx = 60).
(3) A letter placed before a letter of greater value decreases the value of the greater letter
(e.g., iv = 4; xl = 40).
(4) Use the simplest choice among the possible options. For instance, to indicate the
number 60, “lx” would be preferred over “xxxxxx.”
FIGURE 4.9 •  Example of a product bar code used on pharmaceuticals for positive drug identification to reduce medication errors.
(Courtesy of Baxter Healthcare Corporation.)
4 • interpretat on of Prescr pt ons and Med cat on Orders 63
Capital or lowercase letters may be used. Dotting the lowercase “i” or placement of a
horizontal line above the “i” with the dot atop serves to avoid misinterpretation. A “j” may
be used as the final “i” in a sequence (e.g., viij). Additional examples are:

iv = 4 viii = 8 xii = 12 xxiv = 24

xl = 40 xc = 90 cl = 150 lxiv = 64

cdxl = 440 lxxii = 72 cxxvi = 126 lxxxiv = 84

cmxcix = 999 MCDXCII = 1492 mdclxvi = 1666 mm = 2000

W hen Roman numerals are used, the tradition of placing the numerals after the term
or symbol generally is followed (e.g., capsules no. xxiv; fluid ounces xij).
Use of Abbreviations and Symbols
Although reduced by the transition to e-prescribing, the use of abbreviations remains
on prescriptions and medication orders. Many prescription abbreviations are derived
from the Latin through its historical use in medicine and pharmacy, whereas others have
evolved through prescribers’ use of writing shortcuts. A list of some of these abbreviations is presented in Table 4.3. U nfortunately, medication errors can result from the
misuse, misinterpretation, and illegible writing of abbreviations and through the use of
ad hoc, or made-up, abbreviations. T he use of a controlled vocabulary, a reduction in the
use of abbreviations, care in the writing of decimal points, and the proper use of leading
and terminal zeros have been urged to help reduce medication errors.8–10
Among the specific recommendations to help reduce medication errors arising from poorly
written, illegible, or misinterpreted prescriptions and medication orders are the following8–10:
•  A whole number should be shown without a decimal point and without a terminal zero (e.g.,
express 4 milligrams as 4 mg and not as 4.0 mg).
•  A quantity smaller than one should be shown with a zero preceding the decimal point (e.g.,
express two tenths of a milligram as 0.2 mg and not as .2 mg).
•  Leave a space between a number and the unit (e.g., 10 mg and not 10mg).
•  Use whole numbers when possible and not equivalent decimal fractions (e.g., use 100 mg and
not 0.1 g).
•  Use the full names of drugs and not abbreviations (e.g., use phenobarbital and not PB).
•  Use USP designations for units of measure (e.g., for grams, use g and not Gm or gms; for
milligrams, use mg and not mgs or mgm).
•  Spell out “units” (e.g., use 100 units and not 100 u or 100 U since an illegible U may be
misread as a zero, resulting in a 10-fold error, i.e., 1000). The abbreviation I.U., which
stands for “International Units,” should also be spelled out so it is not interpreted as I.V.,
meaning “intravenous.”
•  Certain abbreviations that could be mistaken for other abbreviations should be written out
(e.g., write “right eye” or “left eye” rather than use o.d. or o.l., and spell out “right ear” and
“left ear” rather than use a.d. or a.l.).
•  Spell out “every day,” rather than use q.d.; “every other day,” rather than q.o.d; “four times a
day,” rather than q.i.d; and “three times a week,” rather than t.i.w. to avoid misinterpretation.
•  Avoid using d for “day” or “dose” because of the profound difference between terms, as in
mg/kg/day versus mg/kg/dose.
•  Integrate capital or “tall man” letters to distinguish between “look-alike” drug names, such as
AggraSTAT and AggreNOX, hydrOXYZINE and hydrALAZINE, and DIGoxin and DESoxyn.
•  Amplify the prescriber’s directions on the prescription label when needed for clarity (e.g., use
“Swallow one (1) capsule with water in the morning” rather than “one cap in a.m.”).
64 Pharma euti al c al ulations
T e 4.3 •  SEl Ec TEd a b b REvIaTIOn S, a c ROn yMS, a n d SyMb Ol S USEd In
PRESc RIPTIOn S a n d MEd Ic aTIOn ORd ERSa–c
a re i tio

(l ti Origi d)	Me i g
Prescription-Filling Directions
aa. (ana) ad (ad) disp. (dispensatur) div. (dividatur) d.t.d. (dentur tales doses) ft (fiat) M. (mice) No. (numero) non rep. or NR (non repatatur)	of each up to; to make dispense divide give of such doses
make mix number do not repeat

q.s. (quantum
sufficit)
a sufficient quantity

q.s. ad (quantum sufficiat ad) Sig. (Signa)	a sufficient quantity to make
write (directions on label)
Quantities and Measurement
BSA cm3 f or fl (fluidus) flʒ or fʒe fl ss or f sse g gal gtt (gutta) I.U. or IUb lb (libra) kg L m2 or M2 mcg mEq mg mg/kg	body surface area cubic centimeter or milliliter (mL) fluid fluid dram half-fluid ounce gram gallon drop international unit(s) pound kilogram liter square meter microgram milliequivalent milligram milligrams (of drug) per kilogram (of body weight) milligrams (of drug) per square meter (of body surface area) thousandth of an international unit million international units milliliter milliliters (of drug adminis tered) per hour (as through intravenous administration) milliosmoles ounce pint quart one-half
mg/m2
mIU or milli-IU
MIUb mL mL/h
mOsm or mOsmol oz. pt. qt. ss or ss (semissem) tbsp. tsp.
tablespoonful teaspoonful

a re i tio

(l ti Origi d)	Me i g
Signa/Patient Instructions
a.c. (ante cibos) ad lib. (ad libitum) admin am (ante meridiem) aq. (aqua) ATC b.i.d. (bis in die) c or c (cum) d (die) dil. (dilutus) et h. or hr. (hora) h.s. (hora somni) i.c. (inter cibos) min. (minutum) m&n N&V noct. (nocte) NPO (non per os) p.c. (post cibos) pm (post meridiem) p.o. (per os) p.r.n. (pro re nata) q (quaque) qAM q4h, q8h, etc. q.i.d. (quarter in die) rep. (repetatur) s (sine) s.i.d. (semel in die) s.o.s. (si opus sit) stat. (stamin) t.i.d. (ter in die) ut dict. (ut dictum) wk. Medications	before meals at pleasure, freely administer morning
water around the clock twice a day with day dilute and hour at bedtime between meals minute morning and night nausea and vomiting night nothing by mouth after meals afternoon; evening
by mouth (orally) as needed every every morning every (number) hours four times a day
repeat without once a day if there is need; as needed immediately three times a day as directed week
APAP ASA AZT EES HC HCTZ MTX NSAID	acetaminophen aspirin zidovudine erythromycin ethylsuccinate hydrocortisone hydrochlorothiazide methotrexate nonsteroidal anti-inflammatory drug nitroglycerin
NTG
Clinical
Afib ADR	atrial fibrillation adverse drug reaction

4 • interpretat on of Prescr pt ons and Med cat on Orders 65
aThe abbreviations set in boldface type are considered most likely to appear on prescriptions. It is suggested that these be
learned first.
bIn practice, periods and/or capital letters may or may not be used with the abbreviations. Some abbreviations, acronyms, and
symbols have medication error risks associated with their use. Therefore, the Institute for Safe Medication Practices (ISMP)
and the Joint Commission on Accreditation of Healthcare Organizations (JCAHO) have issued a list of items prohibited
from use and others considered for prohibition (see text).8 These designated items are not included in Table 4.3, with the
exception of hs, I.U., MIU, subQ, AZT, and HCTZ, which are included for instructional purpose due to their remaining use in
practice.
cA database of acronyms and abbreviations related to Food and Drug Administration (FDA) may be found at http://www.fda.gov/
AboutFDA/FDAAcronymsAbbreviations/ucm070296.htm.
dMuldoon HC. Pharmaceutical Latin. 4th Ed. New York: John Wiley & Sons, 1952.
eA fluid dram (flʒ) is 1/8th of a fluid ounce (29.57 mL) or ≈ 3.69 mL; however, when the dram symbol is written in the signa portion of a prescription, the prescriber may intend the interpretation to be “teaspoonful.” Similarly, when a half-ounce symbol
(f ss) is indicated in the signa, a “tablespoon” or 15 mL may be intended.
a re i tio

(l ti Origi d) BM BP BS CAD CHD CHF COPD	Me i g bowel movement blood pressure blood sugar coronary artery disease coronary heart disease congestive heart failure chronic obstructive pulmonary disease gastrointestinal reflux disease chronic renal failure cardiovascular ears, nose, and throat gastrointestinal glomerular filtration rate genitourinary headache heart rate high blood pressure hormone replacement therapy hypertension intraocular pressure myocardial ischemia/infarction osteoarthritis patient quality of life rheumatoid arthritis shortness of breath total parenteral nutrition urine analysis upper respiratory infection urinary tract infection
GERD CRF CV ENT GI GFR GU HA HBP HR HRT HT or HTN IOP MI OA Pt QL RA SOB TPN UA URI UTI Dosage Forms/Vehicles amp. cap. D5LR
ampul capsule dextrose 5% in lactated Ringer’s dextrose 5% in normal saline (0.9% sodium chloride) dextrose 5% in water dextrose 10% in water
D5NS
D5W D10W

a re i tio

(l ti Origi d) elix. inj. NS ½NS oint or ungt. (unguentum) pulv. (pulvis) RL, R/L or LR	Me i g elixir injection normal saline half-strength normal saline ointment
powder Ringer’s lactate or lactated Ringer’s solution suppository
sol. (solutio) supp. (suppositorium) susp. syr. (syrupus) tab. (tabletta)
suspension syrup tablet
Routes/Location of Administration
a.d. (auris dextro) a.s. (auris sinistro) a.u. (auris utro) CIVI	right ear left ear each ear (both) continuous (24 hours) intrave nous infusion intradermal injection intramuscular intrathecal intravenous intravenous bolus intravenous infusion intravenous push intravenous piggyback nasogastric tube right eye left eye each eye (both) by mouth rectal or rectum sublingual subcutaneously topically vaginally
ID inj IM IT IV IVB IV drip IVP IVPB NGT o.d. (oculo dextro) o.s. (oculo sinistro) o.u. (oculo utro) p.o. or PO (per os) rect. (or pro recto) SL SubQ or SC Top. V or PV (pro vagina)

T e 4.3 •  SEl Ec TEd a b b REvIaTIOn S, a c ROn yMS, a n d SyMb Ol S USEd In
PRESc RIPTIOn S a n d MEd Ic aTIOn ORd ERSa–c (Continued )
66 Pharma eu i al c al ula ion
T he Institute for Safe Medication Practices (ISMP) regularly publishes a list of
abbreviations, symbols, and dose designations that it recommends for consideration for
discontinuance of use.9
T he portions of the prescription presenting directions to the pharmacist (the
Subscription) and the directions to the patient (the Signa) commonly contain abbreviated forms of English or Latin terms as well as Arabic and Roman numerals. T he correct
interpretation of these abbreviations and prescription notations plays an important part in
pharmaceutical calculations and thus in the accurate filling and dispensing of medication.
Although described fully in Chapter 7, it should be noted here that when
appearing in the Signa, the symbol ʒi, 5 mL, and the abbreviation tsp. are each taken
to mean “one teaspoonful,” and the symbol ss, 15 mL, and the abbreviation tbsp. are
each taken to mean “one tablespoonful.”
c a SE In POIn T 4.1 A pharma i re eived he following pre rip ion, whi h
require he orre in erpre a ion of abbrevia ion prior o engaging in al ula ion ,
ompounding, labeling, and di pen ing.
Li inopril
Hydro hloro hiazide aa. 10 mg
c al ium pho pha e 40 mg
La o e q. . ad 300 mg
M.f . ap. i D.t .D. # 30
s ig: ap. i AM a. .
(a) How many milligram ea h of li inopril and hydro hloro hiazide are required o fill
he pre rip ion?
(b) Wha i he weigh of la o e required?
( ) t ran la e he label dire ion o he pa ien .
Examples of prescription directions to the pharmacist:
(a) M. ft. ung.
Mix and make an ointment.
(b) Ft. sup. no xii
Make 12 suppositories.
(c) M. ft. cap. d.t.d. no. xxiv
Mix and make capsules. Give 24 such doses.
Examples of prescription directions to the patient:
(a) Caps. i. q.i.d. p.c. et h.s.
Take one (1) capsule four (4) times a day after each meal and at bedtime.
(b) gtt. ii rt. eye every a.m.
Instill two (2) drops in the right eye every morning.
(c) tab. ii stat tab. 1 q. 6 h. × 7 d.
Take two (2) tablets immediately, then take one (1) tablet every 6 hours for 7 days.
AUT H ORS’ N OT E: some abbreviations used in this chapter
may appear only infrequently in practice and are included here
for instructional purposes.
4 • interpretat on of Prescr pt ons and Med cat on Orders 67
Medication Scheduling, Medication Adherence, and Medication
Disposal
Medication scheduling may be de ned as the requency (i.e., times per day) and duration (i.e.,
length o treatment) o a drug’s prescribed or recommended use. Some medications, because
o their physical, chemical, or biological characteristics or their dosage ormulations, may be
taken just once daily or optimum bene t, whereas other drug products must be taken two,
three, our, or more times daily or the desired e ect. Frequency o medication scheduling is
also inf uenced by the patient’s physical condition and the nature and severity o the illness or
condition being treated. Some conditions, such as indigestion, may require a single dose o
medication or correction. Other conditions, such as a systemic in ection, may require multiple daily, around-the-clock dosing or 10 days or more. Long-term maintenance therapy or
conditions such as diabetes and high blood pressure may require daily dosing or li e.
For optimum bene it o the medications prescribed, it is incumbent on the patient to
adhere to the prescribed dosage regimen.
Medication adherence ( ormerly re erred to as compliance) indicates a patient’s ollowing o the instructions or taking the medication prescribed, including the correct dose,
dosing requency, and duration o treatment. Medication nonadherence is a patient’s ailure
to adhere or comply with the instructions.
Patient nonadherence may result rom a number o actors, including unclear or misunderstood directions, undesired side e ects o the drug that discourage use, lack o patient con idence in the drug and/or prescriber, discontinued use because the patient eels better or worse,
economic reasons based on the cost o the medication, absence o patient counseling and understanding o the need or and means o compliance, con usion over taking multiple medications,
and other actors. Frequently, patients orget whether they have taken their medications. Special
compliance aids are available to assist patients in their proper scheduling o medications. T hese
devices include medication calendars, reminder charts, special containers, and smartphone apps.
Patient nonadherence is not entirely the problem o ambulatory or noninstitutionalized patients. Patients in hospitals, nursing homes, and other inpatient settings are generally more compliant because o the e orts o health care personnel who are assigned the
responsibility o issuing and administering medication on a prescribed schedule. Even in
these settings, however, a scheduled dose o medication may be omitted or administered
incorrectly or in an untimely ashion because o human error or oversight.
T he consequences o patient nonadherence may include worsening o the condition, the requirement o additional and perhaps more expensive and extensive treatment
methods or surgical procedures, otherwise unnecessary hospitalization, and increased total
health care cost. Students interested in additional in ormation on medication adherence are
re erred to other sources o in ormation.11–13
Medication nonadherence has been measured in a number o ways, including by biological
sample (i.e., determining medication blood levels), patient surveys, monitoring the on-time re illing o prescriptions, examining prescription drug claim (insurance) data, and by other means.
Consider the ollowing illustrations.
(1)
If the prescription was filled initially on April 15, on about what date should the patient return
to have the prescription refilled?
Answer: 90 tablets, taken 1 per day, should last 90 days, or approximately 3 months,
and the patient should return to the pharmacy on or shortly be ore July 15 o the same year.
H ydrochlorothiazide 50 mg
Tablets N o. XC
Sig. i q AM or H BP
68 Pharma u al c al ula on
(2)
How many milliliters o medicine should be dispensed?
Answer: 5 mL times 4 (doses per day) equals 20 mL times 10 (days) equals 200 mL.
A pharmacist may calculate a patient’s percent compliance rate as follows:
% Compliance rate N mber of days supply of medication
N umber of days
=
u
ssince last Rx refill
× 100
(3) W hat is the percent compliance rate i a patient received a 30-day supply o medicine and
returned in 45 days or a ref ll?
% . Compliance rate days
days
= × =
30
45
100 6 % 6 6
In determining the patient’s actual (rather than apparent) compliance rate, it is important to determine if the patient had available and used extra days’ dosage from some previous filling of the prescription.
Medication disposal is an important consideration for safety and environmental concerns. Medications that are no longer used or out of date may be disposed of by the following
methods: (a) “take back” programs for disposal by pharmacies; (b) mixing medications with
kitty litter, coffee grounds, or other such materials and disposing along with household trash;
and (c) flushing medications down the drain for specific drugs as approved by the FDA.14

c a SE In POIn T 4.2 A 72-y ar-old mal who	d a	adm . t	d o h	m r	r
g n y room w h hor n	of r a h and g n ral w akn	al an m a,
hypo n on, a r al f r lla on, and oronary ar ry lo kag . Dur ng 2 w k of ho –
p al za on, h pa n r	n ra nou nfu on , oral m d a on , and lood
ran fu on ; four ard o a ular	n ar n r d; and h pa n	d harg d
w h h follow ng pr c lop dogr l	r p on :
ulfa (PLAviX) a l	, 75 mg, 1 a q.d.
P ogl azon hydro hlor d (Ac t Os ) a l	, 15 mg, 1 a q.d.
Pan oprazol	od um (PROt ONiX) a l	, 40 mg, 1 a	. .d.
s m a a n (ZOc OR) a l	40 mg, 1 a q.d. h. .
HUMULiN 70/30, nj c ar d lol (c ORe G) a l	35 un	q.d. am and 45 un	q.d. pm
, 3.125 mg 1 a	. .d. × 2 wk; h n 6.25 mg
1 a	. .d.
Am odaron hydro hlor d (c ORDARONe ) a l	, 200 mg, 2 a
. .d. × 7 d; h n 1 a	. .d. × 7 d; h n 1 a q.d.
Dulox n hydro hlor d (c YMb ALt A) ap ul , 30 mg, 1 ap q.d. × 7 d;
h n 1 ap . .d.
(a) How many o al a l	and ap ul would h pa n n ally	ak ng da ly?
( ) if HUMULiN on a n 100 un	p r m ll l r, how many m ll l r would
adm n	r d a h morn ng and a h	n ng?
( ) How many c ORDARONe a l	would on	u a 30-day upply?
(d) if 60 c YMb ALt A ap ul w r n ally d p n d and h pa n r qu	d a
r f ll af r 17 day ,	medication nonadherence and hu h pa n ’ w ll-	ng
a r a ona l	on rn? s how al ula on .

Penicillin V Potassium Oral Solution 125 mg/5 mL
Disp. mL
Sig. 5 mL q 6 h AT C × 10 d
4 • interpretat on of Prescr pt ons and Med cat on Orders 69
PRa c TIc E PROb l EMS
Authors’ Note: some abbreviations used in these practice problems may appear only infrequently in practice and are included here for instructional purposes.
1. Interpret each of the following Subscriptions (directions to the pharmacist) taken
from prescriptions:
(a) Disp. supp. rect. no. xii
(b) M. ft. iso. sol. Disp. 120 mL
(c) M. et div. in pulv. no. xl
(d) DT D vi. N on rep.
(e) M. et ft. ung. Disp. 10 g
(f) M. et ft. caps. DT D xlviii
(g) M. et ft. susp. 1 g/tbsp. Disp. 60 mL
(h) Ft. cap. #1. DT D no.xxxvi N .R.
(i) M. et ft. pulv. DT D #C
(j) M. et ft. I.V. inj.
(k) Label: hydrocortisone, 20 mg tabs
2. Interpret each of the following Signas (directions to the patient) taken from
prescriptions:
(a) Gtt. ii each eye q. 4 h. p.r.n. pain.
(b) T bsp. i in ⅓ gl. aq. q. 6 h
(c) Appl. am & pm for pain prn.
(d) Gtt. iv right ear m. & n.
(e) Tsp. i ex aq. q. 4 or 5 h. p.r.n. pain
(f) Appl. ung. left eye ad lib.
(g) Caps i c aq. h.s. N .R.
(h) Gtt. v each ear 3 × d. s.o.s.
(i) Tab. i sublingually, rep. p.r.n.
(j) Instill gtt. ii each eye of neonate
(k) Dil. c = vol. aq. and use as gargle q. 5 h
(l) Cap. ii 1 h. prior to departure, then cap. i after 12 h
(m) Tab i p.r.n. SOB
(n) Tab i qAM H BP
(o) Tab ii q 6 h AT C UT I
(p) 3ii 4 × d p.c. & h.s.
(q) ss a.c. t.i.d.
(r) Add crushed tablet to pet’s food s.i.d.
3. Interpret each of the following taken from medication orders:
(a) AMBIEN 10 mg p.o. qhs × 5 d
(b) 1000 mL D5W q. 8 h. IV c 20 mEq KC1 to every third bottle
(c) Admin. prochlorperazine 10 mg IM q. 3 h. prn N&V
(d) Minocycline H Cl susp. 1 tsp p.o. q.i.d. DC after 5 d
(e) Propranolol H Cl 10 mg p.o. t.i.d. a.c. & h.s.
(f) N PH U-100 insulin 40 units subc every day am
(g) Cefamandole nafate 250 mg IM q12h
(h) Potassium chloride 15 mEq p.o. b.i.d. p.c.
(i) Vincristine sulfate 1 mg/m2 pt. BSA
(j) Flurazepam 30 mg at H S prn sleep
(k) D5W + 20 mEq KCl/L at 84 mL/h
(l) 2.5 g/kg/day amino acids T PN
(m) Epoetin alfa (PROCRIT ) stat. 150 units/kg subQ . 3 × wk. × 3–4 wks
70 Pharma euti al c al ulations
(n) MT X 2.5 mg tab t.i.d. 1 ×/wk
(o) H CT Z tabs 12.5 mg q.d. am
4. (a) I a 10-mL vial o insulin contains 100 units o insulin per milliliter, and a patient
is to administer 20 units daily, how many days will the product last the patient?
(b) I the patient returned to the pharmacy in exactly 7 weeks or another vial o
insulin, was the patient compliant as indicated by the percent compliance rate?
5. A prescription is to be taken as ollows: 1 tablet q.i.d. the irst day; 1 tablet t.i.d.
the second day; 1 tablet b.i.d. × 5 d; and 1 tablet q.d. therea ter. H ow many tablets
should be dispensed to equal a 30-day supply?
6. In preparing the prescription in Figure 4.3, the pharmacist calculated and labeled
the dose as “1 teaspoon ul every 12 hours.” Is this correct or in error?
7. Re er to Figure 4.1 and identi y any errors or omissions in the ollowing prescription label:
Patient: Mary Smith Dr. JM Brown
Date: Jan 9, 20yy
Take 1 capsule every day in the morning
Ref lls: 5
8. Re er to Figure 4.4A and identi y any errors or omissions in the ollowing prescription label:

Patient: Brad Smith Date: Jan 9, 20yy

Dr. JM Brown

Take two (2) teaspoon uls every twelve (12) hours until all o
the medicine is gone
Amoxicillin 250 mL/5 mL
Ref lls: 0
9. Re er to Figure 4.5 and identi y any errors or omissions in the ollowing prescription label:

Patient: Brad Smith Date: Jan 9, 20yy

Dr. JM Brown

N asal spray or chemotherapy-induced emesis. Use as directed.
Discard a ter 60 days.
Metoclopramide H Cl
10 g/100 mL N asal Spray
Ref lls: 0
10. Re er to Figure 4.2 and identi y any errors or omissions in a transcribed order or
the irst three drugs in the medication order:
(a) Propranolol, 40 mg orally every day
(b) Flutamide, 20 mg orally every morning
(c) Flurazepam, 30 mg at bedtime as needed or sleep
11. Re er to Figure 4.6 and identi y any errors in the ollowing prescription label:

Patient: Mary Jones Date: Oct 20, 20yy

Dr. JM Brown

Swallow one (1) capsule at bedtime.
Gabapentin 100 mg
10 g/100 mL N asal Spray
Rx: 9876543 Ref lls: 6
4 • interpretat on of Prescr pt ons and Med cat on Orders 71
c a l c q UIz
4.A. Interpret the underlined portions taken directly from current product references15:
(a) Dose of ritonavir when coadministered with fluconazole: 200 mg q6h × 4d
(b) Dose of epoetin alpha: 150 units/kg SC TIW
(c) Dose of acetylcysteine: for patients >20 to <40 kg, 150 mg/kg
(d) Pediatric dose of cefuroxime axetil: 30 mg/kg/day, divided dose (b.i.d.)
(e) Dose of ciprofloxacin hydrochloride: 750 mg tablet q12h or 400 mg IV q8h
(f) Dose of interferon alpha-2b: 30 MIU/m2 TIW
(g) Infusion rate, rocuronium bromide: 4 mg/kg/min
(h) Dose of enoxaparin sodium injection: 1.5 mg/kg q.d. SC
(i) Dose of voriconazole: 200 mg po q12h × 8 d
(j) Dose of certolizumab pegol: 200 mg + MTX q2 wk
4.B. The following are hospital medication orders and, in parenthesis, the product available in the pharmacy:
(a) Furosemide 40 mg IV qd (10 mg/mL in 2-mL syringes)
(b) Erythromycin 750 mg IV q6h (500 mg/vial)
(c) Acyclovir 350 mg IV q8h (500 mg/vial)
(d) MEGACE 40 mg PO tid (40 mg/mL oral suspension)
(e) FORTAZ 2 g IV q8h (500 mg/vial)
For each, indicate the quantity to be provided daily by the pharmacy.
12. In a clinical study of drug–drug interactions, the following drugs were
coadministered:
Ritonavir: 600 mg b.i.d. p.o. × 7 d
T heophylline: 3 mg/kg q8h × 7 d
Translate the directions
13. Translate “10 mIU/mL.”
14. T he package insert for interferon alpha-2b states the dose based on body surface
area (BSA) for the treatment of hepatitis B as 3 MIU/m2 TIW for the first week of
therapy followed by dose escalation to 6 MIU/m2 TIW (maximum of 10 MIU/m2 TIW )
administered subcutaneously for a total duration of 16 to 24 weeks. Translate the portion which states “6 MIU/m2 TIW .”
15. Translate “simvastatin 20 mg q.p.m.”
16. Interpret the following from the literature: “lopinavir/ritonavir 400 mg/100 mg
b.i.d + efavirenz 600 mg q.d.”
17. Using the information in Figure 4.5, calculate (a) the number of milligrams of
metoclopramide H Cl in each milliliter of the prescription and (b) the number
of milliliters of nasal spray that would provide a patient with an 80-mg dose of
metoclopramide H Cl.
18. If, in the above problem, each nasal spray actuation delivered 0.4 mL, how many
full days would the prescription last if the patient administered the stated dose
three times daily?
72 Pharma euti al c al ulations
a n SWERS TO “c a SE In POIn T” a n d PRa c TIc E PROb l EMS
Case in Point 4.1
(a) Since aa. means “of each,” 10 mg lisinopril and 10 mg hydrochlorothiazide are
needed for each capsule. And since D.T.D. means “give of such doses,” 30 capsules are to be prepared. T hus,
10 mg lisinopril × 30 (capsules) = 300 mg lisinopril and
10 mg hydrochlorothiazide × 30 (capsules) = 300 mg hydrochlorothiazide are
needed to fill the prescription.
(b) Since q.s. ad means “a sufficient quantity to make,” the total in each capsule is
300 mg. T he amount of lactose per capsule would equal 300 mg less the quantity
of the other ingredients (10 mg + 10 mg + 40 mg), or 240 mg. T hus,
240 mg lactose/capsule × 30 (capsules) = 7200 mg = 7.2 g lactose.
(c) Take one (1) capsule in the morning before breakfast.
Case in Point 4.2
(a) 12 total tablets and capsules.

(b) ? mL =	units	×
. = 0 35 mL in the AM
? mL =
mL	35
mL	U 45 nnits	×

units
AM
units
1
100
1
100
PM
= 0 45 mL in the PM .
(c) First 7 days: 2 tablets × 2 (twice daily) × 7 days = 28 tablets
N ext 7 days: 1 tablet × 2 (twice daily) × 7 days = 14 tablets
N ext 16 days: 1 tablet (daily) = 16 tablets
28 + 14 + 16 = 58 tablets.
(d) 1 capsule daily × 7 days = 7 capsules
1 capsule × 2 (twice daily) × (next) 10 days = 20 capsules
7 + 20 = 27 capsules taken with 33 capsules remaining.
T hus, nonadherence would be a concern.
Practice Problems
1. (a) Dispense 12 rectal suppositories.
(b) Mix and make an isotonic solution. Dispense 120 mL.
(c) Mix and divide into 40 powders.
(d) Dispense six such doses. Do not
repeat.
(e) Mix and make ointment. Dispense
10 g.
(f) Mix and make capsules. Dispense
48 such doses.
(g) Mix and make a suspension
containing 1 g per tablespoon.
Dispense 60 mL.
(h) Make one capsule. Dispense 36
such doses. Do not repeat.
(i) Mix and make powder. Divide
into 100 such doses.
(j) Mix and make an intravenous
injection.
(k) Label: hydrocortisone, 20 mg
tabs.
2. (a) Instill 2 drops in each eye every
four (4) hours as needed for pain.
(b) Take 1 tablespoonful in one-third
glass of water every 6 hours.
4 • interpretat on of Prescr pt ons and Med cat on Orders 73
(c) Apply morning and night as
needed for pain.
(d) Instill 4 drops into the right ear
morning and night.
(e) Take 1 teaspoonful in water every
4 or 5 hours as needed for pain.
(f) Apply ointment to the left eye as
needed.
(g) Take 1 capsule with water at bedtime. Do not repeat.
(h) Instill 5 drops into each ear three
times a day as needed.
(i) Place 1 tablet under the tongue,
repeat if needed.
(j) Instill 2 drops into each eye of
the newborn.
(k) Dilute with an equal volume of
water and use as gargle every
5 hours.
(l) Take 2 capsules 1 hour prior to
departure, then 1 capsule after
12 hours.
(m) Take 1 tablet as needed for shortness of breath.
(n) Take 1 tablet every morning for
high blood pressure.
(o) Take 2 tablets every 6 hours
around the clock for urinary tract
infection.
(p) Take 2 teaspoonfuls four times a
day after meals and at bedtime.
(q) Take 1 tablespoonful before
meals three times a day.
(r) Add crushed tablet to pet’s food
once a day.
3. (a) AMBIEN 10 mg by mouth at
every bedtime for 5 days
(b) 1000 mL of 5% dextrose in water
every 8 hours intravenously with
20 milliequivalents of potassium
chloride added to every third
bottle
(c) Administer 10 mg of prochlorperazine intramuscularly every
3 hours, if there is need, for nausea and vomiting.
(d) One teaspoonful of minocycline hydrochloride suspension by mouth four times a day.
Discontinue after 5 days.
(e) 10 mg of propranolol hydrochloride by mouth three times a
day before meals and at bedtime
(f) 40 units of N PH 100-unit
insulin subcutaneously every
day in the morning
(g) 250 mg of cefamandole nafate
intramuscularly every 12 hours
(h) 15 milliequivalents of potassium chloride by mouth twice
a day after meals
(i) 1 mg of vincristine sulfate per
square meter of patient’s body
surface area
(j) Administer 30 mg of flurazepam at bedtime as needed
for sleep.
(k) Administer 20 milliequivalents of potassium chloride
per liter in D5W (5% dextrose in water) at the rate of
84 milliliters per hour.
(l) Administer 2.5 grams per
kilogram of body weight per
day of amino acids in total
parenteral nutrition.
(m) Start epoetin alfa (PROCRIT )
immediately at 150 units per
kilogram of body weight subcutaneously and then three
times a week for 3 to 4 weeks.
(n) Methotrexate tablets, 2.5 mg
each, to be taken three times a
day 1 day a week
(o) H ydrochlorothiazide tablets,
12.5 mg, to be taken once
each day in the morning
4. (a) 50 days
(b) yes
5. (a) 40 tablets.
6. (a) correct.
7. calls for tablets but label indicates capsules.
Sig: “in the morning” has been
added, which may be correct
if that is the prescriber’s usual
directive.
Refill “5” times is incorrect; the
original filling of a prescription
does not count as a refill.
74 Pharma euti al c al ulations
calls for drug name/strength on
label; an omission.
It should be noted that after filling
the prescription, the pharmacist
would have added a prescription
number, which would also appear
on the label.
8. T he words “all of the medicine”
have been added and the numbers
enhanced; this clarifies the directions and thus is positive. 250 mL
should be 250 mg.
T he prescription number should
appear on the label.
9. Patient’s name is incorrect. T he
active drug name only on the label
is proper for a compounded prescription. T he other ingredients
are “pharmaceutic.”
It should be noted that after filling
the prescription, the pharmacist
would have added a prescription
number, which would also appear
on the label.
10. (1) “Q ID” means four times a day
(2) Drug name is incorrect.
(3) Correct
11. Correct label.
12. Ritonavir: 600 mg twice a day
orally for 7 days.
T heophylline: 3 mg per kilogram
of body weight every 8 hours for
7 days.
13. 10 milli-international units per
milliliter.
14. 6 million international units per
square meter of body surface area
three times a week.
15. (Take) 20 mg of simvastatin every
evening.
16. (T he drug combination of) lopinavir, 400 mg, and ritonavir, 100 mg,
taken twice a day, plus efavirenz,
600 mg, taken once every day.
17. (a) 100 mg metoclopramide
H Cl/mL
(b) 0.8 mL nasal spray
18. 41 days
AUTHORS’ EXTRA POINT A
d RUG n a MES
As stated in this chapter, drug substances may be prescribed by their nonproprietary (generic) name or by
their brand (trademark) name. The designation of nonproprietary names is based on nomenclature reflecting
a drug’s chemical structure and/or pharmacologic activity. In the United States, each nonproprietary name
is assigned by the United States Adopted Names (USAN) Council, which is cosponsored by the American
Medical Association, the United States Pharmacopeial Convention, and the American Pharmacists Association.
To harmonize the program, the USAN Council works in conjunction with the federal Food and Drug
Administration (FDA) as well as the World Health Organization (WHO) and the International Nonproprietary
Name (INN) Expert Committee. Together with the British Approved Names (BANs) and the Japanese
Approved Names (JANs), the USP Dictionary of USAN and International Drug Names database contains
more than 8,400 nonproprietary drug name entries.a
Many of the same drug substances are approved for marketing and available internationally. In the
United States, this approval is within the authority of the federal Food and Drug Administration.b There are
many multinational pharmaceutical companies who engage in the worldwide development and marketing of
pharmaceutical products. The brand names assigned to the same nonproprietary-named drug often differ
country to country. The referenced International Drug Name Database contains more than 40,000 medication names from 185 countries and is presented in multiple languages.c
The nonproprietary names used in the calculation problems in this text are universal; however, the
brand names by their very nature are not.
ahttp://library.dialog.com/bluesheets/html/bl0464.html
bRegulatory approval is within the purview of each country. In Canada, regulatory authority resides with Health Canada’s
Therapeutic Products Directorate (TPD). Within the European Union (EU), the 28 member countries depend collectively upon
the European Medicines Evaluation Agency (EMEA) for drug approvals and regulation. A list of drug regulatory agencies worldwide may be found at http://www.regulatoryone.com/p/websites-of-regulatory-agencies.html
chttp://www.drugs.com/international/
4 • interpretat on of Prescr pt ons and Med cat on Orders 75
AUTHORS’ EXTRA POINT B
El Ec TROn Ic PRESc RIPTIOn S a
The overall integrated system of electronic health information includes electronic health records (EHRs),
computerized physician order entry (CPOE), and electronic prescriptions (e-prescriptions). The system
allows health care providers to electronically insert and access patients’ vital medical information.
In the processing of electronic prescriptions, a complex network of pharmacies, payers, pharmacy benefit
managers (PBMs), physicians, hospitals, health information exchanges (HIEs), and electronic health record
systems (EHRs) must be connected in real time to assure patient eligibility, formulary data, and clinical requirements. As is shown in Figures 4.10 and 4.11, this information connectivity is facilitated by health information
networks (Surescripts in the example), which notify providers of authorization status and requirements.
Pharmacy
Benefit Manager
(PBM)
Pharmacy
Superscripts
eRx – How it Works
Eligibility,
Formulary,
Medication History
Eligibility,
Formulary,
Medication
History/Fill Status
Patient Inquiry
Information
Prescription Data
Maintains an index of
enrolled pharmacies
and routes
prescriptions to the
desired location
Maintains a master
patient index and
routes inquires to
matched PBMs
Prescription Fill
Status
Patient
Demographics/
Prescription
athenaClinicals
FIGURE 4.10 •  Information connectivity in the processing and authorization of an e-prescription. (Image provided through the courtesy of athenahealth, Inc. [Images © athenahealth, Inc., used with permission.] Additional
information from http://surescripts.com/.)
FIGURE 4.11 •  An example of an e-prescription being ordered during a patient’s visit with medical reference
information embedded (Epocrates) to provide real-time decision clinical support. (Image provided through the
courtesy of athenahealth, Inc. [Images © athenahealth, Inc., used with permission.] Additional information from
http://surescripts.com/.)
76 Pharma euti al c al ulations
References
1. Drug Q uality and Security Act. Available at: https://www.govtrack.us/congress/bills/113/hr3204/text. Accessed
April 27, 2014.
2. Draft Guidance. Pharmacy Compounding of H uman Drug Products Under Section 503A of the Federal Food,
Drug, and Cosmetic Act. U.S. Department of H ealth and H uman Services, Food and Drug Administration,
Center for Drug Evaluation and Research, 2013.
3. N CPDP Electronic Prescribing Standards. National Council for Prescription Programs. Available at: http://www.
ncpdp.org/N CPDP/media/pdf/N CPDP-eprescribing-101-201308.pdf. Accessed May 1, 2014.
4. Kilbridge P. E-Prescribing. California H ealthCare Foundation; 2001. Available at: http://www.chcf.org/~/
media/MEDIA%20LIBRARY%20Files/PDF/E/PDF%20EPrescribing.pdf. Accessed May 1, 2014.
5. American College of Physicians. Clinician’s Guide to E-Prescribing. Available at: http://www.acponline.org/
running_practice/technology/eprescribing/clinicians_guide_eprescribing.pdf. Accessed May 1, 2014.
6. H ospital-Forms.com. Engineered Data, llc. Available at: http://www.hospital-forms.com. Accessed October 17,
2015.
7. Burnside N L, Bardo JA, Bretz CJ, et al. Effects of including medication indications on prescription labels.
Journal of the American Pharmacists Association 2007;47:756–758.
8. Institute for Safe Medication Practices. Available at: http://www.ismp.org/tools/errorprone abbreviations.pdf.
Accessed May 1, 2014.
9. Davis N M. A controlled vocabulary for reducing medication errors. Hospital Pharmacy 2000;35:227–228.
10. T he Official “Do N ot Use” List of Abbreviations. The Joint Commission. Available at: http://www.jointcommission.org/assets/1/18/Do_N ot_Use_List.pdf. Accessed May 1, 2014.
11. Improving Medication Adherence in Older Adults. Adult Medication. T he American Society on Aging and T he
American Society of Consultant Pharmacists Foundation; 2006. Available at: http://learning.rxassist.org/sites/
default/files/Adult_Meducation%20All.pdf. Accessed May 1, 2014.
12. Center for H ealth Transformation. 21st Century Intelligent Pharmacy Project. 2101. T he Importance of
Medication Adherence. Available at: http://www.mirixa.com/uploads/pdfs/2010_-_CH T MedAdhrW p.pdf.
Accessed May 1, 2014.
13. World H ealth Organization (W H O ). Adherence to Long-Term T herapies: Evidence for Action, 2013.
Available at: http://www.who.int/chp/knowledge/publications/adherence_report/en/. Accessed May 1, 2014.
14. D isposal of U nused Medicines: W hat You Should Know. U .S. Food and D rug Administration.
Available at: http:/ / www.fda.gov/ D rugs/ ResourcesForYou/ C onsumers/ BuyingU singMedicineSafely/
EnsuringSafeUseofMedicine/SafeDisposalofMedicines/ucm186187.htm. Accessed October 17, 2015.
15. Physicians’ Desk Reference. Montvale, N J: PDR N etwork; 2011:65.
77
Density
Density (d) is mass per unit volume o a substance. It is usually expressed as grams per cubic
centimeter (g/cc). Because the gram is def ned as the mass o 1 cc o water at 4°C, the density
o water is 1 g/cc. For our purposes, because the United States Pharmacopeia1 states that 1 mL
may be used as the equivalent o 1 cc, the density o water may be expressed as 1 g/mL.
Density may be calculated by dividing mass by volume, that is:

Density	Mass
Volume

=
T hus, i 10 mL o sul uric acid weighs 18 g, its density is:
Density
(m )
= =
18
10
( )
g . /
L
1 8 g mL
Specific Gravity
Specif c gravity (sp gr) is a ratio, expressed decimally, o the weight o a substance to the weight
o an equal volume o a substance chosen as a standard, both substances at the same temperature. It is use ul to understand specif c gravity as being a relative value, that is, the weight
o a substance relative to the weight o a standard.
Water is used as the standard or the speci ic gravities o liquids and solids; the most
use ul standard or gases is hydrogen.
Speci ic gravity may be calculated by dividing the weight o a given substance by the
weight o an equal volume o water, that is:
Specific gravity W eight of substance
W eight of equal volume of wate
=
rr
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

D f n	density and specific gravity, and d rm n a h hrough appropr a
al ula on .
c al ula Apply p	p f gra y from da a d r d from h u of a py nom r. f gra y n on r ng w gh o olum and olum o w gh .

Density and Specific
Gravity
5
78 Pharma euti al c al ulations
T hus, i 10 mL o sul uric acid weigh 18 g and 10 mL o water, under similar conditions, weigh 10 g, the speci ic gravity o the acid is:
Specific gravity g)
g)
= =
18
10
(
.
(
1 8
•  Substances that have a specif c gravity less than 1 are lighter than water.
•  Substances that have a specif c gravity greater than 1 are heavier than water.
Table 5.1 presents some representative speci ic gravities. Figure 5.1 depicts the layering o immiscible liquids due to their relative weights.
Although speci ic gravities may be expressed to as many decimal places as the accuracy o
their determination warrants, in pharmacy practice, expressions to two decimal places generally
su ice. In the United States Pharmacopeia, speci ic gravities are based on data rom temperatures o
25°C, with the exception o that or alcohol that is based on 15.56°C by government regulation.1
Density versus Specific Gravity
T he density o a substance is a concrete number (1.8 g/mL in the example), whereas specif c
gravity, being a ratio o like quantities, is an abstract number (1.8 in the example). W hereas
density varies with the units o measure used, specif c gravity has no dimension and is thereore a constant value or each substance. T hus, whereas the density o water may be variously expressed as 1 g/mL, 1000 g/L, or 62½ lb/cu t, the specif c gravity o water is always 1.
T bl 5.1 •  So me Re pRe Se n TaTive Sp e c if ic
GRa viTie S aT 25°c

a g t Ether (at 20°C) Isopropyl alcohol	Sp GR 0.71 0.78
Acetone	0.79
Alcohol	0.81
Liquid petrolatum	0.87
Peppermint oil	0.90
Olive oil	0.91
Peanut oil	0.92
Cod liver oil	0.92
Castor oil	0.96
W t r	1.00
Propylene glycol	1.03
Clove oil	1.04
Liquefied phenol	1.07
Polysorbate 80	1.08
Polyethylene glycol 400	1.13
Glycerin	1.25
Syrup	1.31
Hydrochloric acid	1.37
Nitric acid	1.42
Chloroform	1.47
Nitroglycerin	1.59
Phosphoric acid	1.70
Mercury	13.6

5 • Den ity and s pecific Gravity 79
Calculating the Specific Gravity of Liquids
Known Weight and Volume
Apply the equation:
Specific gravity W eight of substance
W eight of equal volume of wate
=
rr
(1) I 54.96 mL o an oil weighs 52.78 g, what is the specif c gravity o the oil?
54.96 mL o water weighs 54.96 g
Specific gravity of oil g
g
= =
52 78
54 96
. .
.
( )
( )
0 9603
(2) I a pint o a certain liquid weighs 601 g, what is the specif c gravity o the liquid?
1 pint = 16 l. oz.
16 l. oz. o water weighs 473 g
Specific gravity of liquid g
g
= =
601
473
( )
( )
1 27 .
Pycnometer or Specific Gravity Bottle
Apycnometer is a special glass bottle used to determine speci c gravity (Fig. 5.2). Pycnometers
are generally available or laboratory use in volumes ranging rom 1 to 50 mL. Pycnometers
have tted glass stoppers with a capillary opening to allow trapped air and excess f uid to
escape. Some pycnometers have thermometers a xed in order to relate the speci c gravity,
as determined, with temperature.
In using a pycnometer, it is irst weighed empty and then weighed again when illed to
capacity with water. T he weight o the water is calculated by di erence. Since 1 g o water
equals 1 mL, the exact volume o the pycnometer becomes known. T hen, when any other
Mineral oil
(sp gr 0.89)
Water
(sp gr 1.00)
Chloroform
(sp gr 1.47)
f iGURe 5.1 • Depiction of layering of immiscible liquids in a test tube, mineral oil being
lighter than water and chloroform being heavier.
80 Pharma euti al c al ulations
liquid subsequently is placed in the pycnometer, it is of equal volume to the water, and its
specific gravity may be determined.
(1) A 50-mL pycnometer is ound to weigh 120 g when empty, 171 g when f lled with water,
and 160 g when f lled with an unknown liquid. Calculate the specif c gravity o the
unknown liquid.
W eight of water g g g
W eight of unknown liquid g g
: :
171 120 51
160 120
– –
= ==
=
40 g
Specific gravity W eight of substance
W eight of equal volume ofwater
Specific gravity of unknown liquid g
g
= =
40
51
( )
( )
0 78 .
(2) A specif c gravity bottle weighs 23.66 g. W hen f lled with water, it weighs 72.95 g; when
f lled with another liquid, it weighs 73.56 g. W hat is the specif c gravity o the liquid?
73 56 23 66 49 90
72 95 23 66 49 29
. . .
. . .
g g g of liquid
g g g of water
Spe
—
==
ccific gravity of liquid g
g
= =
49 90
49 29
. .
.
( )
( )
1 012
f iGURe 5.2 •  Example of a pycnometer affixed with a thermometer. Pycnometers
are used to determine the specific gravities of liquids at specific temperatures. See text
for additional discussion. (Courtesy of Kimble/Kontes Glass.)
5 • Den ity and s pecific Gravity 81
Use of Specific Gravity in Calculations of Weight and Volume
It is important to remember that specif c gravity is a actor that expresses how much heavier
or lighter a substance is than water, the standard with a specif c gravity o 1.0. For example,
a liquid with a specif c gravity o 1.25 is 1.25 times as heavy as water, and a liquid with a
specif c gravity o 0.85 is 0.85 times as heavy as water.
T hus, i we had 50 mL o a liquid with a speci ic gravity o 1.2, it would weigh 1.2 times
as much as an equivalent volume o water. An equivalent volume o water, 50 mL, would
weigh 50 g, and there ore, the liquid would weigh 1.2 times that, or 60 g.
Calculating Weight, Knowing the Volume and Specific Gravity
Based on the explanation in the previous paragraphs, we can derive the ollowing equation:
Grams Milliliters Specific gravity = ×
Although it is both obvious and true that one cannot multiply milliliters by speci ic gravity
and have a product in grams, the equation “works” because the volume o the liquid in question is
assumed to be the same volume as water or which milliliters equal grams. So, in essence, the true
equation would be:
Grams other liquid Grams of equal volume of water
Specific gr
( ) ( )
(
=
× aavity other liquid)
(1) W hat is the weight, in grams, o 3620 mL o alcohol with a speci c gravity o 0.82?
3620 mL o water weighs 3620 g
3620 g × 0.82 = 2968 g
(2) Sevof urane (ULTANE) is a volatile liquid or inhalation with a speci c gravity o 1.52.
Calculate the weight o the contents o a bottle o 250 mL o the product.
250 mL o water weighs 250 g
250 g × 1.52 = 380 g
(3) W hat is the weight, in grams, o 2 f . oz. o a liquid having a speci c gravity o 1.118?
In this type o problem, it is best to convert the given volume to its metric equivalent irst and then solve the problem in the metric system.
2 × 29.57 mL = 59.14 mL
59.14 mL o water weighs 59.14 g
59.14 g × 1.118 = 66.12 g
Calculating Volume, Knowing the Weight and Specific Gravity
By rearranging the previous equation, we can calculate the volume o a liquid using the
equation:

Milliliters	Grams
Specific gravity

=
(1) W hat is the volume, in milliliters, o 492 g o a liquid with a speci c gravity o 1.40?
492 g o water measure 492 mL
492
1 40
mL
.
= 351 mL
82 Pharma euti al c al ulations
(2) W hat is the volume, in milliliters, o 1 lb o a liquid with a specif c gravity o 1.185?
1 lb = 454 g
454 g o water measure 454 mL
454
1 185
mL
.
383 1 mL .=
(3) W hat is the volume, in pints, o 50 lb o glycerin having a specif c gravity o 1.25?
50 lb = 454 g × 50 = 22,700 g
22,700 g o water measure 22,700 mL and 1 pint = 473 mL
22 700
1 25
, 18 160 473
.
, .
mL
= ÷ = mL mL 38 4 pints
Using Specific Gravity to Determine Weight / Volume Costs
(1) W hat is the cost o 1000 mL o glycerin, specif c gravity 1.25, bought at $5.43 per pound?
1000 mL o water weighs 1000 g
Weight o 1000 mL o glycerin = 1000 g × 1.25 = 1250 g
1 lb = 454 g
$ . . 5 43 1250
454
× =
g g
$14 95
(2) W hat is the cost o 1 pint o chloro orm, specif c gravity 1.475, bought at $25.25 per pound?
1 pint = 473 mL
473 mL o water weighs 473 g
Weight o 473 mL o chloro orm = 473 g × 1.475 = 697.7 g
1 lb = 454 g
$ . 25 25 697 7 . .
454
× =
g
g
$38 80
Special Considerations of Specific Gravity
Pharmaceutical Applications
An interesting special application o speci c gravity is in the use o automated, computercontrolled pharmaceutical equipment, termed automated compounders, in the preparation o
multicomponent mixtures or parenteral nutrition (as describe in Chapter 14). In such systems, the measurement o the nal volume o a mixture is determined by its weight divided
by the solution’s known speci c gravity.2 A complete explanation may be ound in the indicated re erence.
Clinical Application
Speci c gravity is an important actor in urinalysis. In normal adults, the speci c gravity o
urine is usually within the range o 1.020 and 1.028 with a normal f uid intake (this range
may vary with the re erence source).3
5 • Den ity and s pecific Gravity 83
Specific gravity is an indicator of both the concentration of particles in the urine and a
patient’s degree of hydration. A higher-than-normal specific gravity indicates that the urine
is concentrated. T his may be due to the presence of excess waste products or electrolytes
in the urine, the presence of glucose (glucosuria) or protein (proteinuria), excessive water
loss, decreased fluid intake, or other factors. A low specific gravity indicates that the urine
is dilute, which may be a result of diabetes insipidus, renal disease (by virtue of the kidney’s
reduced ability to concentrate urine), increased fluid intake, intravenous hydration, or other
factors.4
CASE IN POINT 5.15
  Lactic acid

Salicylic acid aa. Flexible collodion qs ad

1.5 g 15 mL

Sig: Apply one drop to wart twice a day
Label: Wart remover. For external use only
Lactic acid is available as a liquid containing 85 g of the acid in 100 g of solution (sp gr 1.21).
Calculate the quantity of this solution, in milliliters, needed to fill the prescription.
c a l c Ul aTio n S c a pSUl e
Specific Gravity
The specific gravity (sp gr) of a substance or a pharmaceutical preparation may be
determined by the following equation:
Specific gravity
Weight of substance g
Weight of equal volume of w
( )
=
aater g ( )
The following equation may be used to convert the volume of a substance or pharmaceutical
preparation to its weight*:
Weight of substance Volume of substance Specific gravity = ×
Or simply,
g mL spgr = ¥
The following equation may be used to convert the weight of a substance or pharmaceutical preparation to its volumea:
Volume of substance Weight of substance
Specific gravity
=
Or simply,
mL
g
spgr
=
aT he full explanation on why these equations work may be found in the section “Use of Specific Gravity
in Calculations of Weight and Volume.”
84 Pharma euti al c al ulations
pRa c Tic e pRo b l e mS
Calculations of Density
1. If 250 mL of alcohol weighs 203 g, what is its density?
2. A substance metal weighs 53.6 g and has a volume of 6 mL. Calculate its density.
Calculations of Specific Gravity
3. If 150 mL of a sorbitol solution weigh 170 g, what is its specific gravity?
4. If a liter of a cough syrup weighs 1285 g, what is its specific gravity?
5. If 500 mL of a solution weigh 650 g, what is its specific gravity?
6. If 2 fl. oz. of glycerol weigh 74.1 g, what is its specific gravity?
7. Five pints of a liquid weigh 2.79 kg. Calculate its specific gravity.
8. A pycnometer weighs 21.62 g. Filled with water, it weighs 46.71 g; filled with
another liquid, it weighs 43.28 g. Calculate the specific gravity of the liquid.
9. A modified Ringer’s Irrigation has the following formula:
Sodium chloride 8.6 g

Potassium chloride Calcium chloride PEG 3350 Water for injection to

0.3 g 0.33 g 60 g 1000 mL

Assuming that 980 mL of water is used, calculate the specific gravity of the
irrigation.
Calculations of Weight or Volume Using Specific Gravity
N OT E: Use the information in Table 5.1 as necessary.
10. α-Tocopherol is a form of vitamin E that is a yellow-brown viscous liquid with a
density of 0.950 g/cm3. Calculate its specific gravity.
11. A patient added a 17-g measured dose of polyethylene glycol 3350 (MIRALAX)
to 180 mL of water to use as a laxative. If the volume of the resultant mixture
was 195.6 mL, calculate the apparent density of polyethylene glycol 3350 and the
specific gravity of the mixture.
12. If a pharmacist dissolves 1.2 g of a medicinal agent in 60 mL of a cough syrup
having a specific gravity of 1.20. W hat is the specific gravity (to 3 decimal places)
of the product if the addition of the medicinal agent increases the syrup’s volume
by 0.2 mL?
13. If a pharmacist adds 10 mL of purified water to 30 mL of a solution having a
specific gravity of 1.30, calculate the specific gravity of the product (to three
decimal places).
14. If a pharmacist combined 50-mL portions of three syrups having specific gravities
of 1.10, 1.25, and 1.32, what would be the specific gravity (to two decimal places)
of the combined product?
15. A laboratory utilizes a mixture of 10% dimethyl sulfoxide (DMSO) in the freezing
and long-term storage of embryonic stem cells. If DMSO has a specific gravity
of 1.1004, calculate the specific gravity, to four decimal places, of the mixture
(assume water to be the 90% portion).
5 • Den ity and s pecific Gravity 85
16. Calculate the weight, in grams, o 100 mL o each o the ollowing:
(a) Acetone
(b) Liquid petrolatum
(c) Syrup
(d) N itroglycerin
(e) Mercury
17. W hat is the weight, in kilograms, o 5 liters o a liquid with a speci ic gravity o 1.84?
18. W hat is the weight, in kilograms, o 1 gallon o sorbitol solution having a speci ic
gravity o 1.285?
19. I 500 mL o mineral oil are used to prepare a liter o mineral oil emulsion, how
many grams o the oil, having a speci ic gravity o 0.87, would be used in the
preparation o 1 gallon o the emulsion?
20. Calculate the volume, in milliliters, o 100 g o each o the ollowing:
(a) Peanut oil
(b) Castor oil
(c) Polysorbate 80
(d) Phosphoric acid
(e) Mercury
21. W hat is the volume, in milliliters, o 1 lb o benzyl benzoate having a speci ic
gravity o 1.12?
22. Calculate the corresponding weights o lique ied phenol and propylene glycol
needed to prepare 24 15-mL bottles o the ollowing ormula:

Liquef ed phenol Camphor Benzocaine	0.4 mL 0.5 g 2.2 g
Ethanol Propylene glycol Purif ed water to	65 mL 17 mL 100 mL
23. Calculate the total weight o the ollowing ormula or a pediatric chewable gummy gel base or medication.
Gelatin Glycerin Purif ed water	43.4 g 155 mL 21.6 mL

24. Calculate the number o milliliters o polysorbate 80 required to prepare 48 100-g
tubes o the ollowing ormula or a progesterone vaginal cream.

Progesterone, micronized	3 g 1 g 96 g
Polysorbate 80
Methylcellulose 2% gel
25. I i ty glycerin suppositories are made rom the ollowing ormula, how many milliliters o glycerin, having a speci ic gravity o 1.25, would be used in the preparation o 96 suppositories?
Glycerin Sodium stearate Purif ed water	91 g 9 g 5 g

86 Pharma euti al c al ulations
26.  Testosterone propionate 2 g
Mineral oil, light 10 g
Polysorbate 80 1 g
Methylcellulose 2% gel 87 g
T he specific gravity of light mineral oil is 0.85 and that of polysorbate 80 is 1.08.
Calculate the milliliters of each needed to fill the prescription.
27. A formula for an anesthetic ointment is:
Benzocaine 200 g
Polyethylene glycol 400 600 g
Polyethylene glycol 3350 ad 1000 g
Polyethylene glycol 400 is a liquid, sp gr 1.13, benzocaine and polyethylene glycol
3350 are powders. H ow many milliliters of polyethylene glycol 400 would be used
in the formula?
28. Prior to a computerized tomographic scan (CT scan) of the abdomen, a patient
is instructed to drink 450 mL of a barium suspension. If the suspension has a
specific gravity of 1.05, calculate the weight of the suspension.
Using Specific Gravity to Determine Weight/Volume Costs
29. An international supplier sells Indian castor oil at $1200 a metric ton (1000 kg).
Using the information in Table 5.1 and the previously learned conversion factors,
calculate the corresponding price of a pint of the oil.
30. T he formula for 1000 g of polyethylene glycol ointment calls for 600 g polyethylene glycol 400. At $19.15 per pint, what is the cost of the polyethylene glycol
400, specific gravity 1.140, needed to prepare 4000 g of the ointment?
c a l c q Uiz
5.A. Syrup, USP is prepared by dissolving 850 g of sucrose in sufficient purified water to
make 1000 mL of syrup. Syrup has a specific gravity of 1.31. How many milliliters of
water are used to prepare a liter of syrup?
5.B. A saturated solution of potassium iodide contains, in each 100 mL, 100 g of potassium iodide. The solubility of potassium iodide is 1 g in 0.7 mL of water. Calculate
the specific gravity of the saturated solution.
5.C. Cocoa butter (theobroma oil) is used as a suppository base. It is a solid at room temperature, melts at 34°C, and has a specific gravity of 0.86. If a formula for medicated
suppositories calls for 48 mL of theobroma oil, how many grams are equivalent?
5 • Den ity and s pecific Gravity 87
References
1. United States Pharmacopeial Convention. United States Pharmacopeia 32 National Formulary 27. Vol. 1. Rockville,
MD: United States Pharmacopeial Convention; 2009:9.
2. American Society of H ealth-System Pharmacists. ASH P guidelines on the safe use of automated compounding devices for the preparation of parenteral nutrition admixtures. American Journal of Health-System Pharmacy
2000;57:1343–1348. Available at: http://www.ashp.org/s_ashp/docs/files/BP07/AutoIT _Gdl_Compounders.
pdf. Accessed April 17, 2014.
3. Urine specific gravity. MedlinePlus. Available at: http://www.nlm.nih.gov/medlineplus/ency/article/003587.
htm. Accessed March 6, 2011.
4. T he Internet Pathology Laboratory for Medical Education. Urinalysis tutorial. Available at: http://library.med.
utah.edu/WebPath/T UT ORIAL/URIN E/URIN E.html. Accessed January 18, 2011.
5. Allen LV Jr, ed. International Journal of Pharmaceutical Compounding 1998;2:58.
a n SWe RS To “c a Se in po in T” a n D pRa c Tic e pRo b l e mS
Case in Point 5.1
Q uantity of lactic acid needed to fill :1.5 g
Source of lactic acid: liquid containing 85 g/100 g; or, by using specific gravity:
100 g ÷ 1.21 = 82.64 mL
T hus, 85 g of lactic acid is in 82.64 mL of the source liquid.
By proportion:
85
82 64
1 5
1 46
g
mL
g
x mL
x mL
.
.
= = ; .
Practice Problems
1. 0.812 g/mL
2. 8.933 g/mL
3. 1.133
4. 1.285
5. 1.30
6. 1.25
7. 1.18
8. 0.86
9. 1.05
10. 0.950
11. 1.09, density, and 1.01, specific
gravity
12. 1.216
13. 1.225
14. 1.22
15. 1.0100
16. (a) 79 g acetone
(b) 87 g liquid petrolatum
(c) 131 g syrup
(d) 159 g nitroglycerin
(e) 1360 g mercury
17. 9.2 kg
18. 4.86 kg sorbitol solution
19. 1646.5 g mineral oil
20. (a) 108.7 mL peanut oil
(b) 104.17 mL castor oil
(c) 92.59 mL polysorbate 80
(d) 58.82 mL phosphoric acid
(e) 7.35 mL mercury
21. 405.36 mL benzyl benzoate
22. 1.54 g liquefied phenol
63.04 g propylene glycol
23. 258.75 g
24. 44.44 mL polysorbate 80
25. 139.78 mL glycerin
26. 11.76 mL light mineral oil
0.93 mL polysorbate 80
27. 530.97 mL polyethylene glycol 400
28. 472.5 g barium suspension
29. $ 0.54
30. $85.23
88
Percent
T he term percent and the corresponding “%” sign indicate the number o parts in a hundred.
T he quantity also may be expressed as a common or decimal raction. T hus, 50%, 50/100,
and 0.5 are equivalent.
For the purposes o computation, percents are usually changed to equivalent decimal
ractions. T his change is made by dropping the percent sign (%) and dividing the expressed
numerator by 100. T hus, 12.5% = 12.5/100, or 0.125, and 0.05% = 0.05/100, or 0.0005. We
must not orget that in the reverse process (changing a decimal to a percent), the decimal is
multiplied by 100 and the percent sign (%) is a ixed.
Percent is an essential component o pharmaceutical calculations. It is used to (a) express
the strength o a component in a pharmaceutical preparation as well as to (b) determine the
quantity o a component to use when a certain percent strength is desired.
Percent Preparations
T he percent concentrations o active and inactive constituents in various types o pharmaceutical preparations are def ned as ollows by the United States Pharmacopeia1:
Percent weight in volume (w/v) expresses the number o grams o a constituent in
100 mL o solution or liquid preparation and is used regardless o whether water or

another liquid is the solvent or vehicle. Expressed as:	% w/v.
Percent volume in volume (v/v) expresses the number o milliliters o a constituent in
100 mL o solution or liquid preparation. Expressed as:	% v/v.

Percent weight in weight (w/w) expresses the number o grams o a constituent in 100 g
o solution or preparation. Expressed as: % w/w.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

P rform al ula on	a d on percent weight in volume, percent volume in volume,
and percent weight in weight.
P rform al ula on	a d on ratio strength.
c on r p r n U l z o h r xpr mg/mL.	r ng h o ra o r ng h and ra o r ng h o p r n	r ng h.
on of on n ra on n al ula on , a parts per million and

6
Percent Strength,
Ratio Strength, and Other
Expressions of Concentration
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 89
T he term percent, or the symbol %, when used without qualification means:
•  For solutions or suspensions of solids in liquids, percent weight in volume
•  For solutions of liquids in liquids, percent volume in volume
•  For mixtures of solids or semisolids, percent weight in weight
•  For solutions of gases in liquids, percent weight in volume
Figures 6.1 and 6.2 show product labels for different forms of clindamycin phosphate
(CLEOCIN T ), both 1% in strength. Figure 6.1 is the label of a topical solution containing active ingredient, 10 mg/mL (1% w/v), whereas Figure 6.2 is the label of a topical gel
containing active ingredient, 10 mg/g (1% w/w).
Special Considerations in Percent Calculations
In general, the physical nature of the ingredients in a pharmaceutical preparation determines the basis of the calculation. T hat is, a powdered substance dissolved or suspended
in a liquid vehicle would generally be calculated on a weight-in-volume basis; a powdered
substance mixed with a solid or semisolid, such as an ointment base, would generally be
calculated on a weight-in-weight basis; and a liquid component in a liquid preparation
would be calculated on a volume-in-volume basis. If the designation of the term of a calculation
(e.g., w/v, w/w, or v/v) is not included in a problem, the appropriate assumption must be made.
T he use of percent to indicate the strength of a product generally is limited nowadays
to certain topical products, such as ointments, creams, and eyedrops. H owever, there are
some notable exceptions, such as 5% dextrose injection, used in intravenous infusions. In
FIGURE 6.1 •  A
product label depicting
the strength of the active
ingredient on a w/v basis,
10 mg/mL. (From http://
dailymed.nlm.nih.gov/
dailymed/about.cfm)
FIGURE 6.2 •  A product label depicting the strength of the active ingredient
on a w/w basis, 10 mg/g. (From http://
dailymed.nlm.nih.gov/dailymed/about.
cfm)
90 Pharma euti al c al ulations
most other instances, product strengths are expressed in speci ic quantitative terms, such as
10-mg tablets and 2 mg/mL injections. [The problems in this chapter take certain liberties rom
this standard practice in order to a ord a broad experience in the calculations process.]
Percent Weight in Volume
In calculating percent weight-in-volume (w/v) problems, the assumption is made that the
specif c gravity o the liquid preparation is 1, as i it were water. T hus, or example, 100 mL
o a solution is assumed to weigh 100 g, and there ore, a 5% w/v preparation would contain
5 g o that ingredient [5% o (100 mL taken to be) 100 g].
Examples of Weight-in-Volume Calculations
(1) How many grams o dextrose are required to prepare 4000 mL o a 5% solution?
4000 mL represents 4000 g o solution
5% = 0.05
4000 g × 0.05 = 200 g
Or, solving by dimensional analysis:

5	4000 × = mL 200 g dextrose
100

g mL
(2) How many grams o potassium permanganate should be used in compounding the ollowing
prescription?
Potassium permanganate 0.02%
Purif ed water ad 250 mL
Sig. as directed
250 mL represents 250 g o solution
0.02% = 0.0002
250 g × 0.0002 = 0.05 g potassium permanganate
(3) A cyclosporine ophthalmic emulsion (RESTASIS) contains 0.05% w/v cyclosporine in
0.4-mL vials. Calculate the content o cyclosporine, in milligrams, per vial.
0.4 mL × 0.05% w/v = 0.0002 mL (equivalent in a w/v problem to 0.0002 g)
0.0002 = 0.2 mg cyclosporine
(4) The topical antibacterial solution HIBICLENS contains 4% w/v chlorhexidine gluconate
in 4-f uidounce containers. Calculate the content o chlorhexidine gluconate, in grams.
4 ( luidounces) × 29.57 mL = 118.28 mL
118.28 mL × 4% w/v = 4.73 g chlorhexidine gluconate
(5) Bimatoprost ophthalmic solution (LUMIGAN) contains 0.03% w/v o drug in each
2.5 mL. Calculate the micrograms o bimatoprost in a container o solution.
2.5 mL × 0.03% w/v = 0.00075 g = 0.75 mg = 750 mg bimatoprost
(6) An ophthalmic solution contains 0.1 mg o travoprost (T RAVATAN Z) in 2.5 mL containers. Calculate the percent strength o travoprost in the solution.
0.1 mg = 0.0001 g
0 0001
2 5
. 100
.
g % . / ,
g
× = 0 004 w v travoprost %
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 91
Percent Volume in Volume
Liquids are usually measured by volume, and the percent strength indicates the number o parts by volume o an ingredient contained in the total volume o the liquid
preparation.
Examples of Volume-in-Volume Calculations
(1) How many milliliters o liquef ed phenol should be used in compounding the ollowing
prescription?
 

Liquef ed phenol Calamine lotion ad Sig. or external use

2.5% 240 mL

240 mL × 0.025 = 6 mL
Or, solving by dimensional analysis:
2 5
100
. mL 240 ,
mL
× = mL 6 mL liquefied phenol
(2) In preparing 250 mL o a certain lotion, a pharmacist used 4 mL o liquef ed phenol. W hat
was the percent (v/v) o liquef ed phenol in the lotion?
250
4
( ) 100
( )
( )
( )
%
%
.
mL
mL x
x
= =
1 6%
(3) W hat is the percent strength v/v o a solution o 800 g o a liquid with a specif c gravity o
0.8 in enough water to make 4000 mL?
800 g o water measure 800 mL
800 mL ÷ 0.8 = 1000 mL o active ingredient
4000
1000
( ) 100
( )
(%)
(%)
mL
mL x
x
= =
25%
Or, solving by dimensional analysis:
800
0 8
1
4000
100
mL
. mL
× × = % 25%
(4) I a veterinary liniment contains 30% v/v o dimethyl sul oxide, how many milliliters o
the liniment can be prepared rom 1 lb o dimethyl sul oxide (sp gr 1.10)?
1 lb = 454 g
454 g o water measures 454 mL
454 mL ÷ 1.10 = 412.7 mL of dimethyl sulfoxide
30
100
412 7
1375 7
(%)
(%)
. ( )
( )
.
= =
mL
x mL
x or 1376 mL
92 Pharma euti al c al ulations
Or, solving by dimensional analysis:
1
30
454
1
1
1
1
1 10
lb g 100 1375 7
lb
mL
g
or
% .
× × × × = % . 1376 mL
Percent Weight in Weight
Percent weight in weight indicates the number of parts by weight of active ingredient contained in the total weight of the preparation.
Examples of Weight-in-Weight Calculations
(1) A hydrocortisone cream contains 1% hydrocortisone. Calculate the grams o hydrocortisone
used to prepare each 15-g tube o product.
1% = 0.01
15 g × 0.01 = 0.15 g
(2) FINACEA gel contains 15% azelaic acid in 50-g tubes. Calculate the grams o azelaic acid
in each tube o product.
15% = 0.15
50 g × 0.15 = 7.5 g
(3) ANDROGEL 1.62% is a testosterone gel or topical use. Calculate the grams o gel required
to provide a 40.5 mg dose o testosterone.
1.62% = 1.62 g (testosterone)/100 g (gel) or 1620 mg (testosterone)/100 g (gel)
T hus,
1620
100
mg 40 5
g
mg
x
= =
.
2 5 g gel .
Or,
40 5
100
1 62
1
1000
.
.
mg .
g g
g
mg
× × = 2 5 g gel
Proo : 2.5 g (gel) × 1.62% (testosterone) = 0.0405 g or 40.5 mg testosterone
(4) How many grams o a drug substance are required to make 120 mL o a 20% (w/w)
solution having a specif c gravity o 1.15?
120 mL of water weigh 120 g
120 g × 1.15 = 138 g, weight of 120 mL of solution
138 g × 0.20 = 27.6 g plus enough water to make 120 mL
Or, solving by dimensional analysis:
120 1 15
1
20
100
mL
g
mL
× × =
. %
%
27 6 g .
Sometimes in a weight-in-weight calculation, the weight of one component is
known but not the total weight of the intended preparation. T his type of calculation
is performed as demonstrated by the following example.
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 93
(5) How many grams o a drug substance should be added to 240 mL o water to make a 4%
(w/w) solution?
100% – 4% = 96% (by weight) of water
240 mL of water weigh 240 g
96
4
(%) 240
(%)
( )
( )
= =
g
x g
x 10 g
It is usually impossible to prepare a specified volume of a solution or liquid
preparation of given weight-in-weight percent strength because the volume
displaced by the active ingredient cannot be known in advance. If an excess is
acceptable, we may make a volume somewhat more than that specified by taking the given volume to refer to the solvent or vehicle and from this quantity
calculating the weight of the solvent or vehicle (the specific gravity of the solvent or vehicle must be known). U sing this weight, we may follow the method
just described to calculate the corresponding weight of the active ingredient
needed.
(6) How should you prepare 100 mL o a 2% (w/w) solution o a drug substance in a solvent
having a specif c gravity o 1.25?
100 mL of water weigh 100 g
100 g × 1.25 = 125 g, weight of 100 mL of solvent
100% – 2% = 98% (by weight) of solvent
98
2
(%) 125
(%)
( )
( )
.
= =
g
x g
x 2 55 g
T herefore, dissolve 2.55 g of drug substance in 125 g (or 100 mL) of solvent.
(7) I 1500 g o a solution contains 75 g o a drug substance, what is the percent strength (w/w)
o the solution?
1500
75
( ) 100
( )
(%)
(%)
g
g x
x
= =
5%
Or, solving by dimensional analysis:
75
1500
g 100
g
× = % 5%
(8) I 5 g o boric acid are added to 100 mL o water, what is the percent strength (w/w) o the
solution?
100 mL of water weigh 100 g
100 g + 5 g = 105 g, weight of solution
105
5
( ) 100
( )
(%)
(%)
.
g
g x
x
= =
4 76%
94 Pharma euti al c al ulations
(9) I 1000 mL o syrup with a specif c gravity o 1.313 contain 850 g o sucrose, what is its
percent strength (w/w)?
1000 mL of water weigh 1000 g
1000 g × 1.313 = 1313 g, weight of 1000 mL of syrup
1313

850 ( )

(%) .

( ) 100
(%)
g
g x
x
= =
64 7%
(10) A 60-g tube o DESONATE gel contains 0.05% w/w desonide. Calculate the concentration o desonide on an mg/g basis.
1 g × 0.05% w/w = 0.0005 g = 0.5 mg/g desonide
(11) DIPROLENE lotion contains 0.05% w/w betamethasone dipropionate. I the specif c
gravity o the lotion is 0.96, how many milligrams o betamethasone dipropionate would
be present in a 60-mL container o the lotion?
60 mL × 0.96 = 57.6 g
57.6 g × 0.05% = 0.0288 or 0.029 g = 29 mg betamethasone dipropionate
(12) W hat weight o a 5% (w/w) solution can be prepared rom 2 g o active ingredient?
5
100
( ) 2
( )
( )
( )
% %
= =
g
x g
x 40 g
(13) How many milligrams o hydrocortisone should be used in compounding the ollowing
prescription?

H ydrocortisone H ydrophilic ointment ad Sig. apply ⅛% = 0.125%

⅛% 10 g

10 g × 0.00125 = 0.0125 g or 12.5 mg hydrocortisone
(14) How many grams o benzocaine should be used in compounding the ollowing prescription?

Benzocaine Polyethylene glycol base ad Make 24 such suppositories Sig. insert one as directed

2% 2 g

2 g × 24 = 48 g, total weight of mixture
48 g × 0.02 = 0.96 g benzocaine
Or, solving by dimensional analysis:
24 2
1
2
100
supp
g
supp
.
.
%%
× × = 0 96 g benzocaine .
6 • P r nt s tr ngth, Rat o s tr ngth, and Oth r e xpr on of c on ntrat on 95
Ca l CUl at IOn S Ca PSUl E
Percent Concentration
The amounts of therapeutically active and/or inactive ingredients in certain types of pharmaceutical preparations are expressed in terms of their percent concentrations.
Unless otherwise indicated:
a. Liquid components in liquid preparations have volume-in-volume relationships with
calculations following the equation:
mL of preparation % concentration mL of component ´´ =a
b. Solid components in liquid preparations have weight-in-volume relationships with
calculations following the equation:
mL of preparation % concentration g of component ´´ =a
The terms of this equation are accepted due to the assumption that the specific gravity of
the preparation is 1, as if it were water, and thus each milliliter represents the weight of 1 g.
c. Solid or semisolid components in solid or semisolid preparations have weight-in-weight
relationships with calculations following the equation:
g of preparation % concentration g of component ´´ =a
ain th quat on , “% on ntrat on” xpr d d mally ( .g., 0.05, not 5%).
Use of Percent in Compendial Standards
Percent is used in the United States Pharmacopeia to express the degree o tolerance permitted in the purity o single-chemical entities and in the labeled quantities o ingredients in
dosage orms. For instance, according to the United States Pharmacopeia,2 “Aspirin contains
not less than 99.5% and not more than 100.5% o C 9H 8O 4 (pure chemical aspirin) calculated
on the dried basis.” Further, “Aspirin Tablets contain not less than 90.0% and not more than
110.5% o the labeled amount o C 9H 8O 4.” Although dosage orms are ormulated with the
intent to provide 100% o the quantity o each ingredient declared on the label, some tolerance is permitted to allow or analytic error, unavoidable variations in manu acturing and
compounding, and or deterioration to an extent considered insignif cant under practical
conditions.
T he ollowing problem demonstrates calculations involving percent in compendial
standards.
If ibuprofen tablets are permitted to contain not less than 90% and not more than 110% of the
labeled amount of ibuprofen, what would be the permissible range in content of the drug, expressed
in milligrams, for ibuprofen tablets labeled 200 mg each?
90 200 180
110 200 220
%%
of mg mg
of mg mg
Range
===
180 mg to 220 mg ibuprofen
96 Pharma eu al c al ula ons
Ca SE In POIn t 6.1 3 A pa en w h myas hen a grav s has undergone rea men o
separa e and remove er a n abnormal an bod es and o her unwan ed elemen s rom
he blood (plasmapheres s). t he des red red blood ell omponen s hen re urned
ba k o he blood, bu he pa en has los pro e n and blood volume.
t he pa en ’s phys an orders 2000 mL o a 5% w/v solu on o album n n
0.9% w/v sod um hlor de nje on o repla e los pro e n and lu d.
in ll ng he order, he pharma s de des o use a p e e o au oma ed equ pmen
o ompound he m x ure. t he equ pmen mus be programmed w h he spe
grav es o he solu ons be ng m xed. t he pharma s sele s o use a 25% w/v album n solu on as he sour e o he album n plus a 0.9% w/v sod um hlor de nje on.

From he l era ure, he pharma s	nds ha 0.9% w/v sod um hlor de has a spe
grav y o 1.05. Us ng a pre se 25-mL py nome er w h a are we gh o 28 g,
he pharma s	lls	w h he 25% w/v album n solu on and de erm nes he we gh

o he lask and s on en o be 58 g.
(a) Wha s he spe f grav y o he album n solu on?
(b) How many m ll l ers o he 25% w/v album n solu on are needed o make
2000 mL on a n ng 5% w/v album n?
( ) Wha s he we gh o he 25% w/v album n solu on needed o f ll he order?
(d) i he pharma s m xed he requ red number o m ll l ers o he 25% w/v album n
solu on w h a su f en 0.9% w/v sod um hlor de nje on o make he requ red
2000 mL m x ure, wha would be he spe f grav y o he resul an solu on?
Ca SE In POIn t 6.2 3 A pharma s re e ves he ollow ng pres r p on bu does no
have hydro or sone powder on hand. However, he pharma s does have an nje –
on on a n ng 100 mg o hydro or sone per m ll l er o nje on. A sear h o he

l era ure nd a es ha he nje on has a spe	grav y o 1.5.
Hydro or sone c old ream qs ad	1.5% 30 g

 (a) How many grams o hydro or sone are needed o f ll he pres r p on?
(b) How many m ll l ers o he hydro or sone nje on would prov de he orre
amoun o hydro or sone?
( ) How many grams o old ream are requ red?
Ratio Strength
Percent strength itsel indicates a ratio; that is, a solution which is 5% in strength represents
the ratio o 5 parts in 100 parts, or the ratio 5:100. In expressing ratio strength, it is customary to have the f rst f gure a 1; thus, 5:100 would be reduced to 1:20.
W hen a ratio strength, or example, 1:1000, is used to designate a concentration, it is
to be interpreted as ollows:
• For solids in liquids = 1 g o solute or constituent in 1000 mL o solution or liquid
preparation.
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 97
•  For liquids in liquids= 1 mL o constituent in 1000 mL o solution or liquid preparation.
•  For solids in solids = 1 g o constituent in 1000 g o mixture.
T he ratio and percent strengths o any solution or mixture o solids are proportional,
and either is easily converted to the other by the use o proportion.
Example Calculations Using Ratio Strength
(1) Express 0.02% as a ratio strength.

0 02 100 . % % ( ) ( )

1 ( ) ( ) part x parts

5000
= =
x
Ratio strength 1 5000 == :
(2) Express 1:4000 as a percent strength.
4000
1
( ) 100
( )
( )
( )
%
%
.
parts
part x
x
= =
0 025%
N OT E: To change ratio strength to percent strength, it is sometimes convenient to “convert” the last two zeros in a ratio strength to a percent sign (%) and change the remaining
ratio f rst to a common raction and then to a decimal raction in expressing percent:

1:100 = 1 1 % 1:200 = 1 2% 3:500 = 3 5 % 1:2500 = 1 25% 1:10,000 = 1100%

= 1% = 0.5% = 0.6% = 0.04% = 0.01%

(3) A certain injectable contains 2 mg o a drug per milliliter o solution. W hat is the ratio
strength (w/v) o the solution?
2 mg = 0.002 g

0 002 .	1
1

500
.
( )
( )
( )
( )
g
g
mL
x mL
x mL
= =
Ratio strength 1 :500 ==
(4) W hat is the ratio strength (w/v) o a solution made by dissolving f ve tablets, each containing 2.25 g o sodium chloride, in enough water to make 1800 mL?
2.25 g × 5 = 11.25 g o sodium chloride
11 25
1
1800
160
.
)
.
( )
(
( )
( )
g
g
mL
x mL
x mL
= =
Ratio strength 1 :160 ==
In solving problems in which the calculations are based on ratio strength, it is
sometimes convenient to translate the problem into one based on percent strength
and to solve it accordingly.
98 Pharma euti al c al ulations
(5) How many grams of potassium permanganate should be used in preparing 500 mL of a
1:2500 solution?
1:2500 = 0.04%
500 (g) × 0.0004 = 0.2 g potassium permanganate
Or,
1:2500 means 1 g in 2500 mL of solution
2500
500
( ) 1
( )
( )
( )
.
mL
mL
g
x g
x
= =
0 2 g potassium permanganate
(6) How many milligrams of gentian violet should be used in preparing the following solution?
    

Gentian violet solution 1:10,000

500 mL

Sig. instill as directed
1:10,000 = 0.01%
500 (g) × 0.001 = 0.050 or 50 mg gentian violet
Or,
1:10,000 means 1 g of 10,000 mL of solution

10 000 ,	1
500

0 050
. ,
( )
( )
( )
( )
mL
mL
g
x g
x g or
= =
50 mg gentian violet
(7) How many milligrams of hexachlorophene should be used in compounding the following
prescription?
  H exachlorophene 1:400
H ydrophilic ointment ad 10 g
Sig. apply
1:400 = 0.25
10 (g) × 0.0025 = 0.025 g or 25 mg hexachlorophene
Or,
1:400 means 1 g in 400 g of ointment
400
10
1
0 025
( )
( )
( )
( )
. ,
g
g
g
x g
x g or
= =
25 mg hexachlorophene
Simple Conversions of Concentration to “mg/mL”
Occasionally, pharmacists, particularly those practicing in patient care settings, need to convert rapidly product concentrations expressed as percent strength, as ratio strength, or as
grams per liter (as in IV infusions) to milligrams per milliliter (mg/mL). T hese conversions
may be made quickly by using simple techniques. Some suggestions follow.
6 • P r n s r ng h, Ra io s r ng h, and O h r e xpr ion of c on n ra ion 99
To convert product percent strength to mg/mL, multiply the percent strength, expressed
as a whole number by 10.
(1) Convert 4% (w/v) to mg/mL

4 × 10 Proof or alternate method: 4% (w/v)

= 40 mg/mL = 4 g/100 mL = 4000 mg/100 mL

= 40 mg/mL
To convert product ratio strengths to mg/mL, divide the ratio strength by 1000.
(2) Convert 1: 10,000 (w/v) to mg/mL

10,000 ÷ 1000 Proof or alternate method: 1:10,000 (w/v)

= 1 mg/10 mL = 1 g/10,000 mL = 1000 mg/10,000 mL = 1 mg/10 mL

To convert product strengths expressed as grams per liter (g/L) to mg/mL, convert the
numerator of milligrams and divide by the number of milliliters in the denominator.
(3) Convert a product concentration of 1 g per 250 mL to mg/mL
1000 ÷ 250 = 4 mg/mL
Proof or alternate method: 1 g/250 mL = 1000 mg/250 mL = 4 mg/mL
Ca l CUl at IOn S Ca PSUl E
Ratio Strength
The concentrations of very weak pharmaceutical preparations (usually weight-in-volume
solutions) often are expressed in terms of their ratio strengths.
Ratio strength is another way of expressing percent strength. For example, a 1% w/v
solution and a ratio strength of 1:100 w/v are equivalent.
The preferable style of a ratio strength is to have the numeric value of the solute as 1.
This is accomplished when calculating a ratio strength, by setting up a proportion from the
data as:
g given solute
mL given solutio
( ) then value of
( )
; , :
n x
= x
1
1
In using a ratio strength in a calculations problem, there are two options: (a) convert
it to a percent strength and perform calculations in the usual manner, or (2) use the ratio
strength directly in a problem-solving proportion.
(a) t o onv r a ra io r ng h o a p r n r ng h; for xampl , 1:10,000 w/v:
1 g
10,000 mL
x g
100 mL
( )
=
Solving for x yields percent, by definition (parts per hundred).
(b) Probl m- olving propor ion, for xampl :
1 g
10,000 mL
x g
given quality,mL
; x g in given mL
( )
= =
100 Pharma euti al c al ulations
Milligrams Percent
T he term milligrams percent (mg%) expresses the number o milligrams o substance in
100 mL o liquid. It is used occasionally to denote the concentration o a drug or natural
substance in a biologic f uid, as in the blood. T hus, the statement that the concentration
o nonprotein nitrogen in the blood is 30 mg% means that each 100 mL o blood contains
30 mg o nonprotein nitrogen. H owever, the concentrations o substances in biologic f uids are more o ten expressed in milligrams per deciliter (mg/dL), which is a more accurate
within the context o the International System of Units.
Parts per Million (PPM) and Parts per Billion (PPB)
T he strengths o very dilute solutions are commonly expressed in terms o parts per million
(ppm) or parts per billion (ppb), that is, the number o parts o the agent per 1 million or 1 billion parts o the whole. For example, we are all amiliar with f uoridated drinking water in
which f uoride has been added at levels o between 1 to 4 parts per million (1:1,000,000 to
4:1,000,000) or the purpose o reducing dental caries.
We also are aware o and concerned with the presence o trace amounts o contaminants in our drinking water and ood which can pose a risk to our health and sa ety. Many
pharmacists serve on community committees and boards that address environmental
issues. Although they may not re er to themselves as environmental phar macists, their
backgrounds and interest in public health make them invaluable members o such bodies.
Pharmacists have a special leadership role in providing guidance in the sa e disposal o
unused and/or expired medications.4,5 Federal regulations and guidelines have been established to address this issue.6,7
Example Calculations of Parts per Million and Parts per Billion
(1) Express 5 ppm of iron in water in percent strength and ratio strength.

5 ppm = 5 parts in 1,000,000 parts

= 1:200,000, ratio strength, and =0.0005, percentage strength

 (2) The concentration of a drug additive in an animal feed is 12.5 ppm. How many milligrams
of the drug should be used in preparing 5.2 kg of feed?
12.5 ppm = 12.5 g (drug) in 1,000,000 g ( eed)
T hus,

1 000 000 , ,	5 200
12 5 .

0 065
, .
g
g
g
x g
x g
=
= = 65 mg
(3) The drinking water in a community has detected lead in its drinking water at a level of
2.5 ppb. The EPA’s MCL is set at 15 ppb. Express the difference between these two values
as a ratio strength.
15 ppb – 2.5 ppb = 12.5 ppb = 12.5:1,000,000,000 = 1:80,000,000
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 101
PRa Ct ICE PROb l EmS
Weight-in-Volume Calculations
1. CLOBEX lotion contains 0.05% w/v clobetasol propionate in 118 mL containers. Calculate the content o drug, in milligrams.
2.     Of oxacin ophthalmic solution 0.3%

Disp.	10 mL
H ow many milligrams o of oxacin are contained in each milliliter o the dispensed
prescription?
3.8	D examethasone sodium phosphate 100 mg
Sterile water or injection ad	100 mL

  Calculate the percent strength o dexamethasone sodium phosphate in the
prescription.
4. I 100 mL o a pharmaceutical preparation contains 20 mL o a 50% w/v solution
o benzalkonium chloride, what is the percent strength o that agent in the
solution?
5. A tissue plasminogen activator (T PA) ophthalmic solution is prepared to contain
25 mg/100 mL.
(a) Calculate the percent concentration o T PA in the solution.
(b) W hat volume o a solution containing T PA, 50 mg/50 mL, should be used to
prepare each 100 mL o the ophthalmic solution?
6. H ow many milligrams o methylparaben are needed to prepare 8 luidounces o
a solution containing 0.12% w/v o methylparaben?
7. A pharmacist emptied the contents o eight capsules, each containing 300 mg o
clindamycin phosphate, into a liquid vehicle to prepare 60 mL o a suspension.
Calculate the percent strength o clindamycin phosphate in the preparation.
8.    Ketorolac ophthalmic solution 0.5%
Disp. 5 mL
Sig: One drop q.i.d. prn allergic conjunctivitis
H ow many milligrams o the active constituent would be present in each
drop o the ophthalmic solution i the dropper service delivers 20 drops per
milliliter?
(a) 0.25 mg
(b) 25 mg
(c) 0.025 mg
(d) 1.25 mg
9. A ormula or an anti ungal shampoo contains 2% w/v ketoconazole. H ow
many grams o ketoconazole would be needed to prepare 240 mL o the
shampoo?
10. T he biotechnology drug inter eron gamma-1b (ACT IMMUN E) contains
100 mcg/0.5 mL. Calculate the percent strength o the solution.
11. Filgrastim (N EUPOGEN) pre illed syringes contain 480 mcg o active constituent
in each 0.8 mL. T he equivalent concentration is:
(a) 0.6%
(b) 0.384 mg/mL
(c) 0.06%
(d) 0.6 g/mL
102 Pharma euti al c al ulations
12. Levofloxacin (LEVAQ UIN ) injection contains 5 mg/mL of levofloxacin and 5%
of dextrose. H ow much of each would be delivered to a patient upon the administration of a 100-mL injection?
(a) 5 g levofloxacin and 5 g dextrose
(b) 50 mg levofloxacin and 5 g dextrose
(c) 500 mg levofloxacin and 500 mg dextrose
(d) 0.5 g levofloxacin and 5 g dextrose
13. An injection contains, in each milliliter, 60 mg of darbepoetin alfa (ARAN ESP),
0.05 mg of polysorbate 80, and 8.18 mg of sodium chloride. Calculate the percent
of each in the injection.
14. An injection of adalimumab (H UMIRA) contains 40 mg/0.8 mL. Calculate the
percent concentration of the injection.
15.9      Erythromycin lactobionate 500 mg
Dexamethasone sodium phosphate 100 mg
Glycerin 2.5 mL
Sterile water for injection ad 100 mL
M. ft. ophthalmic solution
(a) W hat is the percent strength of erythromycin lactobionate in the prescription?
(b) If glycerin has a specific gravity of 1.25, what is its percent concentration in
the prescription?
16. CIPRODEX, an otic suspension, contains 0.3% w/v ciprofloxacin and 0.1% w/v
dexamethasone in 7.5-mL drop containers. Calculate the quantities of each agent
based on mg/mL.
17. A 180-mL bottle of an oral solution contains sodium oxybate, 0.5 g/mL.
Calculate (a) the quantity of sodium oxybate, in grams, in the bottle and (b) the
percent strength of sodium oxybate in the solution.
18. In the preparation of an intravenous infusion, a vial containing 115 mg of drug is
diluted to 5 mL with sodium chloride for injection. T hen, the contents of the vial
are added to 110 mL of an infusion solution. Calculate the drug strength of the
final infusion in (a) mg/mL, (b) percent strength, and (c) ratio strength.
19. An ophthalmic solution contains tafluprost, 0.0015% w/v, available in 0.3 mL
pouches for single use. Calculate (a) the quantity of tafluprost, in micrograms, in
each pouch and (b) the number of single-dose pouches that the manufacturer may
prepare from each 1 g of drug.
20. A pharmacist adds 10 mL of a 20% w/v solution of a drug to 500 mL of D5W for
parenteral infusion. W hat is the percentage strength of the drug in the infusion
solution?
(a) 2% v/v
(b) 2% w/v
(c) 1.96% w/v
(d) 0.39% w/v
21. Calculate the percentage strength of an injection that contains 2 mg of hydromorphone hydrochloride in each milliliter of injection.
22. VIRAMUN E oral suspension contains 1% w/v of nevirapine. Calculate the milligrams of nevirapine present in a 240-mL bottle of the suspension.
23.10   Misoprostol 200-mg tablets 12 tablets
Lidocaine hydrochloride 1 g
Glycerin qs ad 100 mL
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 103
Calculate the strength of misoprostol in the prescription.
(a) 2.4% w/v misoprostol
(b) 0.0002% w/v misoprostol
(c) 0.024 mg/mL misoprostol
(d) 2.4 mcg/mL misoprostol
24.11   Fentanyl citrate 20 mg/mL
Bupivacaine hydrochloride 0.125%
Sodium chloride (0.9%) injection ad 100 mL
Calculate the percentage concentration of fentanyl citrate in the prescription.
25. Bepotastine besilate (BEPREVE) ophthalmic solution contains 1.5% w/v of the
therapeutic agent. Express this concentration in mg/mL.
26. If 100 mL of a solution for patient-controlled anesthesia contains 200 mg of morphine sulfate and 8 mg of droperidol, calculate the percentage strength of each of
these ingredients in the solution.
27. Oxycodone hydrochloride oral concentrate solution (OXYFAST ) contains
20 mg/mL. If a dose of 0.75 mL is added to 30 mL of juice prior to administration, calculate (a) the milligrams of oxycodone hydrochloride administered and
(b) the percent concentration of oxycodone hydrochloride in the drink.
28. A morphine sulfate extended-release liposome injection (DEPODUR) contains
morphine sulfate 10 mg/mL of injection. Calculate the percent strength of morphine sulfate in the injection.
29. A topical solution contains 3% w/v hydroquinone. H ow many liters of the solution can be prepared from 30 g of hydroquinone?
Volume-in-Volume Calculations
30. W hat is the percent strength (v/v) if 225 g of a liquid having a specific gravity of
0.8 are added to enough water to make 1.5 L of the solution?
31. Cyclosporine (GEN GRAF) capsules contain a dispersion of 25 mg of cyclosporine in a hydroalcoholic vehicle. T he labeled content of absolute alcohol content
is “12.8% v/v equivalent to 10.1% w/v.” From these data, calculate the specific
gravity of absolute alcohol.
32. A lotion vehicle contains 15% v/v of glycerin. H ow much glycerin should be used
in preparing 5 gallons of the lotion?
(a) 2271 g glycerin
(b) 3339.7 mL glycerin
(c) 2671.8 g glycerin
(d) 3548.4 g glycerin
33. T he formula for 1 L of an elixir contains 0.25 mL of a flavoring oil. W hat is the
percent strength of the flavoring oil in the elixir?
34. A dermatologic lotion contains 1.25 mL of liquefied phenol in 500 mL. Calculate
the percent strength of liquefied phenol in the lotion.
Weight-in-Weight Calculations
35. Each gram of LOT RISON E lotion contains 10 mg of clotrimazole and 0.643 mg
of betamethasone dipropionate. Calculate the percent concentration of each of
these two agents in the lotion.
36. A hemorrhoidal ointment contains, on a weight-in-weight basis, 46.6% mineral
oil, 1% pramoxine H Cl, and 12.5% zinc oxide in an ointment base. Calculate the
grams of each ingredient, including the ointment base, in each 30-g tube.
104 Pharma euti al c al ulations
37. W hat is the percentage strength (w/w) of a solution made by dissolving 62.5 g of
potassium chloride in 187.5 mL of water?
38. If 500 g of dextrose are dissolved in 600 mL of water with a resultant final volume
of 1 L, what is the percentage strength of dextrose in the solution on a w/w basis?
39. H ydromorphone hydrochloride suppositories contain 3 mg of active ingredient
and weigh approximately 2 g each. W hat is the equivalent percentage strength?
(a) 1.5%
(b) 0.15%
(c) 0.015%
(d) N one of the above
40. A metronidazole vaginal gel contains 0.75% of drug in 70-g tubes. An applicator
will hold 5 g of gel for each administration. H ow much drug will be contained in
each application?
(a) 0.0375 mg metronidazole
(b) 3.75 mg metronidazole
(c) 37.5 mg metronidazole
(d) 375 mg metronidazole
41. T he percent of acyclovir and quantity of lidocaine in the filled prescription are:

Acyclovir (ZOVIRAX) Lidocaine 4% cream aa.

5% cream 15 g

(a) 3.75% acyclovir, 0.3 g lidocaine
(b) 5% acyclovir, 1.2 g lidocaine
(c) 2. 5% acyclovir, 0.6 g lidocaine
(d) 2. 5% acyclovir, 1.2 g lidocaine
42. AN DROGEL 1.62% w/w is a testosterone gel applied topically in males for
endogenous testosterone deficiency. For a starting dose of 40.5 mg testosterone,
calculate the quantity, in grams, of gel administered.
43. DESON AT E gel contains 0.05% w/w desonide. Calculate (a) the quantity of
this agent, in grams, in each 60-g tube of product and (b) the concentration of
desonide, in mg/g of gel.
44. Each gram of an ointment contains 2.5 mg of miconazole nitrate. T he ointment
is available in 50-g tubes. Calculate (a) the percent concentration of miconazole
nitrate in the ointment and (b) the quantity of miconazole nitrate, in grams, in
each tube of ointment.
45. A triamcinolone acetonide topical aerosol spray contains 0.147 mg of triamcinolone acetonide in each gram of product. Calculate the percent strength of triamcinolone acetonide in the product.
46. Calcipotriene (SORILUX) foam, 0.005% w/w, is supplied in containers holding
60 g of product. Calculate the number of milligrams of calcipotriene per container.
47. A topical gel contains 1.2% w/w clindamycin phosphate and 0.025% w/w tretinoin. Calculate the quantity of each of these ingredients on an mg/g basis.
Mixed Percent Calculations
48.12   Progesterone, micronized 4 g
Glycerin 5 mL
Methylcellulose (1%) solution 50 mL
Cherry syrup ad 100 mL
(a) W hat is the percent concentration (w/v) of progesterone in the prescription?
(b) W hat is the percent concentration (w/v) of methylcellulose in the prescription?
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 105
(c) W hat is the percent concentration (v/v and w/v) of glycerin (sp gr 1.25) in
the prescription?
49.13   Lactic acid 4 g
Salicylic acid 5 g
T richloroacetic acid 2 g
Flexible collodion qs ad 100 g
Sig: wart remover. Use as directed.
(a) Flexible collodion contains 20% w/w camphor and 30% w/w castor oil.
H ow many grams of each would be contained in 30 g of the mixture?
(b) T he specific gravity of castor oil is 0.955. H ow many milliliters of the oil
is contained in 30 g of the mixture?
(c) If the specific gravity of the mixture is 0.781, what are the percent w/v concentrations of lactic acid, salicylic acid, and trichloroacetic acid in the mixture?
Ratio Strength Calculations
50. Express each of the following as a percent strength:

(a) 1:1500 (b) 1:10,000 (c) 1:250	(d) 1:400 (e) 1:3300 (f ) 1:4000
51. Express each of the following as a ratio strength:
(a) 0.125% (b) 2.5% (c) 0.80%	(d) 0.6% (e) ⅓% (f ) ½%

52. Express each of the following concentrations as a ratio strength:
(a) 2 mg of active ingredient in 2 mL of solution
(b) 0.275 mg of active ingredient in 5 mL of solution
(c) 2 g of active ingredient in 250 mL of solution
(d) 1 mg of active ingredient in 0.5 mL of solution
53. A doxycycline calcium syrup is preserved with 0.08% w/v of methylparaben,
0.02% w/v of propylparaben, and 0.1% w/v of sodium metabisulfite. Express
these concentrations as ratio strengths.
54. An injection contains 0.5% w/v of lidocaine hydrochloride and 1:200,000 w/v
of epinephrine. Express the concentration of lidocaine hydrochloride as a ratio
strength and that of epinephrine as a percent strength.
55. A sample of white petrolatum contains 10 mg of tocopherol per kilogram as a
preservative. Express the amount of tocopherol as a ratio strength.
56.    Potassium permanganate tablets 0.2 g
Disp. #100
Sig: two tablets in 4 pt of water and use as directed.
Express the concentration, as a ratio strength, of the solution prepared according
to the directions given in the prescription.
57. A skin test for fire ant allergy involves the intradermal skin prick of 0.05 mL of
a 1:1,000,000 w/v dilution of fire ant extract. H ow many micrograms of extract
would be administered in this manner?
58. An eyedrop has the following formula:
Fluorometholone 0.1% w/v
N eomycin sulfate 0.35% w/v

Benzalkonium chloride	0.004% w/v
Isotonic vehicle ad	5 mL

106 Pharma euti al c al ulations
(a) Calculate the ratio strength of benzalkonium chloride in the formula.
(b) Calculate the quantity of fluorometholone, in milligrams, in the formula.
59. A lubricating eyedrop has the following formula:
Polyvinyl alcohol 1.4% w/v
Benzalkonium chloride 0.005% w/v
Sterile vehicle ad 10 mL
Calculate the equivalent ratio strength of the benzalkonium chloride
Parts per Million Calculations
60. Purified water contains not more than 10 ppm of total solids. Express this concentration as a percentage.
61. H ow many grams of sodium fluoride should be added to 100,000 L of drinking
water containing 0.6 ppm of sodium fluoride to provide a recommended concentration of 1.75 ppm?
62. If a commercially available insulin preparation contains 1 ppm of proinsulin, how
many micrograms of proinsulin would be contained in a 10-mL vial of insulin?
Ca l Cq UIz
6.A. AURALGAN Otic Drops contain:

Antipyrine Benzocaine Acetic acid u-Polycosanol 410 Glycerin, ad

5.4% 1.4% 0.01% 0.01% 10 mL

(a) What would be the content of antipyrine, in mg/mL?
(b) If a patient used 5 drops of the otic solution, equivalent to 0.25 mL, how many
milligrams of benzocaine would have been administered?
(c) How many microliters of acetic acid would be used to prepare the 10 mL of drops?
(d) What would be the equivalent ratio strength (v/v) of u-polycosanol 410?
6.B. Among its other ingredients, VISINE-A eyedrops contain the active ingredients:
0.025% w/v naphazoline hydrochloride and 0.3% w/v pheniramine maleate and
1:10,000 w/v benzalkonium chloride as a preservative. Calculate (a) the corresponding percent strength of benzalkonium chloride and (b) the quantities of each of the
three ingredients in a 15-mL container.
6.C. An intravenous solution of AVELOX contains 400 mg of moxifloxacin hydrochloride
(1.6 mg/mL). Calculate (a) the percent concentration of moxifloxacin hydrochloride
and (b) the volume of solution in the product.
6.D. ATROVENT Nasal Spray contains 0.03% w/v of ipratropium bromide in a 30-mL
metered dose container. If the container is calibrated to deliver 345 sprays, calculate
(a) the volume of each spray, in microliters, and (b) the number of milligrams of
ipratropium bromide in each spray.
6.E. A homeopathic teething gel states on its product label that it contains 0.0000003%
alkaloid. Express the alkaloid content in ppm.
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 107
a n SwERS t O “Ca SE In POIn t ” a n d PRa Ct ICE PROb l EmS
Case in Point 6.1
(a) 58 g (weight o illed pycnometer) – 28 g (weight o pycnometer) = 30 g (weight
o 25 mL o albumin solution)
30 g ÷ 25 mL = 1.2, specif c gravity o albumin solution
(b) 2000 mL × 0.05 (5%) = 100 g o albumin needed

25	100
400 = x mL, albumin solution needed	=	;

100
g
mL
g
x mL
(c) 400 mL × 1.2 (speci ic gravity) = 480 g, albumin solution needed
(d) 2000 mL (total solution) – 400 mL (albumin solution) = 1600 mL (0.9%
sodium chloride solution)
1600 mL × 1.05 (specif c gravity) = 1680 g (weight o 0.9% sodium chloride
solution)
1680 g + 480 g = 2160 g (total weight o the 2000 mL)
2160 g ÷ 2000 mL = 1.08, specif c gravity o the mixture
Case in Point 6.2
(a) 30 g × 0.015 (1.5% w/w) = 0.45 g hydrocortisone needed

(b)	4 5 ; . = x mL, hydrocortisone injection	=
0 1 .	0 45 .

1
g
mL
g
x mL
(c) 4.5 mL × 1.5 (speci ic gravity) = 6.75 g (weight o hydrocortisone injection)
30 g – 6.75 g = 23.25 g cold cream needed
Practice Problems
1. 59 mg clobetasol propionate
2. 3 mg o loxacin
3. 0.1% w/v dexamethasone
sodium phosphate
4. 0.01% w/v benzalkonium
chloride
5. (a) 0.025% w/v T PA
(b) 0.025 mL
6. 283.9 mg methylparaben
7. 4% w/v clindamycin phosphate
8. (a) 0.25 mg ketorolac
9. 4.8 g ketoconazole
10. 0.02% w/v inter eron gamma-1b
11. (c) 0.06%
12. (d) 0.5 g levo loxacin and 5 g
dextrose
13. 0.006% w/v darbepoetin alpha,
0.005% w/v polysorbate 80, and
0.818% w/v sodium chloride
14. 5% w/v adalimumab
15. (a) 0.5% w/v erythromycin
lactobionate
(b) 3.125% w/v glycerin
16. 3 mg/mL cipro loxacin and
1 mg/mL dexamethasone
17. (a) 90 g sodium oxybate
(b) 50% w/v sodium oxybate
18. (a) 1 mg/mL
(b) 0.1% w/v
(c) 1:1000 w/v
19. (a) 4.5 mcg ta luprost
(b) 222,222 pouches
20. (d) 0.39% w/v
21. 0.2% w/v hydromorphone
22. 2400 mg nevirapine
23. (c) 0.024 mg/mL misoprostol
24. 0.002% w/v entanyl citrate
25. 15 mg bepotastine besilate/mL
108 Pharma euti al c al ulations
26. 0.2% w/v morphine sulfate and
0.008% w/v droperidol
27. (a) 15 mg oxycodone
hydrochloride
(b) 0.049% w/v oxycodone
hydrochloride
28. 1% w/v morphine sulfate
29. 1 L
30. 18.75% v/v
31. 0.79
32. (d) 3548.4 g glycerin
33. 0.025 v/v flavoring oil
34. 0.25% v/v liquefied phenol
35. 1% w/w clotrimazole and
0.0643% w/w betamethasone
dipropionate
36. 13.98 g mineral oil
0.3 g pramoxine H Cl
3.75 g zinc oxide
11.97 g ointment base
37. 25% w/w potassium chloride
38. 45.45% w/w dextrose
39. (b) 0.15%
40. (c) 37.5 mg metronidazole
41. (c) 2.5% acyclovir, 0.6 g
lidocaine
42. 2.5 g of testosterone gel
43. (a) 0.03 g desonide
(b) 0.5 mg desonide/g gel
44. (a) 0.25% w/w miconazole
nitrate
(b) 0.125 g miconazole
nitrate
45. 0.0147 % w/w triamcinolone
acetonide
46. 3 mg calcipotriene
47. 12 mg/g clindamycin phosphate
and
0.25 mg/g tretinoin
48. (a) 4% w/v progesterone
(b) 0.5% w/v methylcellulose
(c) 5% v/v and 6.25% w/v
glycerin
49. (a) 5.34 g camphor and 8.01 g
castor oil
(b) 8.39 mL castor oil
(c) 3.12% w/v lactic acid,
3.91% w/v salicylic acid, and
1.56% w/v trichloroacetic acid
50. (a) 0.067%
(b) 0.01%
(c) 0.4%
(d) 0.25%
(e) 0.03%
(f) 0.025%
51. (a) 1:800
(b) 1:40
(c) 1:125
(d) 1:166.67 or 1:167
(e) 1:300
(f) 1:2000
52. (a) 1:1000
(b) 1:18,182
(c) 1:125
(d) 1:500
53. 1:1250 w/v methylparaben
1:5000 w/v propylparaben
1:1000 w/v sodium metabisulfite
54. 1:200 w/v lidocaine hydrochloride
0.0005% w/v epinephrine
55. 1:100,000 w/w tocopherol
56. 1:4730 w/v potassium
permanganate
57. 0.05 mg fire ant extract
58. (a) 1:25,000 w/v benzalkonium
chloride
(b) 5 mg fluorometholone
59. 1:20,000 w/v benzalkonium
chloride
60. 0.001% w/v
61. 115 g sodium fluoride
62. 10 mg proinsulin
References
1. United States Pharmacopeial Convention. United States Pharmacopeia 32 N ational Formulary 27. Vol. 1.
Rockville, MD: United States Pharmacopeial Convention, 2009:8.
2. United States Pharmacopeial Convention. United States Pharmacopeia 32 N ational Formulary 27. Vol. 2.
Rockville, MD: United States Pharmacopeial Convention, 2009:1582.
3. Flynn Warren, Clinical Pharmacist, Bishop, GA.
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 109
4. Johnson MG. Tools based on experiences of a community pharmacy providing destruction services for
unwanted medications. Journal of the American Pharmacists Association 2010;50(3):388–392.
5. Gray-Winnett MD, Davis CS, Yokley SG, et al. From dispensing to disposal: the role of student pharmacists in
medication disposal and implementation of a take-back program. Journal of the American Pharmacists Association
2010;50(5):613–618.
6. Office of N ational Drug Control Policy. Proper Disposal of Prescription Drugs. Washington, DC: Office of
N ational Drug Control Policy; 2009. http://www.whitehousedrugpolicy.gov/publications. Accessed July 17,
2014.
7. Federal Register. Secure and Responsible Drug Disposal Act of 2010. Vol. 75. Federal Register; 2010:245.
8. Allen LV Jr, ed. Veterinary dexamethasone 0.1% ophthalmic ointment. International Journal of Pharmaceutical
Compounding 1998;2:147.
9. Allen LV Jr, ed. Erythromycin and dexamethasone ophthalmic solution. International Journal of Pharmaceutical
Compounding 2002;6:452.
10. Ford P. Misoprostol 0.0024% and lidocaine 1% in glycerin mouth paint. International Journal of Pharmaceutical
Compounding 1999;3:48.
11. Allen LV Jr, ed. Fentanyl and bupivacaine injection for ambulatory pump reservoir. International Journal of
Pharmaceutical Compounding 1997;1:178.
12. Allen LV Jr, ed. Progesterone Oral Suspension (40-mg/mL). International Journal of Pharmaceutical Compounding
1998;2:57.
13. Prince SJ. Calculations. International Journal of Pharmaceutical Compounding 2003;7:46.
110
Dose Definitions
T he dose of a drug is the quantitative amount administered or taken by a patient for the
intended medicinal effect. T he dose may be expressed as a single dose, the amount taken at
one time; a daily dose; or a total dose, the amount taken during the course of therapy. A daily
dose may be subdivided and taken in divided doses, two or more times per day depending on
the characteristics of the drug and the illness. T he schedule of dosing (e.g., four times per day
for 10 days) is referred to as the dosage regimen.
Q uantitatively, drug doses vary greatly among drug substances; some drugs have small
doses, while other drugs have relatively large doses. T he dose of a drug is based on its
biochemical and pharmacologic activity, its physical and chemical properties, the dosage
form used, the route of administration, and various patient factors. T he dose of a drug for a
particular patient may be determined in part on the basis of the patient’s age, weight, body
surface area, general physical health, liver and kidney function (for drug metabolism and
elimination), and the severity of the illness being treated. Considerations of some specific
patient parameters in dosing are presented in Chapter 8, and an introduction to pharmacokinetic dosing is presented in Chapter 22. Pharmacokinetic dosing takes into account a
patient’s ability to metabolize and eliminate drugs from the body due to impaired liver or
renal function, which often necessitates a reduction in dosage.
T he usual adult dose of a drug is the amount that ordinarily produces the medicinal
effect intended in the adult patient. T he usual pediatric dose is similarly defined for the
infant or child patient. T he “usual” adult and pediatric doses of a drug serve as a guide
to physicians who may select to prescribe that dose initially or vary it depending on the
assessed requirements of the particular patient. T he usual dosage range for a drug indicates
the quantitative range or amounts of the drug that may be prescribed within the guidelines of usual medical practice. Drug use and dose information is provided in the package
inserts that accompany manufacturers’ pharmaceutical products, from online resources,
and through a variety of references such as Drug Facts and Comparisons1; Physicians’ Desk
Reference2; Pediatric Dosage Handbook: Including Neonatal Dosing, Drug Administration, &
Extemporaneous Preparations3; Geriatric Dosage Handbook4; and Drug Information Handbook.5
T he dose response of individuals varies as depicted in Figure 7.1 and may require dosage
adjustment in a given patient. For certain conditions, as in the treatment of cancer patients,
drug dosing is highly specialized and individualized. Frequently, combinations of drugs are
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

P rform g n ral do al ula on .

P rform al ula on r l an o p f do ng r g m n .
Apply do ng rm nology orr ly n p rform ng pharma u al al ula on .
7
Calculation of Doses:
General Considerations
7 • c al ulation of Doses: General c onsiderations 111
used, with the doses of each adjusted according to the patient’s response. Many anticancer
drugs are administered cyclically, usually for 21 to 28 days, with a rest period between dosing cycles to allow recovery from the toxic effects of the drugs. As presented in Chapter 8,
anticancer drugs are most commonly dosed on the basis of the patient’s body surface area.
T he median effective dose of a drug is the amount that produces the desired intensity of
effect in 50% of the individuals tested. T he median toxic dose of a drug is the amount that
produces toxic effects in 50% of the individuals tested. Drugs intended to produce systemic
effects must be absorbed or placed directly into the circulation and distributed in adequate
concentrations to the body’s cellular sites of action. For certain drugs, a correlation exists
between drug dosage, the drug’s blood serum concentration after administration, and the
presentation and degree of drug effects. An average blood serum concentration of a drug can
be measured, and the minimum concentration determined that can be expected to produce
the drug’s desired effects in a patient. T his concentration is referred to as the minimum effective concentration (MEC). T he base level of blood serum concentration that produces doserelated toxic effects is referred to as the minimum toxic concentration (MT C) of the drug.
Optimally, appropriate drug dosage should result in blood serum drug concentrations
that are above the MEC and below the MT C for the period of time that drug effects are
desired. As shown in Figure 7.2 for a hypothetical drug, the serum concentration of the
Resistant
individuals
Majority of
individuals
Sensitive
individuals
Effect Little Average Great
Increasing response to same dose
umberofindividual FI in a population sample. GURE 7.1 •  Drug effect Time after drug administration (hours)
ve
rageserumconcen FI blood level curve for a hypo- thetical drug as a function of the time after oral administra- tion. (MEC, minimum effective concentration; MTC, minimum toxic concentration.) GURE 7.2 •  Example of a 4.0 2.0 0 21 1 2 3 4 6 8 10 12 14 16 20 MTC MEC
112 Pharma euti al c al ulations
drug reaches the MEC 2 hours a ter its administration, achieves a peak concentration in
4 hours, and alls below the MEC in 10 hours. I it would be desired to maintain the drug
serum concentration above the MEC or a longer period, a second dose would be required
at about an 8-hour time rame. In some cases, incremental dose escalation is employed
whereby the patient is started on a known low dose o a drug ollowed by additional doses
until the desired e ect is achieved.
T he frequency or scheduling o dosing is dependent on many actors including whether
the illness or condition is responsive to short-term or long-term treatment; the physical–
chemical and biologic characteristics o the drug substance itsel ; and eatures o the product ormulation and route o drug administration.
For certain drugs, a larger-than-usual initial dose may be required to achieve the
desired blood drug level. T his dose is re erred to as the loading dose. Subsequent maintenance doses, similar in amount to usual doses, are then administered according to the
dosage regimen to sustain the desired drug blood levels or drug e ects. To achieve the
desired drug blood level rapidly, the loading dose may be administered as an injection or
oral liquid, whereas the subsequent maintenance doses may be administered in other orms,
such as tablets or capsules.
As discussed later in this chapter, there are certain instances in which low-dose therapy
or high-dose therapy is prescribed or a particular patient. And, or certain drugs, there may
be di erent doses required depending on whether the use is or monotherapy, that is, as
the primary drug treatment, or adjunctive therapy, that is, additional to or supportive o a
di erent primary treatment.
Certain biologic or immunologic products, such as vaccines, may be administered in
prophylactic doses to protect the patient rom contracting a speci ic disease. Other products, such as antitoxins, may be administered in therapeutic doses to counter a disease a ter
exposure or contraction. T he doses o some biologic products, such as insulin, are expressed
in units of activity, derived rom biologic assay methods. Calculations pertaining to these
types o products are presented in Chapter 9.
Prefabricated products prepared on a large scale within the pharmaceutical industry
and dispensed in community and institutional pharmacies generally contain the dosage
strengths and dosage orms most o ten used. H owever, in instances in which the desired
strength or dosage orm is not available, pharmacists may be called upon to compound the
preparation. Pharmaceutical products may be prepared to contain one or more therapeutic agents. Products containing more than one therapeutic agent are termed combination
products.
One of the primary responsibilities of the pharmacist is to check doses specified in prescriptions
based on knowledge of the usual doses, usual dose ranges, and dosage regimens of the medicines
prescribed. If an unusual dose is noted, the pharmacist is ethically bound to consult the physician to
make certain that the dose as written or interpreted is the dose intended and that it is suitable for
the patient and condition being treated.
Routes of Drug/Dose Administration and Dosage Forms
Doses o drugs are administered by a variety o dosage orms and routes o administration,
as shown in Table 7.1. In addition to the drug itsel , dosage orms contain phar maceutical ingredients, which provide the physical eatures, stability requirements, and aesthetic
characteristics desired or optimal therapeutic e ects. Included in the array o pharmaceutical ingredients are solvents, vehicles, preservatives, stabilizers, solubilizers, binders, llers,
disintegrants, f avorants, colorants, and others.
7 • c al ulation of Doses: General c onsiderations 113
W ith added pharmaceutical ingredients, the quantity of an active ingredient in a dosage form
represents only a portion (often a small portion) of the total weight or volume of a product. For
example, a tablet with 10 mg of drug actually could weigh many times that amount because of the
added pharmaceutical ingredients.
Definitions of the various dosage forms and drug delivery systems are found in
Appendix B.
Dose Measurement
In the institutional setting, doses are measured and administered by professional and paraprofessional personnel. A variety of measuring devices may be used, including calibrated
cups and oral syringes for liquid oral medications (Figs. 7.3 and 7.4). For pediatric patients,
use of oral syringes is recommended as a means of reducing medication dosing errors.6 In
hospitals, many medications are administered by injection and by intravenous infusion.
In the home setting, the patient, the caregiver, or, in the case of a child, the parent
generally measures and administers oral medication. Liquids are measured using household
measures such as teaspoons and tablespoons (Table 7.2), calibrated spoons or cups, oral
Tab e 7.1 •  SEl ECTED Ro UTES o F ADmIn ISTRATIo n An D REpRESEn TATIvE Do SAGE Fo RmS

R ute f Ad i istrati Oral (mouth, GI tract) Sublingual (under the tongue) Parenteral (injection) Epicutaneous/transdermal (skin) Conjunctival (eye) Intranasal (nose) Intrarespiratory (lungs) Rectal (rectum) Vagina (vagina) Urethral (urethra)

Re rese tati e D sage F r s Tablets, capsules, lozenges, solutions, drops, syrups, and suspensions Tablets Solutions and suspensions Ointments, creams, powders, lotions, aerosols, and patches Solutions, suspensions, and ointments Solutions, sprays, and ointments Aerosols and inhalant solutions Ointments, creams, suppositories, solutions, and suspensions Ointments, creams, tablets, suppositories, gels, solutions, and emulsion foams Solutions and suppositories

FIGURE 7.3 •  An example
of a calibrated medication cup
for administering oral liquid
medication.
114 Pharma euti al c al ulations
syringes, or drops. Patients being treated by home health care personnel may receive medications by all routes o administration including parenteral.
Teaspoon and Tablespoon
H ousehold spoons vary greatly in capacities. Due to the variability in capacity, the Food and
Drug Administration has issued the ollowing statement: “Do not use common household spoons
to measure medicines for children since household spoons come in different sizes and are not meant for
measuring medicines.”7 Instead, the FDA urges the use o the measuring device that accompanies a specif c product or another device that is calibrated to deliver the recommended dose.
A calibrated oral syringe o ten is a good option.
In approximate terms, and in dosage calculations, the teaspoon is considered to hold 5 mL of
volume and the tablespoon 15 mL (Table 7.2).8 Occasionally, a prescriber will indicate a teaspoon ul dose by using the luidram symbol (flʒ) in the Signa portion o a prescription, and
the pharmacist interprets it accordingly.a
The Drop as a Unit of Measure
Occasionally, the drop (abbreviated gtt) is used as a measure or small volumes o liquid
medications. A drop does not represent a def nite quantity, because drops o di erent
liquids issued rom di erent droppers vary greatly. In an attempt to standardize the drop
as a unit o volume, the United States Pharmacopeia def nes the o f cial medicine dropper as being constricted at the delivery end to a round opening with an external diameter o about 3 mm.9 T he dropper, when held vertically, delivers water in drops, each o
aT he fluidram ( lʒ) is a quantity in the Apothecaries’ system as presented in Appendix A.
FIGURE 7.4 •  An example of
calibrated Exacta-Med Oral Dispenser
for administering liquid medication to
pediatric patients. (Courtesy of Baxter
Healthcare Corporation.)
Tab e 7.2 •  USEFUl AppRo xImATE Eq UIvAl En T o F Ho USEHo l D mEASURE

H useh d measure (Abbre iati ) 1 teaspoonful (tsp.)

o u ce ≈1/6 fluidounce ≈

metric measure 5 mL

1 tablespoonful (tbsp.) ≈1/2 fluidounce ≈ 15 mL
7 • c al ula ion of Doses: General c onsidera ions 115
which weighs between 45 and 55 mg. Accordingly, the o f cial dropper is calibrated to
deliver approximately 20 drops o water per milliliter (i.e., 1 mL o water = 1 gram or
1000 mg ÷ 50 mg [ave.]/drop 20 drops).
It should be kept in mind that ew medicinal liquids have the same sur ace and
low characteristics as does water, and there ore, the size o drops varies materially
rom one liquid to another. T he drop should not be used as a measure or a speci ic
liquid medication until the volume that the drop represents has been determined or
that liquid. T his determination is made by calibrating the dispensing dropper. Most
manu acturers include a specially calibrated dropper along with their prepackaged
medications or use by patients in measuring dosage. Examples o calibrated droppers
are shown in Figure 7.5.
A dropper may be calibrated by counting the drops o a liquid as they all into a graduate until a measurable volume is obtained. T he number o drops per unit volume is then
established (e.g., 20 drops/mL).
(1) I a pharmacist counted 40 drops o a medication in f lling a graduate cylinder to the
2.5-mL mark, how many drops per milliliter did the dropper deliver?
40 2 5
1
( )
( )
. ( )
( )
drops
x drops
mL
mL
x
= =
16 drops mL
General Dose Calculations
A pharmacist o ten needs to calculate the size o a dose, the number o doses, or the
total quantity o medication to dispense. For these calculations, the ollowing equation
CASE In po In T 7.1 A physi ian asks a pharma is o al ula e he dose of a
ough syrup so ha i may e safely adminis ered dropwise o a hild. t he ough
syrup on ains he a ive ingredien dex rome horphan Hb r, 30 mg/15 mL, in a
120-mL o le.
b ased on he hild’s weigh and li era ure referen es, he pharma is de ermines
he dose of dex rome horphan Hb r o e 1.5 mg for he hild.
t he medi ine dropper o e dispensed wi h he medi a ion is ali ra ed y he
pharma is and shown o deliver 20 drops of he ough syrup per 1 mL.
c al ula e he dose, in drops, for he hild.
FIGURE 7.5 •  Examples of
calibrated droppers used in
the administration of pediatric
medications.
116 Pharma euti al c al ulations
is useful with the terms rearranged depending on the answer required. In using the equation, the units of weight or volume must be the same for the total quantity and size of
the dose.
N umber of doses
T otal quantity
Size of dose
=
Example Calculations of the Number of Doses
(1) If the dose of a drug is 200 mg, how many doses are contained in 10 g?
10 10 000
10 000
200

g

mg mg

N umber of doses mg
=
= =
,
, ( )
( )
50 doses
Or, solving by dimensional analysis:
1
200
1000
1
dose 10
mg
mg
g
× × = g 50 doses
(2) If 1 tablespoonful is prescribed as the dose, approximately how many doses will be contained
in 1 pint of the medicine?
1 15

1 pint	473
473

15
31 5
tablespoonful mL
N umber of doses mL
mL
==
= = . or 31 doses
(3) If the dose of a drug is 50 mg, how many doses are contained in 0.02 g?
0 02 20
50 0 05
20
0 05
.
.
( )
. ( )
g mg
g mg
N umber of doses mg
mg
==
= =
m
400 doses
Example Calculations of the Size of a Dose
Size of dose T otal quantity
N umber of doses
=
T he size of the dose is expressed in whatever denomination is chosen for measuring the given
total quantity.
(1) How many teaspoonfuls would be prescribed in each dose of an elixir if 180 mL contained
18 doses?
Size of dose = = = 180 mL mL
18
10 2 teaspoonfuls
(2) How many drops would be prescribed in each dose of a liquid medicine if 15 mL contained
60 doses? The dispensing dropper calibrates 32 drops/mL.
15 15 32 480 mL drops drops = × =
Size of dose = = 480 drops
60
( )
8 drops
7 • c al ulation of Doses: General c onsiderations 117
Or, solving by dimensional analysis:
32
1
1
60
drops 15
mL doses
× × = mL 8 drops dose /
Example Calculations of the Total Quantity of Product
Total quantity = numbers of doses ¥ size of dose
It is convenient first to convert the given dose to the denomination in which the total
quantity is to be expressed.
(1) How many milliliters of a liquid medicine would provide a patient with 2 tablespoonfuls
twice a day for 8 days?
N umber of doses = 16

Size of dose	= 2 tablespoonfuls or 30 mL
Total quantity	= 16 × 30 mL = 480 mL
(2) How many milliliters of a mixture would provide a patient with a teaspoonful dose to be
taken three times a day for 16 days?
N umber of tsp doses = 16 × 3 = 48 tsp
Total quantity	= 48 × 5 mL = 240 mL

(3) How many grams of a drug will be needed to prepare 72 dosage forms if each is to contain
30 mg?
N umber of doses = 72

Size of dose	= 30 mg
Total quantity	= 72 × 30 mg = 2160 mg = 2.16 g

(4) It takes approximately 4 g of ointment to cover an adult patient’s leg. If a physician
prescribes an ointment for a patient with total leg eczema to be applied twice a day
for 1 week, which of the following product sizes should be dispensed: 15 g, 30 g, or
60 g?
N umber of doses = 2 per day × 7 days = 14

Size of dose	= 4 g
Total quantity	= 14 × 4 g = 56 g; thus 60 g product size

Additional Examples of Calculations of Dose
(1) If 0.05 g of a substance is used in preparing 125 tablets, how many micrograms are represented in each tablet?
0 05 50 50 000
50 000
125
. ,
, ( )
g mg g
g
= =
=
m
m
400 g m
Or, solving by dimensional analysis:
1 000 000
1
1
125
, , mg 0 05 . /
g tablets
× × = g 400 g tablet m
118 Pharma euti al c al ulations
(2) I a preparation contains 5 g o a drug in 500 mL, how many grams are contained in each
tablespoon ul dose?
1 15
500
15
5
tablespoonful mL
mL
mL
g
x
x
= = =
( )
( )
( )
0 15 g .
(3) A cough mixture contains 48 mg o hydromorphone hydrochloride in 8 f . oz. How many
milligrams o hydromorphone hydrochloride are in each 2-teaspoon ul dose?
1 f . oz. = 6 tsp
8 f . oz. = 48 tsp
48 tsp ÷ 2 = 24 doses
48 tsp ÷ 24 = 2 mg
Or,
48
2
( ) 48
( )
( )
( )
tsp
tsp
mg
x mg
x
= =
2 mg
(4) How many milligrams each o hydrocodone bitartrate and guai enesin will be contained in
each dose o the ollowing prescription?

H ydrocodone bitartrate	0.12 g
Guai enesin Cherry syrup ad Sig. teaspoon ul or cough	2.4 g 120 mL

1 teaspoon ul = 5 mL
120 ÷ 5 = 24 doses
0.12 g ÷ 24 = 0.005 g = 5 mg hydrocodone bitartrate and
2.4 g ÷ 24 = 0.1 g = 100 mg guaifenesin
(5) How many grams o a drug substance are required to make 120 mL o a solution each
teaspoon ul o which contains 3 mg o the drug substance?
1 5

5	3
120

72
teaspoonful mL
mL
mL
mg
x mg
x mg or
= = =
( )
( )
( )
( )
0 072 g .
Or, solving by dimensional analysis:
1
1000
3 5
120
g
mg
mg
mL
× × = mL 0 072 g .
(6) A physician ordered 500-mg capsules o tetracycline to be taken twice a day or 10 days.
How many total grams o tetracycline would be prescribed?

Size o dose	= 500 mg
Total number o doses = 2 (a day) × 10 (days) = 20 doses
Total quantity	= 500 mg × 20 (doses) = 10,000 mg = 10 g

7 • c al ulation of Doses: General c onsiderations 119
Dosing Options
Low-Dose and High-Dose Therapies
T he administration o doses that are much smaller or much larger than the usual dose o a
drug is re erred to as low-dose or high-dose therapy, respectively. T his terminology is di erent
in intent rom the normal variation in a standard dose based on a patient’s age, weight, renal
unction, or other speci c parameter.
T he most common example o low-dose therapy is the use o aspirin in 81-mg amounts
(rather than the usual dose o 325 mg) to lower the risk o heart attack and clot-related
stroke. Other examples are low-dose oral contraceptive use10 and low-dose postmenopausal
hormone therapy.11
H igh-dose therapy is commonly associated with the chemotherapeutic treatment o
cancer, in which there is an attempt, through increased dose intensity, to kill tumor cells.
Other examples are the high-dose use o progestin in the treatment o endometriosis12 and
the high-dose in luenza vaccination o the elderly.13
Pharmacists must be aware o the use o high-dose therapies while remaining
vigilant in protecting patients against unintended high doses and consequent drug
overdose.
Example Calculations of Low-Dose and High-Dose Therapies
(1) I a patient is changed rom a daily standard-dose postmenopausal product containing
0.625 mg o conjugated estrogens (CE) to a low-dose ormulation containing 0.35 mg CE,
how many milligrams less o CE would the patient take per week?
0 625 0 35 0 275 7 . . . ( ) . mg mg mg days – = × = 1 925 mg conjugated estrogens
(2) To reduce the inf ammation o an optic nerve, a patient is administered high-dose prednisone, 900 mg/day or 5 days by intravenous in usion. The usual daily dose o prednisone is 5
to 60 mg/day, depending on the condition being treated. Calculate the dose that the patient
received, as a multiple o the highest usual daily dose.
900
60
mg
mg
= 15 multiple of the highest usual dose ,
Fixed-Dose Combination Products
A variety o prescription and nonprescription products are available containing two or more
therapeutic agents in xed-dose combinations. An advantage o combination products is
that two or more needed drugs may be taken in a single dose, which may be more convenient, enhance compliance, and be less expensive or the patient than taking the same drugs
individually. A disadvantage is the relative inf exibility in dosing compared with individual
drug dosing.
W hether the ixed-dose combination is a liquid (e.g., a syrup) or a solid (e.g., a tablet)
dosage orm, when a dose is taken, the component drugs are taken in a ixed-dose ratio. To
provide some options in dosing, many combinations o prescription drugs are ormulated
into di erent strengths. For example, capsules containing amlodipine and benazepril H Cl
(LOT REL), two drugs used in the treatment o hypertension, are available in strengths o
2.5 mg/10 mg, 5 mg/10 mg, 5 mg/20 mg, 5 mg/40 mg, 10 mg/20 mg, and 10 mg/40 mg.
T he prescriber can select the desired combination.
120 Pharma euti al c al ulations
Example Calculation Based on Fixed-Dose Combination Products
Valsartan and hydrochlorothiazide tablets are available separately or in combination in strengths of
80 mg/12.5 mg, 160 mg/12.5 mg, 160 mg/25 mg, and 320 mg/12.5 mg. If a patient was receiving
the lowest-dose combination product and the physician wished to double the dose of hydrochlorothiazide, what is the option?
An additional prescription or 12.5 mg o hydrochlorothiazide or individual prescriptions or 80 mg o valsartan and 25 mg o hydrochlorothiazide may be written.
Tablet Splitting and Crushing
A number o tablets are scored, or grooved, to allow breaking into approximately equal
pieces (usually halves). T his allows dosage f exibility, particularly when a patient is started
at a hal dose and then is titrated up to a ull dosage level. It also enables a patient to take a
product at a strength that is not otherwise available.
Some patients use tablet-splitting devices to cut scored or unscored tablets or economic reasons. For some medications, the price o tablets o twice the strength required is
similar to the lower-strength tablets, and the patient can double his or her supply by tablet
splitting. Un ortunately, this practice o ten results in unequal portions o tablets and thus
in uneven doses.14–17
T he ederal Food and Drug Administration (FDA) has recommended that consumers
consult with their health care pro essional be ore splitting a tablet to discuss the “splitability” o the product.18 (Some products should not be split or crushed, but must remain
intact or proper e ects.) As a part o its drug approval process, the FDA veri ies drug
products that have been shown by testing procedures to be capable o being e ectively
split.19,20
Pharmacists can provide guidance to their patients by (a) veri ying tablets that may be
sa ely split, (b) suggesting that the entire dispensed supply o tablets not be split at one time
but only as needed since split tablets may be more a ected than whole tablets by actors
such as heat and humidity, and (c) suggesting the best device or tablet splitting, especially
or tablets o unique shape and size.
For tablets that can be crushed without destroying desired absorption characteristics,
tablet crushing is a commonly employed practice or home or institutional patients who are
unable to swallow intact solid dosage orms. In these instances, mortars and pestles or specially designed tablet crushers may be used (Fig. 7.6). A ter crushing, the resulting particles
may be suspended in a beverage or mixed with a oodstu such as applesauce or yogurt
prior to administration.
FIGURE 7.6 •  An example of a tablet crusher. A tablet is placed
in a paper cup, covered with a second cup, and then placed in
the crusher. When the handles are gently squeezed, the pressure
reduces the tablet to particles that may then be mixed with food
or drink for administration. The device is used in patient care
facilities and wherever a patient may have difficulty swallowing whole dosage units. (Courtesy of Creative Living Medical,
Brainerd, MN.)
7 • c al ulation of Doses: General c onsiderations 121
Example Calculation Based on Tablet Splitting
A patient attempted to split in half 20-mg unscored tablets of a drug, resulting in “half tablets” differing by 1.5 mg in drug content. Assuming a whole tablet was uniform in drug content, calculate
the amount of drug in each “half tablet.”
If L = larger “half” and S = smaller “half,”

then L + S = 20 mg

L S mg L mg – = = 1 5 2 21 5

.
.
L = 10.75 mg
S = 20 mg – 10.75 mg = 9.25 mg
Proof: 10.75 mg – 9.25 mg = 1.5 mg difference in drug content and
10.75 mg + 9.25 mg = 20 mg total drug content
Special Dosing Regimens
Certain drugs have unique dosing regimens. Among them are chemotherapeutic agents (discussed in Chapter 8) and oral contraceptives. In the case of the latter, the prescribed regimen
is based on a 28-day dosing cycle of 21 consecutive days of tablets containing a combination
of estrogenic and progestational drugs followed by 7 consecutive days of tablets containing
nondrug material. One tablet is taken daily, preferably at approximately the same time. T he
tablets generally are color-coded and packaged in special dispensers to facilitate compliance.
Another example of a drug having a special dosing regimen is methylprednisolone,
as prescribed in dose packs containing 21 tablets of 4 mg each. T he tablets are taken in
descending dosage over a 6-day period in the treatment of responsive allergic and inflammatory conditions as contact dermatitis. In this regimen, 6 tablets are taken during the first
day with 1 fewer tablet being taken each day thereafter.
Example Calculation Based on Special Dosing Regimen
The ORTHO TRI-CYCLEN LO 28-day regimen consists of norgestimate (N), ethinyl estradiol
(EE), and nonmedicated tablets as follows:
7 white tablets containing 0.18 mg ( N ) + 0.025 mg (EE)
7 light blue tablets containing 0.215 mg ( N ) + 0.025 mg (EE)
7 dark blue tablets containing 0.25 mg ( N ) + 0.025 mg (EE)
7 green tablets containing 0 mg ( N) + 0 mg (EE)
How many milligrams each of norgestimate and ethinyl estradiol are taken during each 28-day
cycle?

N orgestimate :

mg mg mg mg . . . . 0 18 7 1 26 0 215 7 1 505 × = × =

mg
. .
0 25 7 1 75
× = mmg
4 515 mg norgestimate and .

Ethinyl estradiol :

mg mg mg mg . . . . 0 025 7 0 175 0 025 7 0 175 × = × =

mg
.
0 025
×× = 7 0 175 .
.
mg
0 525 mg ethinyl estradiol
122 Pharma euti al c al ulations
pRACTICE pRo b l EmS
Doses: Solid Dosage Forms
1. T he ascending dose schedule of ropinirole (REQ UIP) in the treatment of Parkinson’s
disease is:
Week 1: 0.25 mg three times a day
Week 2: 0.5 mg three times a day
Week 3: 0.75 mg three times a day
Week 4: 1 mg three times a day
H ow many 0.25-mg tablets would provide the 4 weeks of treatment?
2. T he following regimen for oral prednisone is prescribed for a patient: 50 mg/
day × 10 days; 25 mg/day × 10 days; 12.5 mg/day × 10 days; and 5 mg/
day × 10 weeks. H ow many scored 25-mg tablets and how many 5-mg tablets
should be dispensed to meet the dosing requirements?
3. A physician reduces a patient’s once-daily dose of conjugated estrogen
(PREMARIN) from tablets containing 0.625 mg to tablets containing 0.45 mg.
W hat is the total reduction in conjugated estrogens taken, in milligrams, during
a 30-day month?
4. A fixed-dose combination product contains amlodipine besylate and atorvastatin
calcium (CADUET ) for the treatment of both hypertension and hypercholesterolemia. If a physician starts a patient on a 5-mg/10-mg dose for 14 days and
then raises the dose to 10 mg/20 mg, how many milligrams of each drug will the
patient take during the first 30 days?
5. A patient cuts 100-mg scored tablets to take his 50-mg prescribed daily dose.
A prescription for thirty 100-mg tablets costs $45, and a prescription for thirty
50-mg tablets costs $40. T he patient asked the pharmacist to weigh an uncut
tablet on an electronic balance into two “halves.” T he uncut tablet was found to
weigh 240 mg, and the cut “halves” weighed 125 mg and 115 mg, respectively.
(a) H ow much money did the patient save on a monthly basis by dosing with half
tablets? (b) W hat was the percentage error in the weight of the cut tablets compared with “exact halves”?
6. T he recommended dose of memantine H Cl (N AMEN DA) is:
Week 1, 5 mg/day
Week 2, 10 mg/day (5 mg b.i.d.)
Week 3, 15 mg/day (10 mg a.m., 5 mg p.m.)
Week 4, 20 mg/day (10 mg b.i.d.)
H ow many 5-mg tablets must be dispensed for a 4-week supply of the medication?
7. Prior to a colonoscopy, a patient is instructed to take OSMOPREP tablets each of
which contains 1.102 g sodium phosphate monobasic monohydrate and 0.398 g
sodium phosphate dibasic anhydrous. T he dose is:
The evening before the procedure: 4 tablets with 8 ounces of clear liquids every
15 minutes for 5 cycles
Starting 3 hours before the procedure: 4 tablets with 8 ounces of clear liquids
every 15 minutes for 3 cycle
How many tablets, how much liquid, and how much total sodium phosphates are taken?
(a) 8 tablets, 16 ounces liquid, 2 g sodium phosphates
(b) 16 tablets, 1000 mL liquid, 32 g sodium phosphates
(c) 32 tablets, 1 quart liquid, 40 g sodium phosphates
(d) 32 tablets, 0.5 gallon liquid, 48 g sodium phosphates
7 • c al ulation of Doses: General c onsiderations 123
8. Varenicline tartrate (CH AN T IX), for smoking cessation, is available in two
strengths, 0.5-mg and 1-mg tablets. T he dose is:
Days 1 to 3: 0.5 mg once daily
Days 4 to 7: 0.5 mg twice daily (am and pm)
Days 8 to end of treatment: 1 mg twice daily (am and pm)
T he treatment period is 12 weeks. H ow many 0.5-mg tablets and 1-mg tablets
should be dispensed?
(a) 7 0.5-mg tablets and 11 1-mg tablets
(b) 8 0.5-mg tablets and 84 1-mg tablets
(c) 10 0.5-mg tablets and 84 1-mg tablets
(d) 11 0.5-mg tablets and 154 1-mg tablets
Doses: Drops
9. A ciprofloxacin otic solution contains 0.5 mg of ciprofloxacin in a 0.25-mL singledose package. Based on 20 drops/mL, (a) how many drops would be administered
and (b) how many micrograms of ciprofloxacin would be in each drop?
10.
(a) If acetaminophen oral drops contain 1.5 g of acetaminophen per 15-mL container, how many milligrams are there in each prescribed dose?
(b) If the dropper is calibrated to deliver 22 drops/mL, how many drops should
be administered per dose?
11. RESTASIS ophthalmic emulsion contains 0.05% w/v cyclosporin. If a dose of
one drop measures 28 mL, how many micrograms of cyclosporin are present?
12.21 T he oral dose of a drug is 2.5 mg. If a solution contains 0.5% w/v of the drug in
a dropper bottle that delivers 12 drops/mL, how many drops would supply the
dose?
13. Infants’ MYLICON antigas drops contain 2 g of simethicone in a 30-mL container. (a) H ow many milligrams of simethicone are contained in each 0.3-mL
dose? And if 12 doses per day are not to be exceeded, calculate the corresponding
12-dose (b) volume and (c) simethicone content.
Doses: Oral Liquids
14. Rimantadine H Cl syrup contains 2.4 g of rimantadine H Cl in each 240 mL of
syrup. H ow many milligrams of rimantadine H Cl would there be in 2.5 mL
delivered by oral dispenser?
15. If a liquid medicine is to be taken three times daily, and if 180 mL are to be taken
in 4 days, how many tablespoonfuls should be prescribed for each dose?
16. T he usual starting dose of sodium oxybate is 4.5 g per night in two equally divided
doses, taken 2.4 to 4 hours apart. A sodium oxybate oral solution is available in
180-mL bottles, containing sodium oxybate, 50% w/v. H ow many divided doses
are available in each container?
17. T he dose of posaconazole in the treatment of oropharyngeal candidiasis is 100 mg
twice a day on the first day and then 100 mg once a day for the next 13 days.
Posaconazole oral suspension (posaconazole, 40 mg/mL) is available in 4-fluidounce
bottles. H ow many bottles should be dispensed to meet the dosing requirements?
Acetaminophen oral drops
Disp. 15 mL
Sig. 0.5 mL t.i.d.
124 Pharma euti al c al ulations
18. A physician prescribes tetracycline H Cl syrup for a patient who is to take 2 teaspoonfuls four times per day for 4 days, and then 1 teaspoonful four times per day
for 2 days. H ow many milliliters of the syrup should be dispensed to provide the
quantity for the prescribed dosage regimen?
19. Ipecac oral solution has the following formula:
Powdered ipecac 70 g

Glycerin Syrup ad

100 mL 1000 mL

Powdered ipecac contains 2 grams of the combined alkaloids emetine and cephaeline in each 100 grams of powder. Calculate the quantity of these alkaloids, in
milligrams, in each 5-mL dose of ipecac oral solution.
20. A dose of digoxin for rapid digitalization is a total of 1 mg, divided into two or
more portions at intervals of 6 to 8 hours. H ow many milliliters of digoxin elixir
containing 50 mg/mL would provide the 1 mg dose?
21. Ciprofloxacin (CIPRO) oral suspension contains 250 mg of ciprofloxacin per
5 mL. A physician prescribed 125 mg of ciprofloxacin q.i.d. × 10 days. (a) H ow
many doses are needed? (b) H ow many milliliters should be given per dose? (c)
H ow many milliliters of ciprofloxacin oral suspension containing 250 mg per
5 mL should be dispensed?
22. A patient has been instructed to take 15 mL of alumina and magnesium oral suspension every other hour for four doses daily. H ow many days will two 12-fl. oz.
bottles of the suspension last?
23.
H ow many grams of dextromethorphan H Br would be needed to fill the
prescription?
24. T he dose of AUGMEN T IN oral suspension for a patient is 5 mL b.i.d. Each
5 mL of suspension contains 400 mg of amoxicillin and 57 mg of clavulanic acid.
If the suspension is to be taken for 10 days and is available in 50-mL, 75-mL, and
100-mL containers, calculate (a) the least wasteful package size to dispense and
(b) total quantity of amoxicillin taken during the treatment period.
Doses: Injections
25. A physician ordered 20 mg of MEPERGAN and 0.3 mg of atropine sulfate to be
administered preoperatively to a patient. MEPERGAN is available in a syringe
containing 25 mg/mL, and atropine sulfate is in an ampul containing 0.4 mg per
0.5 mL. H ow many milliliters of each should be used in filling the medication order?
26. H ow many milliliters of an injection containing 250 mg of aminophylline in
each 10 mL should be used in filling a medication order calling for 15 mg of
aminophylline?
27.22 Pediatric LAN OXIN injection contains digoxin, 100 mcg/mL. W hat volume
must be administered to provide a dose of 0.04 mg?
28. In treating Crohn’s disease, the recommended dose of the monoclonal antibody
adalimumab (H UMIRA) is 160 mg as the first dose, a second dose of 80 mg
2 weeks later, then a third dose of 40 mg 2 weeks after the second dose, and
followed by a maintenance dose of 40 mg every 2 weeks. H ow many prefilled
syringes, each containing adalimumab, 40 mg/0.8 mL, would be required for the
initial 2 months of treatment?
Dextromethorphan H Br 50 mg/tsp
Guaifenesin syrup ad 120 mL
Sig. ʒi q.i.d. a.c. & h.s.
7 • c al ulation of Doses: General c onsiderations 125
29. BYET TA injection, as an adjunct for glycemic control in type 2 diabetes mellitus, contains 250 mcg of exenatide in each milliliter of solution. T he injection is
available in 1.2-mL prefilled pens. At a starting dose of 5 mcg b.i.d, (a) how many
milliliters are injected per dose, (b) how many doses are contained in each pen,
and (c) how many days will the dosing pen last the patient?
30. T he biotechnology drug peginterferon alpha-2b is administered at a starting
dose of 6 mcg for each kilogram of a patient’s body weight (6 mcg/kg). T he
drug is available in single-use 0.74-mL injections containing 40 mcg/0.1 mL,
60 mcg/0.1 mL, or 120 mcg/0.1 mL. W hich product size would be most efficacious for administration to a 156-lb patient?
Doses: Other Dosage Forms
31. T he recommended maintenance dose of beclomethasone dipropionate
(BECLOVEN T ), an aerosolized inhalant, is 100 mcg administered twice daily.
T he commercial inhaler delivers 50 mcg per metered inhalation and contains
200 inhalations. H ow many inhalers should be dispensed to a patient if a 60-day
supply is prescribed?
32. A 16-week regimen for a brand of a nicotine patch calls for a patient to wear a
21-mg patch each day for the first 6 weeks, followed by a 14-mg patch each day
for the next 2 weeks, and then a 7-mg patch for the next 2 weeks to conclude the
treatment regimen. In all, how many milligrams of nicotine are administered?
33. A transdermal patch contains 5 mg of fentanyl and has a drug-release rate of
50 mcg/hour. T he patch is worn for 72 hours. Calculate (a) the milligrams of fentanyl delivered daily, (b) the milligrams of fentanyl remaining in the patch when it is
removed, and (c) the percentage of drug remaining in the patch when it is removed.
34. If a VEN T OLIN inhaler contains 20 mg of albuterol, how many inhalation doses
can be delivered if each inhalation dose contains 90 mcg?
35. FLON ASE nasal spray contains 50 mcg of fluticasone propionate per actuation
spray in each 100 mg of formulation. Each container provides 120 metered sprays.
H ow many milligrams of fluticasone propionate are contained in each container?
36. T he dose of diclofenac sodium (VOLTAREN GEL), when applied to the hands
in the treatment of arthritic pain, is 2 g four times a day. T he gel contains diclofenac sodium 1% and is available in 100-g tubes. H ow many grams of the drug
diclofenac sodium would be administered per day, and how many days of treatment would be available per tube of gel?
(a) 8 g diclofenac sodium per day for 8 days
(b) 8 g diclofenac sodium per day for 12.5 days
(c) 80 mg diclofenac sodium per day for 8 days
(d) 0.08 g diclofenac sodium per day for 12.5 days
37. SYMBICORT 80/4.5 is an oral inhalation product containing 80 mcg of budesonide
and 4.5 mcg of formoterol fumarate per inhalation. T he dose is stated as “two inhalations twice daily.” H ow much of each drug would be administered daily?
(a) 160 mcg budesonide and 9 mcg formoterol fumarate
(b) 0.32 mg budesonide and 0.18 mg formoterol fumarate
(c) 320 mcg budesonide and 0.18 mg formoterol fumarate
(d) 0.32 mg budesonide and 0.018 mg formoterol fumarate
38. An aerosol oral inhaler delivers, per actuation, 40 mcg of beclomethasone dipropionate. T he recommended starting dose is 40 to 80 mcg twice daily. T he highest
recommended dose is 320 mcg twice daily. Compare the number of daily inhaler
actuations to deliver the lowest starting dose and the highest recommended dose.
126 Pharma euti al c al ulations
CAl Cq UIz
7.A. The ophthalmic solution ALPHAGAN P contains 0.15% brimonidine tartrate in
10-mL containers. The recommended dose is one drop in the affected eye(s) three
times daily. If a glaucoma patient doses each eye, and the dropper used delivers
20 drops/mL, calculate the quantity, in milligrams, of brimonidine tartrate administered each day.
7.B. The starting dose of sodium oxybate oral solution (XYREM) is 4.5 g/night divided
into two equal doses and administered 2.5 to 4 hours apart. How many milliliters of
the oral solution containing sodium oxybate, 500 mg/mL, should be administered in
each divided dose?
7.C. A pediatric stool softener contains 393.3 mg of docusate sodium in each four fluid
ounce (118 mL) container. If the labeled dose is 2 tablespoonful for a 5-year-old
child, how many milligrams of docusate sodium would be contained per dose?
7.D. An oral inhalation (DULERA) to treat asthma provides in each inhalation 100 µg of
mometasone furoate and 5 µg of formoterol fumarate. The recommended dose is
“two inhalations twice daily (morning and evening).” Calculate the quantity, in milligrams, of each drug inhaled daily.
7.E. In an experiment of tablet-splitting effectiveness, a pharmacist had a pharmacy
student split a previously weighed lisinopril tablet containing 20 mg of drug. On
an electronic balance, the whole tablet weighed 111.62 mg. After splitting, one
“half tablet” weighed 51.21 mg and the other “half,” 58.49 mg. There was residue powder remaining. Calculate (a) the percent of lost tablet (residue), (b) the
percent accuracy in actual weight (to ideal weight) for each “half tablet,” and
(c) the supposed quantity of drug, in milligrams (not assayed, of course) in each
“half tablet.”
An SwERS To “CASE In po In T” An D pRACTICE pRo b l EmS
Case in Point 7.1
First, calculate the volume of cough syrup containing the child’s dose of 1.5 mg of
dextromethorphan H Br:

30 mg	1 5 mg
0 75 = x mL	=

15
mL
x mL
.
; .
T hen determine the number of drops of cough syrup that will provide the 0.75-mL
dose:
1
20
0 75
15
mL
drops
mL
x drops
x drops of cough syrup
= =
.
;
7 • c al ulation of Doses: General c onsiderations 127
Practice Problems
1. Two hundred ten 0.25-mg ropinirole tablets
2. T hirty-five 25-mg tablets and
seventy 5-mg tablets
3. 5.25 mg conjugated estrogen
4. 230 mg amlodipine besylate and
460 mg atorvastatin calcium
5. (a) $17.50
(b) 4.2%
6. 70 tablets
7. (d) 32 tablets, 0.5 gallon liquid,
48 g sodium phosphates
8. (d) 11 0.5-mg tablets and 154
1-mg tablets
9. (a) 5 drops ciprofloxacin otic
solution
(b) 100-mg ciprofloxacin/drop
10. (a) 50 mg acetaminophen
(b) 11 drops
11. 14 mcg cyclosporine
12. 6 drops
13. (a) 20 mg simethicone
(b) 3.6 mL of infants’ MYLICON
drops
(c) 240 mg simethicone
14. 25 mg rimantadine H Cl
15. 1 tablespoonful
16. 40 divided doses sodium oxybate
oral solution
17. 1 bottle of posaconazole oral
suspension
18. 200 mL tetracycline H Cl syrup
19. 7 mg alkaloids
20. 20 mL digoxin elixir
21. (a) 40 doses
(b) 2.5 mL/dose
(c) 100 mL ciprofloxacin oral
suspension
22. 11 + days
23. 1.2 g dextromethorphan H Br
24. (a) 100-mL package
(b) 8000 mg or 8 g of amoxicillin
25. 0.8 mL MEPERGAN and 0.375
mL atropine sulfate injections
26. 0.6 mL aminophylline injection
27. 0.4 mL LAN OXIN injection
28. 9 prefilled syringes, 40 mg/0.8 mL
29. (a) 0.02 mL per dose
(b) 60 doses per pen
(c) 30 days
30. 60 mcg/0.1 mL
31. 2 inhalers
32. 1176 mg nicotine
33. (a) 1.2 mg fentanyl
(b) 1.4 mg fentanyl
(c) 28%
34. 222 doses
35. 6 mg fluticasone propionate
36. (d) 0.08 g diclofenac sodium per
day for 12.5 days
37. (d) 0.32 mg budesonide and
0.018 mg formoterol fumarate
38. 2 actuations (lowest daily starting
dose) and 16 actuations (highest
daily recommended dose)
References
1. Drug Facts and Comparisons. St. Louis, MO: Wolters Kluwer H ealth; 2014.
2. Physicians’ Desk Reference. Montvale, N J: Medical Economics; 2014:68.
3. Taketomo CK. Pediatric & N eonatal Dosage Handbook. 20th Ed. H udson, OH : Lexicomp/Wolters Kluwer
H ealth Clinical Solutions; 2013–2014.
4. Semla T P. Geriatric Dosage Handbook. 19th Ed. H udson, OH : Lexicomp/Wolters Kluwer H ealth Clinical
Solutions; 2013–2014.
5. Drug Information Handbook. 23rd Ed. H udson, OH : Lexicomp/Wolters Kluwer H ealth Clinical Solutions;
2014–2015.
6. T he Joint Commission. Available at: http://www.jointcommission.org/assets/1/18/SEA_39.PDF. Accessed
May 1, 2014.
128 Pharma euti al c al ulations
7. U.S. Food and Drug Administration. Use of over-the-counter cough and cold products in infants and children.
Available at: http://www.fda.gov/Drugs/DrugSafety/DrugSafetyPodcasts/ucm077935.htm. Accessed July 24,
2014.
8. United States Pharmacopeial Convention. United States Pharmacopeia 32 N ational Formulary 27. Vol. 1.
Rockville, MD: United States Pharmacopeial Convention; 2009:728.
9. United States Pharmacopeial Convention. United States Pharmacopeia 32 N ational Formulary 27. Vol. 1.
Rockville, MD: United States Pharmacopeial Convention; 2009:604.
10. Actavis Pharma, Inc. LO LOEST RIN FE, product information. Available at: http://www.loloestrin.com/
Accessed July 24, 2014.
11. Santen RJ, Allred DC, Ardoin SP, et al. Postmenopausal hormone therapy: an endocrine society scientific
statement. J Clin Endocrinol Metab 2010;95:S1–S66.
12. Available at: http://www.women.webmd.com/endometriosis/high-dose-progestin-for-endometriosis. Accessed
July 25, 2014.
13. Foster SL, Moore W P. H igh-dose influenza vaccination in the elderly. J Am Pharm Assoc 2010;50:546–547.
14. Rashed SM, N olly RJ, Robinson L, et al. Weight variability of scored and unscored split psychotropic drug
tablets. Hosp Pharm 2003;38:930–934.
15. H ill SW, Varker AS, Karlage K, et al. Analysis of drug content and weight uniformity for half-tablets of 6 commonly split medications. J Manag Care Pharm 2009;15:253–261.
16. Verrue C, Mehuys E, Boussery K, et al. Tablet-splitting: a common yet not so innocent practice. J Adv Nurs
2010;67:26–32.
17. Green G, Berg C, Polli JE, et al. Pharmacopeial standards for the subdivision characteristics of scored tablets.
Pharmacopeial Forum 2009;35:1598.
18. Food and D rug Administration, D epartment of H ealth and H uman Services. Tablet splitting.
Available at: http:/ / www.fda.gov/ D rugs/ ResourcesForYou/ C onsumers/ BuyingU singMedicineSafely/
EnsuringSafeUseofMedicine/ucm265754.htm. Accessed May 1, 2014.
19. Food and Drug Administration, Department of H ealth and H uman Services. Best Practices for Tablet Splitting.
Available at: http:/ / www.fda.gov/ D rugs/ ResourcesForYou/ C onsumers/ BuyingU singMedicineSafely/
EnsuringSafeUseofMedicine/ucm184666.htm. Accessed May 1, 2014.
20. Food and D rug Administration, Center for Drug Evaluation and Research, Department of H ealth and
H uman Services. Guidance for Industry: Tablet Scoring: N omenclature, Labeling, and Data for Evaluation.
Available at: http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/
UCM269921.pdf. Accessed May 1, 2014.
21. Prince S. Calculations. International Journal of Pharmaceutical Compounding 2003;7:212.
22. Beach W. College of Pharmacy. Athens, GA: T he University of Georgia; 2004.
129
As noted in the previous chapter, the usual dose o a drug is the amount that ordinarily produces the desired therapeutic response in the majority o patients in a general, or otherwise
de ned, population group. T he drug’s usual dosage range is the range o dosage determined
to be sa e and e ective in that same population group. T his provides the prescriber with
dosing guidelines in initially selecting a drug dose or a particular patient and the f exibility to change that dose as the patient’s clinical response warrants. Usual doses and dosage
regimens are based on the results o clinical studies conducted during the drug development
process as well as on clinical in ormation gathered ollowing the initial approval and marketing o the drug (postmarketing surveillance/postmarketing studies).
For certain drugs and or certain patients, drug dosage is determined on the basis o
speci ic patient parameters. T hese parameters include the patient’s age, weight, body surace area, and nutritional and unctional status. Drug selection and drug dosage in patients
who are pregnant and in nursing mothers are especially important considerations due to
potential harm to the etus or child.
Among patients requiring individualized dosage are neonates and other pediatric patients,
elderly patients with diminished biologic unctions, individuals o all age groups with compromised liver and/or kidney unction (and thus reduced ability to metabolize and eliminate drug
substances), critically ill patients, and patients being treated with highly toxic chemotherapeutic
agents. Certain drugs with a narrow therapeutic window o ten require individualized dosing
based on blood level determinations and therapeutic monitoring. Digoxin, or example, at a
blood level o 0.9 to 2 ng/mL is considered therapeutic, but above 2 ng/mL, it is toxic.1
Since age, body weight, and body sur ace area are o ten-used actors in determining
the doses o drugs or pediatric and elderly patients, these parameters represent the majority o the calculations presented in this chapter. T he dosing o chemotherapeutic agents
also is included because it represents a unique dosing regimen compared with most other
categories o drugs.
Pediatric Patients
Pediatrics is the branch o medicine that deals with disease in children rom birth through
adolescence. Because o the range in age and bodily development in this patient population,
the inclusive groups are de ned urther as ollows: neonate (newborn), rom birth to
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

c al ula do	a d on fa or of ag , ody w gh , and ody urfa ar a.
U l z do ng a l and nomogram n al ula on .
c al ula do	for ngl and om na on h mo h rapy r g m n .

8
Calculation of Doses: Patient
Parameters
130 Pharma eut al c al ulat ons
1 month; infant, 1 month to 1 year; early childhood, 1 year through 5 years; late childhood,
6 years through 12 years; and adolescence, 13 years through 17 years of age.2 A neonate is
considered premature if born at less than 37 weeks’ gestation.
Proper drug dosing of the pediatric patient depends on a number of factors, including
the patient’s age and weight, overall health status, the condition of such biologic functions
as respiration and circulation, and the stage of development of body systems for drug
metabolism (e.g., liver enzymes) and drug elimination (e.g., renal system). In the neonate,
these biologic functions and systems are underdeveloped. Renal function, for example,
develops over the span of the first 2 years of life. T his fact is particularly important because
the most commonly used drugs in neonates, infants, and young children are antimicrobial
agents, which are eliminated primarily through the kidneys. If the rate of drug elimination is not properly considered, drug accumulation in the body could occur, leading to
drug overdosage and toxicity. T hus, the use of phar macokinetic data (i.e., the rates and
extent of drug absorption, distribution, metabolism, and elimination; see Chapters 10 and
22), together with individual patient factors and therapeutic response, provides a rational
approach to pediatric drug dosage calculations.2
Special Considerations in Dose Determinations for Pediatric Patients
T he majority of medications commercially available are formulated and labeled for adult
use. W hen used for the pediatric patient, appropriate dosage calculations must be made,
and often, so must adjustments to the concentration of the medication. In the absence of a
suitable commercial preparation, pharmacists may be called upon to compound a medication for a pediatric patient.
Among the special considerations in pediatric dosing are the following3:
•  Doses should be based on accepted clinical studies as reported in the literature.
•  Doses should be age appropriate and generally based on body weight or body surface
area.
•  Pediatric patients should be weighed as closely as possible to the time of admittance
to a health care facility and that weight recorded in kilograms.
•  As available, pediatric formulations rather than those intended for adults should be
administered.
•  All calculations of dose should be double-checked by a second health professional.
•  All caregivers should be properly advised with regard to dosage, dose administration,
and important clinical signs to observe.
•  Calibrated oral syringes should be used to measure and administer oral liquids.
Doses of drugs used in pediatrics, including neonatology, may be found in individual
drug product literature as well as in references, such as those listed at the conclusion of this
chapter.4,5
CASE IN POINT 8.1 A hosp tal pharma st s asked to determ ne the dose of
l ndamy n for a 3-day-old neonate we gh ng 3 lb 7 oz. in he k ng the l terature,
the pharma st determ nes that the dose s l sted as follows4:
<1200 g: 10 mg/kg/day d v ded q12h
<2000 g and 0 to 7 days old: 10 mg/kg/day d v ded q12h
<2000 g and >7 days old: 15 mg/kg/day d v ded q8h
>2000 g and 0 to 7 days old: 15 mg/kg/day d v ded q8h
>2000 g and >7 days old: 20 to 30 mg/kg/day d v ded q12h
8 • c al ula on of Do : Pa n Param r 131
Geriatric Patients
Although the term elderly is subject to varying def nitions with regard to chronologic age, it
is clear that the unctional capacities o most organ systems decline throughout adulthood,
and important changes in drug response occur with advancing age. Geriatric medicine or
geriatrics is the f eld that encompasses the management o illness in the elderly.
In addition to medical conditions a ecting all age groups, some conditions are particularly common in the elderly, including degenerative osteoarthritis, congestive heart
ailure, venous and arterial insu iciency, stroke, urinary incontinence, prostatic carcinoma,
parkinsonism, and Alzheimer’s disease. Many elderly patients have coexisting pathologies
that require multiple-drug therapies.
Most age-related physiologic unctions peak be ore age 30, with subsequent gradual
linear decline.2 Reductions in physiologic capacity and unction are cumulative, becoming
more pro ound with age. Kidney unction is a major consideration in drug dosing in the
elderly because reduced unction results in reduced drug elimination.
Because reduced kidney unction increases the possibility o toxic drug levels in the body
and adverse drug e ects, initial drug dosing in the elderly patient o ten re lects a downward
variance rom the usual adult dose. T here is also a requent need or dosage adjustment or
medication change due to adverse e ects or otherwise unsatis actory therapeutic outcomes.

e a h d d d do	o	add d o an n ra nou nfu on a h	h dul d
hour and nfu d o r a p r od of 20 m nu	.
t h produ	hown n F gur 8.1 wa u d o pr par an iv ag on a n ng

600 mg/50 mL of nj a l olu on. How many m ll l r of h olu on hould
g n for a h d d d do ?
FIGURE 8.1 •  Product label showing the drug concentration in mg/mL for an injectable product.
(Source: http://dailymed.nlm.nih.gov/dailymed/about.cfm. Courtesy of Pfizer, Inc.)

CASE IN POINT 8.2 A p d a r pa n	ng adm n	r d nalapr la (vAs Ot e c
iv)	ry 12 hour	y n ra nou nj	on o manag hyp r n on and po	l
h ar fa lur .4 b a d on a do of 5 m g/kg, h pa n	r	ng 55 m g of
nalapr la p r do . t h phy	an w h	o on r h pa n o oral nalapr l a
a do ag of 100 m g/kg a a ngl da ly do . t h	andard pro dur	o ru h a
2.5-mg a l of nalapr l, m x w h	r l wa r o mak 12.5 mL, and adm n	r
h appropr a do u ng a al ra d oral d p n r. c al ula	h do , n m ll l –
r , o	adm n	r d o h pa n .

132 Pharma euti al c al ulations
T here are a number o other common eatures o medication use in the elderly, including the long-term use o maintenance drugs; the need or multidrug therapy, with the attendant increased possibility o drug interactions and adverse drug e ects; and di iculties in
patient adherence. T he latter is o ten due to impaired cognition, con usion over the various
dosing schedules o multiple medications, and economic reasons in not being able to a ord
the prescribed medication.
Special Considerations in Dose Determinations for Elderly Patients
Dose determinations or elderly patients requently require consideration o some or all o
the ollowing:
•  T herapy is o ten initiated with a lower-than-usual adult dose.
•  Dose adjustment may be required based on the therapeutic response.
•  T he patient’s physical condition may determine the drug dose and the route o
administration used.
•  T he dose may be determined, in part, on the patient’s weight, body sur ace area,
health and disease status, and pharmacokinetic actors.
•  Concomitant drug therapy may a ect drug/dose e ectiveness.
•  Adrug’s dose may produce undesired adverse e ects and may a ect patient adherence.
•  Complex dosage regimens o multiple drug therapy may a ect patient adherence.
The adult dose of a drug is 500 mg every 8 hours. For an elderly patient with impaired renal
function, the dose is reduced to 250 mg every 6 hours. Calculate the reduction in the daily dose, in
milligrams.
Daily doses mg every hours mg
mg every hours
: ( )
( )
500 3 8 1500
250 4 6
× =
× =
– =
1000
1500 100
mg
mg mg 500 mg
Dosage Forms Applicable to Pediatric and Geriatric Patients
In the general population, solid dosage orms, such as tablets and capsules, are pre erred or the
oral administration o drugs because o their convenience, precise dose, ease o administration,
ready identif cation, transportation, and lower cost per dose relative to other dosage orms.
H owever, solid dosage orms are o ten di f cult or impossible or the pediatric, geriatric, or
inf rm patient to swallow. In these instances, liquid orms are pre erred, such as oral solutions,
syrups, suspensions, and drops. With liquid orms, the dose can be adjusted by changing the
volume administered. W hen necessary, liquid orms o medication may be administered by
oral eeding tube. Pharmacists are sometimes asked to compound an oral liquid rom a counterpart solid dosage orm when a liquid product is not available. Chewable tablets and solid gel
orms (medicated “gummy bears”) that disintegrate or dissolve in the mouth are o ten used or
pediatric and geriatric patients. In addition, and as noted in the previous chapter, tablet splitting
and tablet crushing are options or individuals unable to swallow whole tablets.
For systemic e ects, injections may be used rather than the oral route o administration when needed or pediatric and elderly patients, with the dose or strength o the preparation adjusted to meet the requirements o the individual patient.
Drug Dosage Based on Age
For reasons stated earlier, the young and the elderly require special dosing considerations
based on actors characteristic o these groups.
8 • c al ulation of Doses: Patient Parameters 133
Before the physiologic differences between adult and pediatric patients were clarified,
the latter were treated with drugs as if they were merely miniature adults. Various rules of
dosage in which the pediatric dose was a fraction of the adult dose, based on relative age,
were created for youngsters (e.g., Young’s rule). Today these rules are not in general use because
age alone is no longer considered a singularly valid criterion in the determination of accurate dosage
for a child, especially when calculated from the usual adult dose, which itself provides wide clinical
variations in response. Some of these rules are presented in the footnote for perspective and historical
purposes.a
Currently, when age is considered in determining dosage of a potent therapeutic agent,
it is used generally in conjunction with another factor, such as weight. T his is exemplified
in Table 8.1, in which the dose of the drug digoxin is determined by a combination of the
patient’s age and weight.
aYoung’s rule, based on age:
Age
Age
Adult dose Dose for child
+
× =
12
Cowling’s rule:
Age at next birthday in years Adult dose
Dose for child
( ) ×
=
24
Fried’s rule for infants:
Age in months Adult dose
Dose for infant
( ) ×
=
150
Clark’s rule, based on weight:
W eight in lb Adult dose
average weight of adult in lb
Dose fo
( )
( )
×
=
150
rr child
N OT E: T he value of 150 in Fried’s rule was an estimate of the age (12.5 years or 150 months) of an individual
who would normally receive an adult dose, and the number 150 in Clark’s rule was an estimate of the weight of
an individual who likewise would receive an adult dose.
Tab e 8.1 •  Il l USTRATIvE PEDIATRIC DOSAGES
OF DIGOxIN BASED ON AGE AND WEIGh Ta

Age	Digo in Dose (mg/kg/day)
Premature	4–8
Full term 1–24 mo 2–5 y 5–10 y Over 10 y	7–11 11–18 9–13 6–11 3–5

aThese are illustrative doses. Specific pediatric doses for various age
groups, clinical conditions, and by various routes of administration
may be found at https://online.epocrates.com/u/102198/digoxin/
Pediatric+Dosing.
134 Pharma euti al c al ulations
Example Calculations of Dose Based on Age
(1) An over-the-counter cough remedy contains 120 mg of dextromethorphan in a 60-mL
bottle of product. The label states the dose as 1½ teaspoonfuls for a child 6 years of age. How
many milligrams of dextromethorphan are contained in the child’s dose?
1 7 5
60
120
7 5
1
2 teaspoonfuls mL
mL
mg
mL
x mg
x
= = =
..
15 mg dextromethorphan
(2) The dose of a drug for an adolescent is acceptable as either 10 mg/kg or 300 mg. Calculate
the difference in these alternative doses for a 9-year-old child weighing 70 lb.
Dose at 10 mg/kg: 70 lb ÷ 2.2 lb/kg = 31.8 kg; 31.8 kg × 10 mg/kg = 318.2 mg
Di erence in dose = 318.2 mg – 300 mg = 18.2 mg
(3) From the data in Table 8.1, calculate the dosage range for digoxin for a 20-month-old
infant weighing 6.8 kg.
11 1
6 8
18 1
6 8
74 8 122 4
mcg
mcg
kg
kg
and mcg
mcg
kg
kg
x mcg and x
x x
= =
= =
. .
. . mcg
D osage range between 74.8 and 122.4 mcg digoxin
Drug Dosage Based on Body Weight
Drug doses based on weight are expressed as a specif c quantity o drug per unit o patient
weight, such as milligrams of drug per kilogram of body weight (abbreviated [mg/kg]). Dosing
in this manner makes the quantity o drug administered specif c to the weight o the patient
being treated.
Example Calculations of Dose Based on Body Weight
A use ul equation or the calculation o dose based on body weight is
Patient s dose mg Patient s weight kg Drug dose mg
kg
’ ( ) ’ ( ) ( )
( )
= ×
1
T his equation is based on a drug dose in mg/kg and the patient’s weight in kilograms.
W hen di erent units are given or desired, other units may be substituted in the equation as
long as the terms used are consistently applied.
(1) The usual initial dose of chlorambucil is 150 mcg/kg of body weight. How many milligrams
should be administered to a person weighing 154 lb?
Solving by the equation:
150 mcg = 0.15 mg
Patient s dose mg lb mg
lb
’ ( ) .
.
= 154 × = .
0 15
2 2
10 5 mg chlorambucil
Or, solving by ratio and proportion:
150 mcg = 0.15 mg 1 kg = 2.2 lb
8 • c al ula ion of Doses: Pa ien Parame ers 135
2 2
154
. . 0 15
; .
lb
lb
mg
x mg
= = x 10 5 mg chlorambucil
Or, solving by dimensional analysis:
1
1000
150
1
1
2 2

154 lb	mcg	kg
1	kg	lb .
× × × = 10 5 mg chlorambucil .

mg
mcg
(2) The usual dose o sulf soxazole or in ants over 2 months o age and children is 60 to 75 mg/kg
o body weight. W hat would be the usual range or a child weighing 44 lb?
1 kg = 2.2 lb
20 kg = 44 lb
60 mg/kg × 20 kg = 1200 mg
75 mg/kg × 20 kg = 1500 mg
T hus, the dosage range would be 1200 to 1500 mg
(3) The dose o minocycline to treat acne vulgaris is given as 1 mg/kg/day × 12 weeks. Tablet
strengths available include 45 mg, 55 mg, 65 mg, 80 mg, 90 mg, 105 mg, and 115 mg o
minocycline. W hat strength tablet and how many tablets should be prescribed or the entire
course o treatment or a 100-lb patient?
100 2 2 45 5
1 45 5 45 5
lb lb kg kg
mg kg day kg mg day
÷ =
× = ≈
. / .
/ / . . / 45 mg min – ocycline tablets
84 tablets
,
/ ; ,
and
12 7 84 week day week days thus × = rrequired
(4) A dose o enoxaparin sodium injection (LOVENOX) is “1 mg/kg q12h SC.” I a graduated
pref lled syringe containing 80 mg/0.8 mL is used, how many milliliters should be administered per dose to a 154-lb patient?
154 2 2 70
1 70 70
0 8 70
80
lb lb kg kg
mg kg kg mg
mL
mg
mg
÷ =
× =
× =
. /
/
. . 0 7 mL enoxaparin sodium injection
Dosing Tables Based on Body Weight
For some drugs dosed according to body weight or body surface area, dosing tables appear
in product literature to assist the physician and pharmacist. An example is presented in
Table 8.2.
CASE IN POINT 8.3 A hospi al pharma is is alled o a pedia ri nursing s a ion o
al ula e he quan i y of an inje ion o adminis er o a pedia ri pa ien . t he daily
dose of he inje ion for he hild’s weigh is s a ed as 15 mg/kg/day, divided in o
hree equal por ions. t he hild weighs 10 kg. t he inje ion on ains 5 mg/mL of he
pres ribed drug.
How many millili ers of inje ion should be adminis ered?
136 Pharma euti al c al ulations
(1) Using Table 8.2 and a daily dose of 0.5 mg/kg, how many 20-mg capsules of the drug
product should be dispensed to a patient weighing 176 lb if the dosage regimen calls for
15 weeks of therapy?
2 capsules/day × 7 days/week × 15 weeks = 210 capsules
(2) A pharmacist compounds a suspension from oseltamivir phosphate capsules to contain 15 mg
of drug per milliliter. Using Table 8.3, calculate the single dose in milliliters for a pediatric
patient weighing 40 lb.
From Table 8.3, the dose for the pediatric patient is 45 mg.
45
1
15
mg
mL
mL
× = 3 mL dose of oseltamivir phosphate suspension ,
Drug Dosage Based on Body Surface Area
T he body surface area (BSA) method of calculating drug doses is widely used for two types of
patient groups: cancer patients receiving chemotherapy and pediatric patients.
Table 8.4 shows the approximate relation between body weight and body surface area,
in square meters (m2), based on average body dimensions. T he average adult is considered
to have a BSA of 1.73 m2. T hus, in reading Table 8.4, a person with a BSA of 1.30 (or about
75% of that of the average adult) would receive about 75% of the adult dose.
Example Calculations of Dose Based on Body Surface Area
A useful equation for the calculation of dose based on BSA is:
Tab e 8.3 •  DOSING OF OSEl TAmIvIR Ph OSPh ATE IN Th E
TREATmENT OF INFl UENzA IN PEDIATRIC PATIENTSa

Bod Weig t	Reco	ended Dose × 5 Da s
15 kg or less 15.1 to 23 kg 23.1 to 40 kg 40.1 kg or more	30 mg twice daily 45 mg twice daily 60 mg twice daily 75 mg twice daily

aAdapted from product literature for oseltamivir phosphate (TAMIFLU); Genentech, 2014
@ http://www.drugs.com/pro/tamiflu.html
Tab e 8.2 •  DOSING By BODy WEIGh T FOR A h yPOTh ETICAl DRUG

Bod Weig t	Tota	g/da
Ki ogra s	Pounds	0.5 g/kg	1 g/kg

40 88 20 40 80
50 110 25 50 100
60 132 30 60 120
70 154 35 70 140
80 176 40 80 160
90 198 45 90 180
100 220 50 100 200
8 • c al ulation of Doses: Patient Parameters 137
Patient s dose Patient s BSA m
m
’ ’ ( ) Drug dose mg
.
= × ( )
2
1 73 2
If the adult dose of a drug is 100 mg, calculate the approximate dose for a child with a BSA of
0.83 m2, using (a) the equation and (b) Table 8.4.
(a) Child s dose m
m
’ . mg or
.
= × = .
0 83
1 73
100 47 97
2 2
48 mg
(b) According to Table 8.4, a BSA of 0.83 m2 represents 48% of the average adult BSA
of 1.73 m2; thus, the child dose would be 48% of the average adult dose:
100 mg × 0.48 = 48 mg dose for child
Dosing Tables Based on Body Surface Area
For certain drugs, dosing tables may be provided to determine the approximate
dose based on a patient’s body surface area. Table 8.5 presents an example for a
hypothetical drug.
Using Table 8.5, find the dose of the hypothetical drug at a dose level of 300 mg/m2 for a child
determined to have a BSA of 1.25 m2. Calculate to verify.
From Table 8.5, the dose = 375 mg
From calculations, 300 mg/m2 × 1.25 m2 = 375 mg dose
Nomograms for Determining Body Surface Area
Most BSA calculations use a standard nomogram, which includes both weight and height.
N omograms for children and adults are shown in Figures 8.2 and 8.3. T he BSA of an
Tab e 8.4 •  APPROxImATE REl ATION OF SURFACE AREA AND WEIGh TS OF INDIvIDUAl S
OF AvERAGE BODy DImENSION
Ki ogra s Pounds Surface Area in Square meters Percentage of Adu t Dosea
2 4.4 0.15 9
3 6.6 0.20 11.5
4 8.8 0.25 14
5 11.0 0.29 16.5
6 13.2 0.33 19
7 15.4 0.37 21
8 17.6 0.40 23
9 19.8 0.43 25
10 22.0 0.46 27
15 33.0 0.63 36
20 44.0 0.83 48
25 55.0 0.95 55
30 66.0 1.08 62
35 77.0 1.20 69
40 88.0 1.30 75
45 99.0 1.40 81
50 110.0 1.51 87
55 121.0 1.58 91
aBased on average adult surface area of 1.73 m2.
Adapted from Martin EW, et al. Techniques of Medication. J.B. Lippincott; 1969:31, who adapted it from Modell’s Drugs of
Choice (Mosby).
138 Pharma euti al c al ulations
individual is determined by drawing a straight line connecting the person’s height and
weight. T he point at which the line intersects the center column indicates the person’s BSA
in square meters. In the example shown in Figure 8.2, a child weighing 15 kg and measuring
100 cm in height has a BSA o 0.64 m2.
(1) If the adult dose of a drug is 75 mg, what would be the dose for a child weighing 40 lb and
measuring 32 inches in height using the BSA nomogram?
From the nomogram, the BSA = 0.60 m2
0 60
1 73
75
2 2
. .
m m
× mg = 26 mg
(2) The usual pediatric dose of a drug is stated as 25 mg/m2. Using the nomogram, calculate
the dose for a child weighing 18 kg and measuring 82 cm in height.
From the nomogram, the BSA = 0.60 m2
25 mg × 0.60 = 15 mg
T he nomogram in Figure 8.3 designed specif cally or determining the BSA o
adults may be used in the same manner as the one previously described. T he adult
dose is then calculated as ollows:
BSA of adult m
m
( ) Usual adult dose Dose for adult
.
2
1 73 2 × =
Tab e 8.5 •  PEDIATRIC DOSING GUIDEl INE FOR A h yPOTh ETICAl DRUG BASED ON BSA
Patient’s BSA (m2)
Dose l eve
250 mg/m2 Dose 300 mg/m2 Dose 350 mg/m2 Dose 400 mg/m2 Dose
0.25 62.5 mg 75 mg 87.5 mg 100 mg
0.50 125 mg 150 mg 175 mg 200 mg
1.00 250 mg 300 mg 350 mg 400 mg
1.25 312.5 mg 375 mg 437.5 mg 500 mg
1.50 375 mg 450 mg 525 mg 600 mg
CAl CUl ATIONS CAPSUl E
Dose Based on Body Surface Area
A useful equation for the calculation of dose based on body surface area is:
Patient s dose Patient s BSA m
m
’ ’ Drug dose (mg)
.
( )
= ×
2
1 73 2
If there is need to determine a patient’s BSA, a nomogram or the following equation
may be used:
Patient s BSA (m ) ’ 2 Patient s height (cm) Patient s weight (kg) ’ ’
36
=
×
000
8 • c al ulation of Doses: Patient Parameters 139
Nomogram for Determination of Body Surface Area From Height and Weight
Height Body surface area Weight
1.10 m2
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.074 m2
47 in
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10 in
cm 120
115
110
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
cm 25
90 lb
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
9 8 6 5 4 3
2.2 lb
kg 40.0
35.0
30.0
25.0
20.0
15.0
10.0
9.0
8.0
7.0
6.0
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
kg 1.0
Example:
BSA for a
15-kg. child,
100 cm. tall =
0.64 M2

From the formula of Du Bois and Du Bois, Arch Intern Med 17, 863 (1916): S W 0 .425	H 0 .725	71.84, or height in cm).
log S	log W	0.425	log H	0.725	1.8564 (S	body surface in cm2, W	weight in kg, H

FIGURE 8.2 •  Body surface area of children. (From Diem K, Lentner C, Geigy JR. Scientific Tables. 7th Ed.
Basel, Switzerland: JR Geigy; 1970:538.)
140 Pharma euti al c al ulations
cm 200
195
190
185
180
175
170
165
160
155
150
145
140
135
130
125
120
115
110
105
cm 100
79 in
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39 in
330 lb
320
310
300
290
280
270
260
250
240
230
220
210
200
190
180
170
160
150
140
130
120
110
105
100
95
90
85
80
75
70
66 lb
kg 150
145
140
135
130
125
120
115
110
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
kg 30
2.80 m2
2.70
2.60
2.50
2.40
2.30
2.20
2.10
2.00
1.95
1.90
1.85
1.80
1.75
1.70
1.65
1.60
1.55
1.50
1.45
1.40
1.35
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0.95
0.90
0.86 m2
Nomogram for Determination of Body Surface Area from Height and Weight
thgieH aeraecafrusydoB thgieW

From the formula of Du Bois and Du Bois, Arch Intern Med 17, 863 (1916): S	W 0 .425	H 0 .725	71.84, or height in cm).
log S	log W	0.425	log H	0.725	1.8564 (S	body surface in cm2, W	weight in kg, H

FIGURE 8.3 •  Body surface area of adults. (From Diem K, Lentner C, Geigy JR. Scientific Tables. 7th Ed.
Basel, Switzerland: JR Geigy; 1970:538.)
8 • c al ulation of Doses: Patient Parameters 141
(1) If the usual adult dose of a drug is 120 mg, what would be the dose based on BSA for a
person measuring 6 feet tall and weight 200 lb?
BSA from the nomogram m
m m
mg mg or
( ) .
. .
.
=
× =
2 13
2 13
1 73
120 147 75
2
2 2
148mg
(2) If the dose of a drug is 5 mg/m2, what would be the dose for a patient with a BSA of 1.9 m2?
5 mg × 1.9 = 9.5 mg
BSA Equation
In addition to the use of the nomogram, BSA may be determined through use of the following Mosteller formula6:
BSA m
H t cm W t kg
,
2 ( ) ( )
3600
=
×
Calculate the BSA for a patient measuring 165 cm in height and weighing 65 kg.
BSA m
cm kg
BSA
,
( ) ( )
.
2 165 65
3600
=
×
= 1 73 m 2
N OT E: For the sake of comparison, check Figure 8.3 to derive the BSA for the same
patient using the nomogram.
Dosage Based on the Medical Condition to Be Treated
In addition to the factors previously discussed that might be used to determine a drug’s
dose, the medical condition to be treated and the severity of that condition must also be
considered.
Table 8.6 presents an example of a dosage schedule for a drug based both on a patient’s
age and the medical condition to be treated.
Tab e 8.6 •  PARENTERAl DOSAGE SCh EDUl E FOR A h yPOTh ETICAl ANTI-INFECTIvE
DRUG BASED ON PATIENT AGE AND CONDITION BEING TREATED

Dose	Route	Frequenc
Adu ts
Urinary tract infection	250 mg	IV or IM	q12h
Bone and joint infections	2 g	IV	q12h
Pneumonia	500 mg–1g	IV or IM	q8h
Mild skin infections Life-threatening infections Lung infections (normal kidney function) Neonates (up to 1 month) Infants and C i dren (1 mo to 12 y)	500 mg–1g 2 g 40 mg/kg (NMT 6 g/day) 30 mg/kg 30–50 mg/kg (NMT 6 g/day)	IV or IM IV IV IV IV	q8h q8h q8h q12h q8h

142 Pharma euti al c al ulations
(1) By using Table 8.6, calculate the IV drug dose for a 3-lb 3-oz neonate.
3 3 454 1362
3 3 28 35 85
1362 85
l g g
oz g g
W eight of neonate g g
b = × =
= × =
= + =
.
11447
1447 1000 1 447
30 1 447
g
g kg
mg kg kg
/ .
/ . .
=

×	= 43 4 mg every 12 hours
(2) By using Table 8.6, calculate the daily IV dose of the drug in the treatment of a lung infec
tion for a patient weighing 160 lb.
160	2 2	72 72

72 72 40 2909

lb lb kg mg kg dose ÷ = = . / / /

kg mg dose eve / ( ry ho rs u )

kg ×

.

.

mg doses per day mg or
8
2909 3 8727
× = 8 73 g daily dose .
Dosage Adjustment Based on Coadministered Drugs
T he usual dose o a drug may require adjusting based on the coadministration o another
drug when there is a known or suspected risk or a drug interaction. Drug interactions may
result in diminished drug e f cacy and/or in increased toxicity due to a number o actors
including those a ecting a drug’s pharmacokinetics (i.e., absorption, distribution, metabolism, and elimination).
The usual adult dose of colchicine in the prevention of gout flares is 6 mg once or twice a day.
However, when coadministered with protease inhibitors (e.g., ritonavir), the dose is reduced to
0.3 mg once daily or once every other day. For “once every other day” treatment, how many whole
or split 0.6-mg tablets are required for a 30-day supply?
15 days (o treatment) × 0.3 mg/day = 4.5 mg, colchicine
4.5 mg/0.6 mg (tablet) = 7.5 whole tablets or 15 split tablets
Dosage Based on Reduced Kidney and/or Liver Function
T he status o a patient’s hepatic (liver) and renal (kidney) unction plays a major role in
determining drug dosage due to their roles in drug metabolism and elimination. Specif c
calculations o dosage based on reduced kidney unction are presented in Chapter 10.
Other Patient Factors Affecting Drug Dosage and Utilization
In addition to actors o renal and/or hepatic impairment and age (pediatric, geriatric), other
patient actors play a role in drug selection and dosage including gender, genetics (e.g., pharmacogenetics), metabolic disorders, pregnancy, breast eeding, current health status, medical
and medication history, and others.
Special Dosing Considerations in Cancer Chemotherapy
T he term chemotherapy applies to the treatment o disease with chemical drugs or chemotherapeutic agents. Chemotherapy is primarily associated with the treatment o cancer
patients and is considered the mainstay o such treatment in that it is e ective in widespread
8 • c al ula on of Do : Pa n Param r 143
or metastatic cancer, whereas treatments such as surgery and radiation therapy are limited
to speci c body sites. Chemotherapeutic agents most o ten are administered orally, by intravenous injection, or by continuous intravenous in usion.
Although a single anticancer drug may be used in a patient’s treatment plan, combination chemotherapy perhaps is more usual. By using combinations o drugs having
di erent mechanisms o action against the target cancer cells, the e ectiveness o treatment may be enhanced, lower doses used, and side e ects reduced. T he combination
chemotherapy plans o ten include two-agent regimens, three-agent regimens, and fouragent regimens.7–11
Cancer chemotherapy is unique in the ollowing ways:
•  It may involve single or multiple drugs o well-established drug therapy regimens or
protocols, or it may involve the use o investigational drugs as a part o a clinical trial.
•  Combinations o drugs may be given by the same or di erent routes o administration, most o ten oral and/or intravenous.
•  T he drugs may be administered concomitantly or alternately on the same or di erent days during a prescribed treatment cycle (e.g., 28 days). T he days o treatment
generally ollow a prescribed ormat o written instructions, with D or “day,” ollowed by the day(s) o treatment during a cycle, with a dash (-) meaning “to” and a
comma (,) meaning “and.” T hus, D 1–4 means “days 1 to 4,” and D1,4 means “days
1 and 4.”9
•  T he drugs used in combination chemotherapy o ten t into a standard drug/dosage
regimen identi ed by abbreviations or acronyms. For example, a treatment or bladder cancer re erred to as MVAC consists o methotrexate + vinblastine + doxorubicin
(or actinomycin) + cisplatin; a treatment or colorectal cancer called FU/LU consists o f uorouracil + leucovorin; a treatment or lung cancer called PC consists o
paclitaxel + carboplatin; and one or ovarian cancer called CH AD consists o cyclophosphamide + hexamethylmelamine + Adriamycin + diamminedichloroplatinum
(cisplatin).

CASE IN POINT 8.4 A ho p al pharma	on ul d on h appropr a do of
lop na r/r ona r (KALe t RA) oral olu on n h r a m n of an Hiv-1 nf	on n a
12-mon h-old p d a r pa n . t h oral olu on on a n , n a h m ll l r, 80 mg
of lop na r and 20 mg of r ona r, xpr pharma y’ pro o ol, h p d a r do	d a “KALe t RA 80/20.” A ord ng o h
for pa n gr a r han 6 mon h of ag , no
r	ng o h r on om an h rapy, may	al ula d a d on	h r b s A or ody
w gh a follow :
• 230/57.5 mg/m2, adm n	r d w	da ly

• 12/3 mg/kg for pa n <15 kg, adm n r d w da ly

• 10/2.5 mg/kg for pa n >15 kg adm n	r d w	da ly
t h pa n m a ur 28 n h	n l ng h and w gh 22 l .
(a) c al ula ( ) t ran la	h h	ngl do , n mg, u ng h b s A qua on.
al ula d ngl do	from (a) n o orr pond ng m ll l r of
h oral olu on.
( ) c al ula (d) t ran la	h da ly do , n mg, a d on h pa n ’ w gh .
h da ly do	from ( ) n o orr pond ng m ll l r of oral olu on.

144 Pharma euti al c al ulations
•  In addition to the use o abbreviations or the drug therapy regimens, the drugs themselves are commonly abbreviated in medication orders, such as MT X or “methotrexate,” DOX or “doxorubicin,” VLB or “vinblastine,” and CDDP or “cisplatin.”
Tables o standard chemotherapy treatments, dosing regimens, and abbreviations o
the drugs and treatment regimens may be ound in the indicated re erences.7–11
•  For systemic action, chemotherapeutic agents are usually dosed based either on body
weight or on body sur ace area. O ten, the drug doses stated in standard regimens
must be reduced, based on a particular patient’s diminished kidney or liver unction
and, thus, his or her ability to metabolize and eliminate the drug(s) rom the body.
•  For certain patients, high-dose chemotherapy is undertaken in an e ort to kill tumor cells.
To help prevent errors in chemotherapy, pharmacists must correctly interpret medication orders or the chemotherapeutic agents prescribed, ollow the individualized dosing
regimens, calculate the doses o each medication prescribed, and dispense the appropriate
dosage orms and quantities/strengths required.12
Example Calculations of Chemotherapy Dosage Regimens
(1) Regimen: VC11
Cycle: 28 days; repeat or 2–8 cycles
Vinorelbine, 25 mg/m2, IV, D 1,8,15,22
Cisplatin, 100 mg/m2, IV, D 1
For each o vinorelbine and cisplatin, calculate the total intravenous dose per cycle or
a patient measuring 5 eet 11 inches in height and weighing 175 lb.
From the nomogram or determining BSA, (a) f nd the patient’s BSA and (b)
calculate the quantity o each drug in the regimen.
(a) BSA = 2.00 m2
(b) Vinorelbine: 25 mg × 2.00 (BSA) × 4 (days o treatment) = 200 mg
Cisplatin: 100 mg × 2.00 (BSA) × 1 = 200 mg
(2) Regimen: CMF11
Cycle: 28 days
Cyclophosphamide, 100 mg/m2/day PO, D 1–14
Methotrexate, 40 mg/m2, IV, D 2,8
Fluorouracil, 600 mg/m2, IV, D 1,8
Calculate the total cycle dose or cyclophosphamide, methotrexate, and f uorouracil or
a patient having a BSA o 1.5 m2.
Cyclophosphamide: 100 mg × 1.5 (BSA) × 14 (days) = 2100 mg = 2.1 g

Methotrexate: Fluorouracil:

40 mg × 1.5 × 2 600 mg × 1.5 × 2

= 120 mg = 1800 mg = 1.8 g

(3) Using Table 8.7 as a re erence, calculate the quantities o doxorubicin and cyclophosphamide administered per treatment cycle to a woman measuring 5 eet 4 inches in height and
weighing 142 lb during the “AC” protocol or breast cancer.
BSA ( rom Table 8.2) = 1.70 m2
1.70 m2 × 60 mg/m2 doxorubicin = 102 mg doxorubicin
1.70 m2 × 600 mg/m2 cyclophosphamide = 1020 mg cyclophosphamide
(4) A variation o the “AC” protocol, re erred to as “AC → T,” ollows 4 cycles o the AC
protocol with paclitaxel (TAXOL), 175 mg/m2 by intravenous in usion every 14 to 21 days
8 • c al ula on of Doses: Pa en Parame ers 145
for 4 cycles.11 Calculate the total quantity of paclitaxel, in milligrams, that the patient in
the previous problem would receive during this treatment plan.
BSA m
m mg m paclitaxel mg per cycle cy
=
× = ×
1 70
1 70 175 297 5 4
2
2 2
.
. / . ( ) ( cles)
= 1190 mg paclitaxel
(5) If an injection is available containing paclitaxel, 6 mg/mL, calculate the volume required
per cycle to treat the patient in the previous problem.
297.5 mg ÷ 6 mg/mL = 49.6 mL paclitaxel injection
CASE IN POINT 8.5 13 in rea ng a 54-year-old female pa en , an on olog s sele s
he drug emozolom de, an an umor agen used n he rea men of refra ory as ro yoma (bra n umor). t he drug s used as par of a 28-day reg men, dur ng wh h he f rs
5 days of rea men n lude emozolom de a a on e-da ly dose of 150 mg/m2/day.
t he pa en ’s med al har nd a es ha she measures 5 fee n he gh and we ghs
117 lb. t he phys an asks he pharma s o de erm ne he proper omb na on of
ava lable apsules o use n dos ng he pa en . t he drug s ava lable n apsules
on a n ng 5, 20, 100, and 250 mg of emozolom de. Wha omb na on of apsules
would prov de he da ly dose of h s drug?
Tab e 8.7 •  ExAmPl ES OF DOSAGE REGImENS IN CANCER Ch EmOTh ERAPya
T pe of
Cancerb Abbreviation Drug/Dose Route
Da (s) of Ad inistration
per Treat ent C c ec
Bladder MVAC methotrexate, 30 mg/m2
vinblastine, 3 mg/m2
doxorubicin (Adriamycin),30 mg/m2
cisplatin, 70 mg/m2
IV
IV
IV
IV
days 1, 15, and 22
days 2, 15, and 22
day 2
day 2
Breast AC doxorubicin (Adriamycin), 60 mg/m2
cyclophosphamide, 600 mg/m2
IV
IV
day 1
day 1
Esophagus DCF docetaxel, 75 mg/m2
cisplatin, 75 mg/m2
5-fluorouracil, 750 mg/m2/day
IV
IV
IV
day 1
day 1
days 1–5
Lung CAE cyclophosphamide, 1000 mg/m2
doxorubicin, 45 mg/m2
etoposide, 100 mg/m2
IV
IV
IV
day 1
day 1
days 1–3
Stomach ELF etoposide, 120 mg/m2
leucovorin, 150 mg/m2
5-fluorouracil, 500 mg/m2
IV
IV
IV
days 1–3
days 1–3
days 1–3
aTable from references.8–11
bTypes of cancer are stated broadly and not differentiated by subclassifications.
cThe frequency and number of treatment cycles vary according to the specific protocols employed.
146 Pharma euti al c al ulations
PRACTICE PROBl EmS
Calculations Based on Body Weight
1. T he dose of a drug is 500 mcg/kg of body weight. H ow many milligrams should
be given to a child weighing 55 lb?
2. T he dose of gentamicin for premature and full-term neonates is 2.5 mg/kg
administered every 12 hours. W hat would be the daily dose for a newborn weighing 5.6 lb?
3. T he dose of gentamicin for patients with impaired renal function is adjusted to
ensure therapeutically optimal dosage. If the normal daily dose of the drug for
adults is 3 mg/kg/day, administered in three divided doses, what would be the
single (8-hour) dose for a patient weighing 165 lb and scheduled to receive only
40% of the usual dose, based on renal impairment?
4. A patient weighing 120 lb was administered 2.1 g of a drug supposed to be dosed
at 30 mg/kg. Was the dose administered correct, or was it an overdose, or was it an
underdose?
5. In a clinical trial of ciprofloxacin (CIPRO), pediatric patients were initiated on 6 to
10 mg/kg intravenously every 8 hours and converted to oral therapy, 10 to 20 mg/kg,
every 12 hours. Calculate the ranges of the total daily amounts of ciprofloxacin
that would have been administered intravenously and orally to a 40-lb child.

6.	Erythromycin ethylsuccinate 400 mg/5 mL
Disp. Sig.	100 mL tsp. q.i.d. until all medication is taken.

If the dose of erythromycin ethylsuccinate is given as 40 mg/kg/day
(a) W hat would be the proper dose of the medication in the signa, if the prescription is for a 44-lb child?
(b) H ow many days will the prescribed medication last?
7. If the pediatric dosage of chlorothiazide (DIURIL) is 10 to 20 mg/kg of body
weight per day in a single dose or two divided doses, not to exceed 375 mg/day,
calculate the daily dosage range of an oral suspension containing 250 mg chlorothiazide per 5 mL that should be administered to a 48-lb child.
8. Cyclosporine is an immunosuppressive agent administered before and after organ
transplantation at a single dose of 15 mg/kg. H ow many milliliters of a 50-mL
bottle containing 100 mg of cyclosporine per milliliter would be administered to
a 140-lb kidney transplant patient?
9. T he adult dose of a liquid medication is 0.1 mL/kg of body weight. H ow many
teaspoonfuls should be administered to a person weighing 220 lb?
10. A hospitalist prescribed dimenhydrinate to treat a 48-lb child. T he labeled dose
of the drug is 1.125 mg/kg. T he available oral solution contains dimenhydrinate,
12.5 mg/5 mL. Prior to administering the solution, the floor nurse decides to
check her calculated dose of 9.8 mL with the hospital pharmacist. Were her calculations correct?
11. Fluconazole tabs 100 mg
Disp. tabs
Sig: tab ii stat, then 3 mg/kg b.i.d. × 7 days thereafter.
Calculate the number of tablets to dispense to a patient weighing 147 lb.
12. A physician desires a dose of 10 mcg/kg of digoxin for an 8-lb newborn child.
H ow many milliliters of an injection containing 0.25 mg of digoxin per milliliter
should be given?
8 • c al ulation of Doses: Patient Parameters 147
13. Intravenous digitalizing doses of digoxin in children are 80% of oral digitalizing
doses. Calculate the intravenous dose for a 5-year-old child weighing 40 lb if the
oral dose is determined to be 10 mcg/kg.
14. An intratracheal suspension for breathing enhancement in premature infants
is dosed at 2.5 mL/kg of birth weight. H ow many milliliters of the suspension
should be administered to a neonate weighing 3 lb?
15. A 142-lb patient was receiving filgrastim (N EUPOGEN ) in doses of 10 mcg/kg/day
when, as a result of successful blood tests, the dose was lowered to 6 mcg/kg/day.
Using an injection containing 0.3 mg filgrastim per 0.5 mL, calculate the previous
and new dose to be administered.
(a) 17.7 mL and 64.6 mL
(b) 5.23 mL and 3.14 mL
(c) 1.08 mL and 0.65 mL
(d) 3.87 mL and 2.3 mL
16. A 25-lb child is to receive 4 mg of phenytoin per kilogram of body weight daily
as an anticonvulsant. H ow many milliliters of pediatric phenytoin suspension
containing 30 mg per 5 mL should the child receive?
17. T he loading dose of digoxin in premature infants with a birth weight of less than
1.5 kg is 8 mcg/kg administered in three unequally divided doses (½, ¼, ¼) at
8-hour intervals. W hat would be the initial dose for an infant weighing 1.2 kg?
18. T he pediatric dose of cefadroxil is 30 mg/kg/day. If a child was given a daily dose
of 2 teaspoonfuls of a pediatric suspension containing 125 mg of cefadroxil per
5 mL, what was the weight, in pounds, of the child?
19. H ow many milliliters of an injection containing 1 mg of drug per milliliter
of injection should be administered to a 6-month-old child weighing 16 lb to
achieve a dose of 0.01 mg/kg?
20. Prior to hip replacement surgery, a patient receives an injection of an anticoagulant drug at a dose of 30 mg. Following the patient’s surgery, the drug is injected
at 1 mg/kg. For a 140-lb patient, calculate the total of the pre- and postsurgical
doses.
21. Using Table 8.2 and a daily dose of 2 mg/kg, how many 20-mg capsules would
a 176-lb patient be instructed to take per dose if the daily dose is to be taken in
divided doses, q.i.d.?
22. For a 22-lb pediatric patient, the dose of cefdinir (OMNICEF) was determined to
be 7 mg/kg. W hat quantity of an oral suspension containing 125 mg of cefdinir
in each 5 mL should be administered?
(a) 2.8 mL
(b) 5.6 mL
(c) 8.9 mL
(d) 13.6 mL
23. H ow many capsules, each containing 250 mg of clarithromycin, are needed to
provide 50 mg/kg/day for 10 days for a person weighing 176 lb?
24. If the pediatric dose of dactinomycin is 15 mcg/kg/day for 5 days, how many
micrograms should be administered to a 40-lb child over the course of treatment?
25. If the administration of gentamicin at a dose of 1.75 mg/kg is determined to result
in peak blood serum levels of 4 mcg/mL, calculate the dose, in milligrams, for a
120-lb patient that may be expected to result in a blood serum gentamicin level
of 4.5 mcg/mL.
148 Pharma euti al c al ulations
26. A medication order calls for tobramycin sulfate, 1 mg/kg of body weight, to be
administered by IM injection to a patient weighing 220 lb. Tobramycin sulfate is
available in a vial containing 80 mg per 2 mL. H ow many milliliters of the injection should the patient receive?
27. T he usual pediatric dose of acyclovir is 20 mg/kg administered by infusion and
repeated every 8 hours. W hat would be the single dose, in milligrams, for a child
weighing 33 lb?
28. If the recommended dose of tobramycin for a premature infant is 4 mg/kg/day,
divided into two equal doses administered every 12 hours, how many milligrams
of the drug should be given every 12 hours to a 2.2-lb infant?
29. If a 3-year-old child weighing 35 lb accidentally ingested twenty 81-mg aspirin
tablets, how much aspirin did the child ingest on a milligram per kilogram basis?
30. T he recommended pediatric dose of epinephrine for allergic emergencies is
0.01 mg/kg. If a physician, utilizing this dose, administered 0.15 mg, what was the
weight of the patient in pounds?
31. T he initial maintenance dose of vancomycin for infants less than 1 week old is
15 mg/kg every 18 hours.
(a) W hat would be the dose, in milligrams, for an infant weighing 2500 g?
(b) H ow many milliliters of an injection containing 500 mg per 25 mL should be
administered to obtain this dose?
32. T he loading dose of indomethacin in neonates is 0.2 mg/kg of body weight by
intravenous infusion.
(a) W hat would be the dose for a neonate weighing 6 lb 4 oz?
(b) H ow many milliliters of an injection containing 1 mg of indomethacin per
0.5 mL should be administered to obtain this dose?
33. 13 Jimmy Jones Age: 8 years
W t: 88 lb
Metronidazole suspension
7.5 mg/kg/day
M.ft. dose = 5 mL
Sig: 5 mL b.i.d. × 10 days
(a) H ow many milligrams of metronidazole will the patient receive per dose?
(b) H ow many milliliters of the prescription should be prepared and dispensed?
(c) If metronidazole is available in 250-mg tablets, how many tablets will be
needed to fill the prescription?
34. 13 Betty Smith Age: 4 years
Weight: 52.8 lb
Erythromycin ethylsuccinate (EES) 200 mg/5 mL
Disp. 300 mL
Sig: mL q.i.d. until gone
(a) If the dose of EES is 50 mg/kg/day, how many milliliters would provide each
dose?
(b) H ow many days would the prescription last the patient?
Calculations Based on Body Surface Area
N OT E: As needed, refer to the BSA nomograms, Mosteller Formula, and/or tables
in this chapter.
8 • c al ulation of Doses: Patient Parameters 149
35. If the daily dose of a drug is given in the literature as 8 mg/kg of body weight
or 350 mg/m2, calculate the dose on each basis for a patient weighing 150 lb and
measuring 5 feet 8 inches in height.
36. If the dose of a drug is 10 mg/m2/day, what would be the daily dose, in milligrams,
for a child weighing 30 lb and measuring 26 inches in height?
37. T he dose of mitomycin injection is 20 mg/m2/day. Determine the daily dose for
a patient who weighs 144 lb and measures 68 inches in height.
38. T he pediatric starting dose of ritonavir (N ORVIR) is 250 mg/m2 by mouth twice
daily. T he available oral solution contains 600 mg of ritonavir in each 7.5 mL
of solution. T he correct volume and corresponding quantity of ritonavir to be
administered to a child with a body surface area of 0.75 m2 per dose is:
(a) 5.6 mL (450.4 mg)
(b) 2.8 mL (450.4 mg)
(c) 2.8 mL (225.2 mg)
(d) 2.3 mL (187.5 mg)
39. Calculate the dose for a child 4 years of age, 39 inches in height, and weighing
32 lb for a drug with an adult dose of 100 mg, using the following: (a) Young’s
rule, (b) Cowling’s rule, (c) Clark’s rule, and (d) BSA (use the BSA equation).
40. T he daily dose of diphenhydramine H Cl for a child may be determined on the
basis of 5 mg/kg of body weight or on the basis of 150 mg/m2. Calculate the dose
on each basis for a child weighing 55 lb and measuring 40 inches in height.
Calculations of Chemotherapeutic Regimens
41. T he drug cabazitaxel is used treating prostate cancer in doses of 25 mg/m2.
Calculate the dose for a patient measuring 73 inches in height and weighing 190 lb.
42. Calculate the quantities of each drug administered to a patient on day 2 of the
ELF protocol if the patient’s BSA is 1.64 m2.
43. If the dose of etoposide for a patient on the CAE protocol is increased to 120 mg/m2,
calculate the increase in the dose, in milligrams, if the patient measures 150 cm
and weighs 48 kg.
44. T he drug carboplatin for ovarian carcinoma is administered intravenously at a
dose of 360 mg/m2 except in patients with impaired kidney function, in which case
the dose is reduced by 30%. H ow many milligrams of the drug should be administered to a renally impaired patient measuring 5 feet 2 inches and weighing 110 lb?
45. A high-dose treatment of osteosarcoma includes the use of methotrexate at a
starting dose of 12 g/m2 as a 4-hour intravenous infusion. For a patient having a
BSA of 1.7 m2 and weighing 162 lb, calculate the dose on the basis of mg/kg/min.
46. A two-agent dosage regimen, termed MP, for the treatment of multiple myeloma
is as follows11:

Melphalan	0.25 mg/kg, PO, D1–4/week × 6 weeks 2 mg/kg, PO, D1–4/week × 6 weeks
Prednisone

(a) Calculate the total milligrams each of melphalan and prednisone taken per
week by a patient who weighs 165 lb.
(b) If melphalan is available in 2-mg tablets, how many tablets are required to
dose this patient for the entire treatment cycle?
(c) If the patient prefers prednisone oral solution to prednisone tablets, how
many milliliters of the solution (5 mg/mL) should be dispensed weekly?
150 Pharma euti al c al ulations
47. A three-agent dosage regimen, termed VAD, for the treatment of multiple
myeloma includes the following drugs taken over a 28-day cycle11:

Vincristine Doxorubicin Dexamethasone

0.4 mg/day, CIVI, D 1–4 9 mg/m2/day, CIVI, D 1–4 40 mg/day, PO, D 1–4, 9–12, 17–20

Calculate the total quantity of each drug administered over the course of the
treatment cycle for a patient with a BSA of 1.65 m2.
48. A four-agent dosage regimen, termed MOPP, for the treatment of H odgkin’s
lymphoma includes the following drugs taken over a 28-day cycle11:

Mechlorethamine Vincristine Procarbazine Prednisone

6 mg/m2, IV, D 1,8 1.4 mg/m2, IV, D 1,8 100 mg/m2/day, PO, D 1–14 40 mg/m2/day, PO, D 1–14

Calculate the total number of 20-mg tablets of prednisone and 50-mg tablets of
procarbazine to dispense to treat a patient with a BSA of 1.5 m2 during the course
of one treatment cycle.
49. T he oncolytic agent lapatinib (T YKERB) is administered in the treatment of
breast cancer in daily doses of 1250 mg for 21 consecutive days in combination with the drug capecitabine (XELODA), which is administered in doses of
1000 mg/m2/day during days 1 to 14 of the 21-day treatment cycle. Calculate
the total quantity of each drug to be administered during the treatment cycle to a
5-feet 2-inch woman weighing 110 lb.
50. Among the single chemotherapeutic agents for breast cancer is docetaxel
(TAXOT ERE), which is administered @ 60 mg/m2 IV every 3 weeks. Calculate
the dose for a 5-feet-4-inch patient who weighs 160 lb.
51. Based on the dose calculated in the above problem, how many milliliters of an
injection containing 80 mg/2 mL docetaxel would be administered per dose?
52. T he chemotherapy regimen “CAF” during a 21-day cycle is11:
Cyclophosphamide 500 mg/m2, D1

Doxorubicin 5-Fluorouracil

50 mg/m2, D1 500 mg/m2, D1,8

Calculate the dose of each drug/cycle for a patient with a BSA of 1.9 m2.
Miscellaneous Practice Problems
53. T he literature states the pediatric dose of the antibiotic clarithromycin as “7.5 mg/kg
q12h.” Calculate the daily dose in milligrams for a child weighing 55 lb.
54. If, in the previous problem, the medication is administered as a suspension containing 125 mg clarithromycin/5 mL, what volume should be administered for
each single dose?
55. T he recommended initial once-a-day dose of the neurologic drug divalproex
sodium is 25 mg/kg/day, to be increased as indicated to an absolute maximum
dose of 60 mg/kg/day. Calculate these quantities for a 182-lb patient.
56. Diproex sodium is available in 250 mg and 500 mg strength tablets. From the
information in the previous problem, what strength tablet and quantity could a
pharmacist recommend for an initial dose?
8 • c al ulation of Doses: Patient Parameters 151
57. T he recommended pediatric dose of leuprolide acetate suspension for intramuscular injection is 7.5 mg, once per month, for a child weighing 25 kg. W hat is the
equivalent dose, based on mg/m2, for this child measuring 36 inches in height?
Use the BSA equation as needed.
58. T he starting pediatric dose of ritonavir is 250 mg/m2 twice daily. Calculate the
single dose, in milliliters, of an oral solution containing 600 mg of ritonavir in
7.5 mL of solution, for a child with a body surface area of 0.64 m2.
59. Beractant intratracheal sterile suspension may be administered to premature neonates within 15 minutes of birth, as indicated, for the prevention and treatment
of respiratory distress syndrome. T he suspension is available in 4-mL and 8-mL
vials containing 25 mg of drug per milliliter. T he dose is 100 mg/kg of birth
weight. Calculate the dose of the suspension for a newborn weighing 1800 g.
60. T he dose of the drug ixabepilone is 40 mg/m2, but if a patient’s BSA is above
2.2 m2, the dose is calculated based on 2.2 m2. Using Figure 8.3, determine which
dose parameter should be used for a patient who is 6 feet tall and weighs 200 lb.
61. T he pediatric dose of levothyroxine sodium is based on both age and body
weight, according to the following:
0 to 3 months, 10 to 15 mcg/kg/day
3 to 6 months, 8 to 10 mcg/kg/day
6 to 12 months, 6 to 8 mcg/kg/day
1 to 5 years, 5 to 6 mcg/kg/day
6 to 12 years, 4 to 5 mcg/kg/day
Verify the correctness of a physician’s order for the dispensing of 100-mcg tablets
to be taken once a day by a 6-year-old child weighing 48 lb.
62. Levothyroxine sodium tablets may be crushed and suspended in water and
administered by spoon or drop to infants and children who cannot swallow intact
tablets. From the information in the previous problem, should a 25-mcg tablet,
a 50-mcg tablet, or a 75-mcg tablet be crushed and suspended for administration
to a 10-month-old infant weighing 17 lb?
63. T he pediatric dose of nelarabine is 650 mg/m2 administered intravenously over
a period of 1 hour daily for 5 consecutive days. T he drug is available in vials
containing nelarabine, 250 mg/50 mL. Using Figure 8.2, calculate (a) the daily
dose of drug, in milligrams, for a child weighing 15 kg and measuring 100 cm in
height, and (b) the total volume of injection to infuse per treatment period.
64. T he oral dose of topotecan in the treatment of small cell lung cancer is 2.3 mg/
m2/day once daily for 5 consecutive days, repeated every 21 days. T he medication
is available in 0.25 mg and 1 mg capsules. Recommend the strength and number
of capsules to dispense for the initial course of treatment of a patient who weighs
165 lb and measures 5 feet 11 inches in height. Use the BSA equation.
65. A patient who is 6 feet tall and weighs 187 lb has been given 170 mg of a medication based on a 2 mg/kg basis. Calculate the same dose, based on mg/m2. Use the
BSA equation as needed.
66. T he recommended dosage of lapatinib for metastatic breast cancer is 1250 mg
given orally once daily on days 1 to 21, in combination with capecitabine
2000 mg/m2/day given orally on days 1 to 14 of a 21-day cycle. H ow many 250-mg
tablets of lapatinib and 150-mg or 500-mg tablets of capecitabine should be dispensed for each cycle of therapy for a patient with a calculated BSA of 1.75 m2?
(Also, refer to the package inserts online and think about the possible prescriptionlabeling instructions for the patient.).
152 Pharma euti al c al ulations
CAl Cq UIz
8.A. The drug eribulin mesylate is used in late-stage metastatic breast cancer at an intravenous dose of 1.4 mg/m2. It is administered on days 1 and 8 of a 21-day cycle.
The dose is reduced by 20% for patients with moderate renal impairment. Calculate
the reduced dose, in (a) mg/m2, (b) mg/kg, and (c) the treatment-day dose, in milligrams, for a 110-lb patient measuring 5 feet 2 inches in height.
8.B. A parent takes her 5- and 7-year-old boys to the pediatrician, both with pharyngitis.
The boys weigh 40 and 50 lb, respectively. The doctor prescribes an oral suspension
of cefuroxime axetil (CEFTIN) at a dose of 20 mg/kg/day divided b.i.d. × 10 days.
The suspension has a cefuroxime axetil concentration of 125 mg/mL. How many
milliliters of suspension will be needed during the course of treatment?
8.C. The first-day loading dose of a drug is 70 mg/m2 followed by a dose of 50 mg/m2
daily thereafter. Irrespective of the patient’s BSA, a dose is not to exceed 70 mg. For
a 5-feet 8-inch 150-lb patient, calculate the (a) BSA using the Mosteller formula, (b)
loading dose, and (c) maintenance dose, and indicate whether each dose is within
the safe limit.
8.D. The pediatric oral dose of ciprofloxacin is given as 10 to 20 mg/kg every 8 hours, not
to exceed a single dose of 400 mg irrespective of body weight. If a child weighing
55 lb is prescribed a one-teaspoonful dose of a 5% ciprofloxacin oral suspension every
8 hours, calculate whether or not the dose prescribed is within the therapeutic range.
8.E. The drug peginterferon alpha-2b is sometimes administered according to a “stepdown” protocol from a starting dose of 1.5 mcg/kg/week to 1 mcg/kg/week to
0.5 mcg/kg/week. Calculate the three doses for a 5-feet 5-inch 132-lb patient (a) in
micrograms and (b) on a mcg/m2 basis.
67. Cefixime, an anti-infective agent, is available in oral suspensions of the following
strengths: 100 mg/5 mL, 200 mg/5 mL, and 500 mg/5 mL. T he pediatric dose is
8 mg/kg/day, administered in divided dosage. Calculate (a) the daily dose of cefixime for a 55-lb patient, (b) the most appropriate product strength to dispense, and
(c) the quantity of oral suspension, in milliliters, required for a 10-day course of
treatment.
68. Pertuzumab, for the treatment of late-stage breast cancer, is administered at an
initial dose of 840 mg by intravenous infusion. It is coadministered every 3 weeks
with trastuzumab 8 mg/kg and docetaxel 75 mg/m2. Calculate the doses of trastuzumab and docetaxel, for a patient who is 60 inches in height and weighs 158 lb.
Use the BSA equation as needed.
8 • c al ulation of Doses: Patient Parameters 153
ANSWERS TO “CASE IN POINT” AND PRACTICE PROBl EmS
Case in Point 8.1
T he metric weight of a 3-lb 7-oz neonate is calculated:
1 lb = 454 g; 1 oz = 28.35 g
3 lb × 454 g/lb = 1362 g
7 oz × 28.35 g/oz = 198.45 g
1362 g + 198.45 g = 1560.45 g, weight of the neonate
According to the dosing table, the dose for a 3-day-old neonate weighing less than
2000 g is 10 mg/kg/day divided every 12 hours.
T he dose, in mg, may be calculated by dimensional analysis:
1
1000
10
1
1560 45
15 6
kg
g
mg
kg day
g
mg clindamycin day
× ×
=
/
.
. /
Since the daily dose is administered in two divided doses, each divided dose is:
15 6
2
. mg
= 7.8 mg clindamycin every 12 hours
T he volume of injectable solution is then calculated:
50
600
7 8 0 65
mL
mg
× . . = mg mL
Case in Point 8.2
To calculate the oral dose of enalapril for the patient, it is necessary to know the
patient’s weight. T his may be calculated from the intravenous dose:
1
5
55
11
kg
mcg
mcg
kg the weight of the patient
×
= ,
T hen, the oral dose may be calculated:
100
1
11 1100 1 1
mcg
kg
× = = kg mcg mg .
By crushing and mixing the 2.5-mg enalapril tablet with sterile water to make 12.5 mL,
the oral dose may be calculated:
2 5
12 5
1 1
5 5
.
.
.
; .
mg
mL
mg
x mL
= = x mL
Case in Point 8.3
Daily dose: 15 mg/kg × 10 kg = 150 mg
Single dose: 150 mg ÷ 3 = 50 mg
Q uantity of injection mg mL
mg
: 50 1 mL
5
× = 10
154 Pharma euti al c al ulations
Case in Point 8.4
(a) 28 inches × 2.54 cm/1 inch = 71.12 cm
22 lb × 1 kg/2.2 lb = 10 kg
BSA m
H t cm W t kg
,
2 ( ) ( )
3600
=
×
=
71 12 10 ×
3600
. ( ) ( ) cm kg
= 0 198 .
BSA m , . 2 = 0 44
230 mg (lopinavir) × 0.44 m2 = 101.2 mg
57.5 mg (ritonavir) × 0.44 m2 = 25.3 mg
T hus, 101.2 mg (lopinavir) and 25.3 mg (ritonavir)
(b) 101.2 mg × 1 mL/80 mg = 1.27 mL
25.3 mg × 1 mL/20 mg = 1.27 mL
T hus, 1.27 mL or 1.3 mL oral solution (administered by calibrated oral syringe).
(c) KALET RA, 12/3 mg/kg
12 mg (lopinavir)/kg × 10 kg = 120 mg (lopinavir, single dose)
3 mg (ritonavir)/kg × 10 kg = 30 mg (ritonavir, single dose)
T hus, 120 mg × 2 (doses/day) = 240 mg (lopinavir), and
30 mg × 2 (doses/day) = 60 mg (ritonavir)
(d) 240 mg (lopinavir) × 1 mL/80 mg = 3 mL
60 mg (ritonavir) × 1 mL/20 mg = 3 mL
T hus, 3 mL oral solution, daily dose (administered by calibrated oral syringe).
It should be noted that since the ratio of lopinavir to ritonavir in the oral solution is fixed, that
is, 80 mg:20 mg (or 4 mg:1 mg), the calculation of one component will automatically yield the
quantity of the second component.
Case in Point 8.5
To calculate the dose for the patient, the pharmacist must first determine the patient’s
body surface area. T he pharmacist elects to use the following equation:
BSA m
H t cm W t kg
,
2 ( ) ( )
3600
=
×
To use this equation, the patient’s weight and height are converted to metric units:
H eight = 5 feet = 60 inches × 2.54 cm/inch = 152.4 cm
Weight = 117 lb ÷ 2.2 lb/kg = 53.2 kg
Solving the equation:
BSA m , m
. .
( ) 2 152 4 53 2 . 2
3600
= 1 50
×
=
T he daily dose is calculated as 150 mg/m2 × 1.50 m2 = 225 mg.
To obtain 225 mg, the patient may take two 100-mg capsules, one 20-mg capsule,
and one 5-mg capsule daily.
8 • c al ulation of Doses: Patient Parameters 155
Practice Problems
1. 12.5 mg
2. 12.73 mg gentamicin
3. 30 mg gentamicin
4. Overdose
5. IV: 327.3 to 545.5 mg ciprofloxacin
Oral: 363.6 to 727.3 mg
ciprofloxacin
6. (a) ½ tsp. (2.5 mL) erythromycin
ethylsuccinate
(b) 10 days
7. 4.4 to 7.5 mL chlorothiazide oral
suspension
8. 9.55 mL cyclosporin
9. 2 tsp.
10. Yes, calculations were correct.
11. 30 tablets
12. 0.15 mL digoxin injection
13. 145.5 mcg digoxin
14. 3.41 mL
15. (c) 1.08 mL and 0.65 mL filgrastim injection
16. 7.58 mL phenytoin suspension
17. 4.8 mcg digoxin
18. 18.33 lb
19. 0.073 mL
20. 93.64 or 94 mg
21. 2 capsules
22. (a) 2.8 mL cefdinir oral suspension
23. 160 clarithromycin capsules
24. 1364 mcg dactinomycin
25. 107.39 mg gentamicin
26. 2.5 mL tobramycin injection
27. 300 mg acyclovir
28. 2 mg tobramycin
29. 101.83 mg/kg aspirin
30. 33 lb
31. (a) 37.5 g vancomycin
(b) 1.875 mL vancomycin injection
32. (a) 0.57 mg indomethacin
(b) 0.28 mL indomethacin injection
33. (a) 150 mg metronidazole
(b) 100 mL
(c) 12 metronidazole tablets
34. (a) 7.5 mL
(b) 10 days
35. 545.5 mg and 630 mg
36. 4.5 mg
37. 35.4 mg mitomycin
38. 2.3 mL (187.5 mg) ritonavir
39. (a) 25 mg
(b) 20.83 mg
(c) 21.33 mg
(d) 36.57 mg
40. (a) 125 mg diphenhydramine H Cl
(b) 120 mg diphenhydramine H Cl
41. 52.7 mg cabazitaxel
42. 196.8 mg etoposide
246 mg leucovorin
820 mg 5-fluorouracil
43. 29.7 mg etoposide
44. 372.96 mg carboplatin
45. 1.15 mg/kg/min methotrexate
46. (a) 75 mg melphalan and 600 mg
prednisone
(b) 225 tablets
(c) 120 mL prednisone oral solution
47. 1.6 mg vincristine
59.4 mg doxorubicin
480 mg dexamethasone
48. 42 procarbazine tablets
42 prednisone tablets
49. 26.25 g lapatinib and 20.72 g
capecitabine
50. 108.7 mg docetaxel
51. 2.7 mL docetaxel injection
52. 1900 mg 5-fluorouracil
95 mg doxorubicin
950 mg cyclophosphamide
53. 375 mg clarithromycin
54. 7.5 mL clarithromycin suspension
55. 2068.2 mg divalproex sodium, initial dose
4963.6 mg divalproex sodium,
maximum dose
56. Four 500-mg tablets, initial dose
57. 9.4 mg/m2
58. 1 mL ritonavir oral solution
59. 7.2 mL beractant suspension
60. 40 mg/m2
61. Correct
156 Pharma euti al c al ulations
62. A 50-mcg levothyroxine sodium
tablet
63. (a) 416 mg nelarabine
(b) 416 mL nelarabine injection
64. Twenty 1-mg topotecan capsules
(4/day) and ten 0.025 mg topotecan capsules (2/day)
65. 81.8 mg/m2
66. O ne hundred five 250-mg
lapatinib tablets and ninety-eight
500-mg capecitabine tablets
67. (a) 200 mg cefixime
(b) 100 mg/5 mL
(c) 100 mL cefixime suspension
68. 574.5 mg trastuzumab and
130.8 mg docetaxel
References
1. Ferri FF. Practical Guide to the Care of the Medical Patient. 8th Ed. Maryland H eights, MO: Elsevier; 2011.
2. Berkow R, ed. The Merck Manual. 16th Ed. Rahway, N J: Merck Research Laboratories; 1992.
3. T he Joint Commission. Available at: http://www.jointcommission.org/assets/1/18/SEA_39.PDF. Accessed
May 5, 2014.
4. Gomella T L, ed. Neonatology: Management, Procedures, On-Call Problems, Diseases, and Drugs. 6th Ed. N ew York,
N Y: McGraw-H ill; 2009.
5. Taketomo CK. Pediatric & N eonatal Dosage Handbook. 20th Ed. H udson, OH : Lexicomp/Wolters Kluwer
H ealth Clinical Solutions; 2013–2014.
6. Mosteller RD. Simplified calculation of body surface area. The New England Journal of Medicine 1987;317:1098.
7. American Cancer Society. Available at: http://www.cancer.org/Treatment/TreatmentsandSideEffects/
TreatmentTypes/index. Accessed February 10, 2011.
8. CancerTreatment.net. Available at: http://regimens.cancertreatment.net/. Accessed May 5, 2014.
9. Chemotherapy Advisor. Available at: http://www.chemotherapyadvisor.com/cancer-treatment-regimens/
section/2412/. Accessed May 5, 2014.
10. N ational Cancer Institute. Available at: http://www.cancer.gov/cancertopics/druginfo/alphalist. Accessed May
5, 2014.
11. MediLexicon. Cancer drugs and oncology drugs. Available at: http://www.medilexicon.com/drugs-list/cancer.
php. Accessed May 5, 2014.
12. Schwarz LR. D elivering cytotoxic chemotherapy safely in a community hospital. Hospital Pharmacy
1996;31:1108–1118.
13. Beach W. College of Pharmacy. Athens GA: T he University of Georgia; 2004.
157
T he potencies o some antibiotics, endocrine products, vitamins, products derived through
biotechnology, and biologics (e.g., vaccines) are based on their activity and are expressed
in terms o units of activity, in micrograms per milligram, or in other standardized terms o
measurement. T hese measures o potency meet standards approved by the Food and Drug
Administration as set orth in the United States Pharmacopeia (USP).1 In addition, the World
H ealth Organization (W H O) through the International Pharmacopeia (IP) provides internationally agreed upon standards or biological preparations, which def ne potency or activity,
as expressed in international units (I.U. or IU).2
T he activity o a drug or biologic agent is determined by comparison against a corresponding reference standard—an authenticated specimen used in compendial tests and
assays. T he required potencies and respective weight equivalents or some drugs are given
in Table 9.1. A USP Unit for one drug has no relation to a USP Unit for another drug.
O the drugs or which potency is expressed in units, insulin is perhaps the most common. Commercially available types o insulin vary according to time or onset o action,
peak action, and duration o action; however, all are standardized to contain either 100
or 500 insulin units per milliliter o solution or suspension. T hese products are labeled as
“U-100” (Fig. 9.1) or “U-500.” Insulin is dosed by the administration o a speci ic number
o units. Specially calibrated insulin syringes (Fig. 9.2) or pre illed, dial-a-dose insulin pens
(KwikPen [Lilly] and FlexPen [N ovo N ordisk]) are employed.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:
P rform al ula on n ol ng un of a y and o h r m a ur of po n y.
9

Ca cu a io	I vo vi g
U i of Ac ivi y a d O h r
M a ur of Po	cy

CAl CUl At IOn s CAPs Ul e
Units of Activity
The potency of many pharmaceutical products derived from biological sources is based
on units of activity. Units of activity are determined against specific biologic standards and
vary between products. Generally, there is an established relationship between a product’s
units of activity and a measurable quantity (e.g., units per milligram; units per milliliter).
This relationship may be used in a ratio and proportion to determine either the number of
units of activity or the weight or volume containing a specified number of units:
Units of activity given
Weight or volume given
( ) Units of activit
( ) =
y given or desired
Weight or volume given or desired
( )
( )
158 Pharma euti al c al ulations
t ab 9.1 •  e xAMPl e s Of Dr Ug POt e n Cy e q UIvAl e n t s

D u	U i o m o Po	c P W i h e ui a	a
Alteplase	580,000 USP Alteplase Units per mg of protein
Bacitracin zinc	NLT 65 Bacitracin Units per mg
Cefdinir	NLT 960 µg and NMT 1020 µg of cefdinir per mg
Clindamycin hydrochloride	NLT 800 µg of clindamycin per mg
Cod liver oil	In each gram: NLT 180 µg (600 USP Units) and NMT 750 µg (2500 USP Units) of Vitamin A and NLT 1.5 µg (60 USP Units) and NMT
6.25 µg (250 USP Units) of Vitamin D NLT 600 µg of erythromycin per mg NLT 590 µg of gentamicin per mg NLT 180 USP Heparin Units per mg NLT 26.5 USP Insulin Units per mg	Erythromycin estolate Gentamicin sulfate Heparin sodium Insulin
Insulin glargine Insulin glulisine	27.5 units/mg 28.7 units/mg
Insulin human Insulin lispro Interferon alpha-2b Interferon alpha-n3 Interferon beta-1b Neomycin sulfate Nystatin	NLT 27.5 USP Insulin Human Units per mg NLT 27 USP Insulin Lispro Units per mg 2.6 × 108 international units per mg 2 × 108 international units per mg 3.2 × 107 international units per mg NLT 600 µg of neomycin per mg NLT 4400 USP Nystatin Units per mg
Penicillin G benzathine Penicillin G potassium Penicillin V potassium	NLT 1090 and NMT 1272 Penicillin G Units per mg NLT 1440 and NMT 1680 Penicillin G Units per mg NLT 1380 and NMT 1610 Penicillin V Units per mg
Polymyxin B sulfate Somatropin Tobramycin Vancomycin Vasopressin	NLT 6000 Polymyxin B Units per mg 3 international units per mg NLT 900 µg of tobramycin per mg NLT 900 µg vancomycin per mg NLT 300 Vasopressin Units per mg
Vitamin A	1 USP Vitamin A Unit equals the biologic activity of 0.3 µg of the all-trans
isomer of retinol 40 units per µg	Vitamin D

aData taken or derived from various literature sources including the United States Pharmacopeia and the International Pharmacopeia.
As noted previously in this text, medication errors can occur when the term units is
abbreviated with a “U.” For example, “100U” could be mistaken or “1000” units. T hus, it
is recommended that the term units be spelled out as a matter o practice.
Another e ort to reduce medication errors has been implemented by clari ying the
contents o certain packages o multidose injections. Figure 9.3 shows the dual statement
o strength in the labeling o a H eparin Sodium Injection in which the drug concentration
or the entire contents (30,000 USP Units/30 mL) and the concentration per milliliter
(1,000 USP Units/mL) are displayed.
Various Expressions of Potency
Biologics are preparations produced rom a living source. T hey include vaccines, toxoids,
and immune sera, used or the development o immunity or resistance to disease; certain
antitoxins and antivenins, used as treatment against specif c antigens; and toxins and skin
9 • c al ulat ons involv ng Un ts of A t v ty and Other Measures of Poten y 159
f Ig Ur e 9.1 •  Example of a pharmaceutical product standardized in units
of activity.
f Ig Ur e 9.2 •  Example of an insulin syringe calibrated in Units. (Courtesy of Becton, Dickinson and Company.)
f Ig Ur e 9.3 •  Label for a multidose package of Heparin Sodium Injection, USP, displaying a dual statement
of strength to clarify contents and reduce misinterpretation and medication errors. (Source: http://dailymed.nlm.
nih.gov/dailymed/about.cfm. Courtesy of Pfizer, Inc.)
160 Pharma eu al c al ula o
antigens, used as diagnostic aids. Biologics are prepared rom human serum (e.g., immune
globulin), horse serum (e.g., tetanus antitoxin), chick cell culture (e.g., measles virus vaccine), and other such animate media.
T he strengths o the various biologic products are expressed in a number o ways. T he
strength o a bacterial vaccine commonly is expressed in terms o micrograms or units o
antigen per milliliter. T he strength o a viral vaccine is expressed most commonly in terms
o the tissue culture infectious dose (TCID50), which is the quantity o virus estimated to in ect
50% o inoculated cultures. Viral vaccines may also be described in terms o units, micrograms o antigen, or number or organisms per milliliter. T he strength o a toxoid is generally expressed in terms o flocculating units (Lf Unit), with 1 L Unit having the capacity to
locculate or precipitate one unit o standard antitoxin.
Vaccines are available or a large number o diseases, including cervical cancer (human
papillomavirus), hepatitis A and B, in luenza, measles, mumps, pneumococcal, shingles
(herpes zoster), smallpox, and tuberculosis. In addition, many additional vaccines are in
various stages o development. T he N ational Institute o Allergy and In ectious Diseases
(N IAID) o the N ational Institutes o H ealth (N IH ) lists all vaccines licensed or use in the
United States as well as the status o vaccines in current research and development.3 T he
Centers or Disease Control and Prevention (CDC) o ers current guidelines or vaccine
use in di erent population groups, as in ants, children, adults, and pregnant women.4
Speci ic examples o the potency o vaccines expressed in terms other than weight are:
H epatitis A vaccine, inactivated, 1440 EL.U (ELISA units) per 1-mL dose
In luenza virus vaccine, live (intranasal), 106.5–7.5 FFU ( luorescent ocus units) per
0.2-mL dose
Measles virus vaccine, live N LT 1000 T CID 50 (50% tissue culture in ectious dose) in
each 0.5-mL dose
Zoster Vaccine, Live, 19,400 PFU (plaque- orming units) per 0.65-mL dose
Products of Biotechnology
In addition to the biologic types o products described above, the activities o some products
o biotechnology also are expressed in terms o units o activity (e.g., inter eron alpha-2b contains 2.6 × 108 international units per milligram).
Pharmacy-Based Immunizations
Pharmacy-based immunization programs are commonplace nowadays. Many colleges o
pharmacy and pharmacy organizations have developed pharmacy immunization training
programs, and states permit pharmacists to administer immunizations under established
guidelines and protocols.
Example Calculations of Measures of Activity or Potency
Determinations o the activity or potency o a biologic material considered in this chapter
may be per ormed through the use o ratio and proportion or dimensional analysis, as demonstrated by the ollowing examples.
Un it s Of Ac t ivit y
Calculations involving units o activity are exemplif ed as ollows.
(1) How many milliliters of U-100 insulin should be used to obtain 40 units of insulin?
U-100 insulin contains 100 units/mL
100

40 ( ) units x

( ) . x mL

( ) 1
( )
units
mL
= =
0 4 mL U 100 insulin –
9 • c a u a o i o U o A a O M a u o Po 161
Or, solving by dimensional analysis:
40 1
100
units mL
units
× = 0 4 mL U 100 insulin . –
(2) A physician prescribed 100 units o insulin to be added to 500 mL o D5W in treating a
patient with severe diabetic acidosis. How many milliliters o insulin injection concentrate,
U-500, should be used?
U-500 insulin contains 500 units/mL
500
100
( ) 1
( )
( )
( )
.
units
units
mL
x mL
x
= =
0 2 mL U 500 insulin –
Or, solving by dimensional analysis:
100 1
500
units

mL units = 0 2 mL U 500 insulin . –

×

(3) How many milliliters o a Heparin Sodium Injection containing 200,000 units in 10 mL
should be used to obtain 5,000 heparin sodium units that are to be added to an intravenous
dextrose solution?
200 000
5000
, ( ) 10
( )
( )
( )
.
units
units
mL
x mL
x
= =
0 25 mL heparin sodium injection
(4) I a 2.5-mL vial contains 100 units o onabotulinumtoxinA (BOTOX), and 0.1 mL is injected
into each o f ve sites during a procedure, how many units o drug would remain in the vial?

Used in procedure	mL mL	sites	mL
Remaining in vial	. mL mL =

: . ( ) .
: .
0 1 5 0 5
2 5
× =
– 00 5 2
100 2
2 5
.
units mL
mL
×
= 80 units onabotulinumtoxinA
Ac t ivit y b As e d On We ig h t
Calculations involving the determination o activity per unit o weight are exemplif ed as ollows.
I neomycin sul ate has a potency o 600 mg o neomycin per milligram, how many milligrams
o neomycin sul ate would be equivalent in potency to 1 mg o neomycin?
600
1000
( ) 1
( )
m ( )
m
g of neomycin
g of neomycin
mg of neomycin sulfate
=
xx mg of neomycin sulfate
x
( )
1 67 mg neomycin sulfate .=
d Os e Or An t ig e n c On t e n t Of A b iOl Og ic b As e d On POt e n c y
Calculations o the dose or the antigen content o a biologic product are exemplif ed as ollows:
(1) A biologic contains 50 L Units o diphtheria toxoid in each 2.5 mL o product. I a pediatric
patient is to receive 10 L Units, how many milliliters o product should be administered?
50
10
( ) 2 5
( )
. ( )
( )
.
Lf Units
Lf Units
mL
x mL
x
= =
0 5 mL
162 Pha ma eu a c a u a on
(2) Measles virus vaccine live is prepared to contain 1000 TCID50 per 0.5-mL dose. W hat is
the TCID50 content of a 50-mL multiple-dose vial of the vaccine?
1000 0 5

50 ( ) , mL

50 50 ( ) x T CID

x

( )
. ( )
T CID
mL
= =
100 000 T CID
50
Pr ACt ICe Pr Ob l e Ms
Authors’ Note: some abbreviations in this section are as they appear in certain product literature, and their use here is strictly for instructional purposes and not an endorsement of style.
Units of Activity Calculations
1. H ow many milliliters of U-100 insulin zinc suspension should be used to obtain
18 units of insulin?
2. If a diabetic patient injects 20 units of insulin twice daily, how many days will a
10-mL vial of the U-100 product last the patient?
3. T he biotechnology-derived product interferon beta-1b contains 32 million international units per milligram. Calculate the number of international units present
in a vial containing 0.3 mg of interferon beta-1b.
4. ALFERON N injection contains 5 million international units of interferon
alpha-n3 per milliliter. H ow many units will an injection of 0.05 mL deliver?
5. Insulin glargine (LAN T US) injection is available in 10-mL vials, containing
100 units/mL. H ow many milliliters would a patient administer for (a) a starting
dose of 10 units and (b) a maintenance dose of 4 units?

CAs e In POIn t 9.1 a A pha ma	a ked o a	n de e m n n he o e
do e o epoe n a a (Pr Oc r it ) nje on o a 76-yea -o d, 165- ma e pa en u –
e n om anem a, n pa due o h on	ena a u e. t he pa en ’ n a hemo o
n	9.2 /dl .
t he	e a u e a e he a n adu do e o epoe n a a o e “50 o 100
un /k s c t iW” o	mu a e ed ood e p odu on. f	y, (a) wha wou d e he
o e	n e p e a on o h do a e a emen ?b
t he	e a u e u he	a e ha he do e	o e reduced y 2 5 % when he
pa en ’ hemo o n ea he a eve u a e o avo d an u on o n ea e
>1 /dl n any 2 -week pe od. t he do e	o e increased o “3 0 0 un /k t iW”
a e 2 –4 week	he hemo o n e pon e	n u	en o	an u on a e
equ ed.
U n epoe n a a nje on, 10,000 un /ml , and he m n ma	a n do e,
a u a e ( ) he num e o m	e	equ ed o he n a do e and ( ) he o a
num e o m	e	o e adm n e ed du n he	week o	ea men . i he ea men , wha wou d
pa en ’ hemo o n n ea e o 10.5 /dl a e 2 week o
e he new do e n (d) un	o epoe n a a and n (e) m	e o nje on?

a
c a e n Po n ou e y o f ynn Wa en, b hop, g A.
bi un u e o he a ev a on , e e o c hap e 4 o u dan e.
9 • c al ulat ons involv ng Un ts of A t v ty and Other Measures of Poten y 163
6. T he content of a vial of penicillin G potassium weighs 600 mg and represents
1 million units. H ow many milligrams are needed to prepare 15 g of an ointment
that is to contain 15,000 units of penicillin G potassium per gram?
7. H UMALOG contains 100 units of insulin lispro (rDN A origin) per milliliter.
H ow many complete days will a 3-mL H UMALOG PEN last a patient whose
dose is 35 units bid?
8. A physician prescribes 2.5 million units of penicillin G potassium daily for
1 week. If 1 unit of penicillin G potassium equals 0.6 mg, how many tablets, each
containing 250 mg, will provide the prescribed dosage regimen?
9.
Using soluble penicillin tablets, each containing 200,000 units of crystalline
penicillin G potassium, explain how you would obtain the penicillin G potassium
needed in compounding the prescription.
10. FOSAMAX PLUS D contains 70 mg alendronate and 140 mcg of vitamin D 3, the
latter equivalent to 5600 international units of vitamin D. At a once-a-week dose,
calculate the daily intake of vitamin D 3 in milligrams and units.
11. A vial for preparation of 100 mL of injection of the drug alteplase (ACT IVASE)
contains 100 mg of drug equivalent to 58 million international units to be administered by intravenous infusion. Calculate (a) the units administered to a 176-lb
patient at a dose of 0.9 mg/kg and (b) the milliliters of injection to use.
12. Calcitonin is available as an injection containing 200 international units per milliliter. Adult doses of up to 32 units per kilogram have produced no adverse effects.
On this basis, if a 120-lb patient were administered 0.75 mL of injection, would
adverse effects be anticipated?
13. A physician’s hospital medication order calls for a patient to receive 1 unit
of insulin injection subcutaneously for every 10 mg/dL of blood sugar over
175 mg/dL, with blood sugar levels and injections performed twice daily in the
morning and evening. T he patient’s blood sugar was 200 mg/dL in the morning
and 320 mg/dL in the evening. H ow many total units of insulin injection were
administered?
14. A physician’s hospital medication order calls for isophane insulin suspension to
be administered to a 136-lb patient on the basis of 1 unit/kg per 24 hours. H ow
many units of isophane insulin suspension should be administered daily?
15. Somatropin (N UT ROPIN ) contains 5 mg of drug equivalent to approximately
15 IU of drug in a vial to prepare 10 mL of injection. If the starting adult dose
is 0.006 mg/kg, calculate the dose (a) in units and (b) in milliliters for a 132-lb
patient.
16. Cod liver oil is available in capsules containing 0.6 mL per capsule. Using
Table 9.1, calculate the amounts, in units, each of vitamins A and D in each capsule. T he specific gravity of cod liver oil is 0.92.
17. A hepatitis B immune globulin contains 312 IU/mL. If the dose is 0.06 mL/kg
for certain at-risk persons, calculate the dose (a) in units and (b) in milliliters for
a 132-lb person.
18. If a 5-mL vial of H U MAT RO PE, a biosynthetic somatropin of rD N A
origin, contains 5 mg of somatotropin equivalent to 13 IU , how many
milligrams of somatotropin and how many IU would be administered in a
0.6-mL dose?
Penicillin G potassium 5000 units/mL
Isotonic sodium chloride solution ad 15 mL
164 Pharma euti al c al ulations
19. EPOGEN injection is available containing in each milliliter, 2000, 3000, 4000, or
10,000 units of epoetin alfa. If the staring dose for a 160-lb patient is prescribed
at 50 units/kg, which of the following would provide that dose?
(a) 4 mL of 2000 units/mL
(b) 1 mL of 3000 units/mL
(c) 0.9 mL of 4000 units/mL
(d) 0.8 mL of 10,000 units/mL
20. T he prophylactic dose of tetanus antitoxin is 1500 units for persons weighing less than
65 lb and 3000 to 5000 units for persons weighing more than 65 lb. T he antitoxin is
available in dose vials of 1500 units, 3000 units, 5000 units, and 20,000 units. W hich
vial should a pharmacist provide for administration to a patient weighing 25 kg?
Additional Calculations of Potency
21. T he product CREON (pancrelipase) contains 3000 units of lipase, 9,500 units of
protease, and 15,000 units of amylase in delayed-release capsules. T he capsules
are to be swallowed whole or the contents added uncrushed to food immediately
prior to administration. T he dose should not exceed 2500 lipase units/kg of body
weight. If the contents of one capsule are added to 120 mL of the feeding formula
for a 12-lb infant, is the dose within accepted limits?
22. Define “<1.75 mIU/mL” as stated in the package insert for the drug leuprolide
acetate (LUPRON DEPOT-PED).
23. W hat is the numerical difference between “1 mIU” and “1 MIU?”
24. During cholecystography to determine gallbladder function, the contents of one
bottle of cholecystokinin containing 75 units is dissolved in physiological saline
solution to make 7.5 mL. T hen, 1 unit per kilogram of body weight is administered by slow intravenous injection. Calculate the dose, in units, and the volume,
in milliliters, to be administered to a patient weighing 154 pounds.
25. Using Table 9.1, calculate the clindamycin potency equivalence, in milligrams per
milliliter, of a solution containing 1 g of clindamycin hydrochloride in 10 mL of
solution.
26. Each 1-mL adult dose of hepatitis A vaccine contains 1440 EL.U. of viral antigen.
W hat would be the pediatric dose of this vaccine if 360 EL.U. of viral antigen are
to be administered?
(a) 0.8 mL
(b) 0.25 mL
(c) 4 mL
(d) 0.4 mL
27. Each 0.01 mL of a mumps vaccine contains 400 T CID 50 of the mumps virus. If
the usual dose contains 20,000 T CID 50, how many milliliters of vaccine should
be administered?
28. If a biologic product contains 7.5 Lf Units of diphtheria toxoid per 0.5 mL, how
many flocculating units would be present in a 7.5-mL multiple-dose vial?
29. Zoster Vaccine Live (ZOSTAVAX) contains about 29,850 plaque-forming units
(PFU) of attenuated virus per 0.1 cL. Approximately how many PFUs would be
contained in each 0.65-mL dose?
(a) 45,900 PFU
(b) 4590 PFU
(c) 1940 PFU
(d) 19,400 PFU
9 • c al ulat ons involv ng Un ts of A t v ty and Other Measures of Poten y 165
CAl Cq UIz
9.A. If a 5-mL quantity of a nystatin oral suspension is prepared to contain 500,000 USP
Nystatin Units, using Table 9.1, calculate (a) the concentration of nystatin in the suspension in mg/mL. If a child’s dose is 2 mL four times a day, how many (b) nystatin
units and (c) milligrams of nystatin would be administered daily?
9.B. The drug dalteparin sodium (FRAGMIN) is administered by subcutaneous injection
in patients with unstable angina or myocardial infarction at doses of 120 units/kg but
not to exceed 10,000 units. Prefilled calibrated syringes are available with the following strengths (units/mL): 2500/0.2 mL, 5000/0.2 mL, 7500/0.3 mL, 10,000/0.4 mL,
12,500/0.5 mL, and 15,000/0.6 mL. Calculate (a) the most efficient product strength
to use to dose a patient weighing 148 lb, (b) the volume of that injection to administer, and (c) the weight of a hypothetical patient, in pounds, to reach the maximum
dose of 10,000 units.
9.C. An injection contains 5 million international units (MIU) of interferon alpha-n3
(ALFERON N) proteins per milliliter. The recommended dose is 0.05 mL. The literature states that the activity of interferon alpha-n3 is approximately equal to 2.6 × 108
international units/mg of protein. Calculate (a) the number of international units and
(b) the micrograms of interferon alfa-n3 proteins administered per dose.
9.D. One general guideline for the maintenance dosing of heparin in pediatric patients is
100 units/kg every 4 hours, or 20,000 units/m2/24 hour administered continuously. The
available injection for use by intravenous infusion contains 1000 USP Heparin Units/mL.
For a 44-lb child, measuring 42 inches in height, calculate the difference between
the quantities of heparin administered over a 24-hour period in (a) heparin units,
(b) in milligrams of heparin (sodium), and (c) in milliliters of heparin injection.
An s We r s t O “CAs e In POIn t ” An D Pr ACt ICe Pr Ob l e Ms
Case in Point 9.1
(a) T IW = three times a week (It should be noted that although this abbreviation
appears in the literature, it is considered error prone and thus its use is not approved
by the Institute of Safe Medication Practices.)
(b) 165 lb ÷ 2.2 lb/kg = 75 kg, weight of patient
Minimal starting dose = 50 units/kg; thus, 50 units × 75 (kg) = 3750 units
3750 units ÷ 10,000 units/mL = 0.375 mL of epoetin alfa injection
(c) 0.375 mL/dose × 3 (times per week) = 1.125 mL epoetin alfa injection
(d) Dose reduced by 25% or 937.5 units; thus, 3750 – 937.5 = 2812.5 units
epoetin alfa
(e) 2812.5 units ÷ 10,000 units/mL = 0.28 mL epoetin alfa injection
Practice Problems
1. 0.18 mL U-100 insulin zinc suspension
2. 25 days
3. 9,600,000 units interferon beta 1-b
4. 250,000 international units
5. (a) 0.1 mL insulin glargine
(b) 0.04 mL insulin glargine
166 Pharma euti al c al ulations
6. 135 mg penicillin G potassium
7. 4 days
8. 42 penicillin G potassium tablets
9. Dissolve 1 tablet in enough isotonic sodium chloride solution to make 8 mL, and
take 3 mL of the dilution.
10. 800 units and 0.02 mg/day
11. (a) 41.76 million units alteplase
(b) 72 mL alteplase injection
12. N o
13. 17 units insulin
14. 61.82 units isophane insulin
15. (a) 1.08 units somatropin
(b) 0.72 mL somatropin injection
16. 331.2 to 1380 units of vitamin A 33.12 to 138 units of vitamin D
17. (a) 1123.2 IU hepatitis B immune globulin
(b) 3.6 mL hepatitis B immune globulin
18. 0.6 mg, and 1.56 or 1.6 IU somatropin
19. (c) 0.9 mL of 4000 units/mL
20. 1500-unit vial
21. Yes
22. Less than 1.75 milli-international units per milliliter
23. 1 billion international units
24. 70 Units/dose and 7 mL/dose
25. 80 mg/mL clindamycin
26. (b) 0.25 mL
27. 0.5 mL mumps vaccine
28. 112.5 Lf Units diphtheria toxoid
29. (d) 19,400 PFU
References
1. United States Pharmacopeia 32 National Formulary 27. Vol. 1. Rockville, MD: T he United States Pharmacopeial
Convention; 2009;419–420.
2. World H ealth Organization (W H O). Available at: http://www.who.int/biologicals/reference_preparations/en/.
Accessed May 8, 2014.
3. N ational Institute of Allergy and Infectious Diseases. Vaccine Research Center. Available at: http://www.niaid.
nih.gov/about/organization/vrc/Pages/default.aspx. Accessed May 8, 2014.
4. Centers for Disease Control and Prevention. Vaccines and Immunizations. Available at: http://www.cdc.gov/
vaccines/. Accessed May 8, 2014.
167
Heparin-Dosing Calculations
H eparin, also known as unfractionated heparin or UFH , is a heterogenous group of
mucopolysaccharides that have anticoagulant properties. H eparin slows clotting time. It
is derived from the intestinal mucosa or other suitable tissues of domestic animals (often
porcine) used for food by man. Salt forms of heparin, such as heparin sodium, are standardized to contain 180 USP H eparin Units in each milligram. H eparin salts are administered
as sterile aqueous solutions by intravenous infusion, intermittent intravenous injection, or
deep subcutaneous injection for the prophylaxis and treatment of venous thrombosis. T he
commercial preparations, available in single-use syringes and multiple-dose vials, indicate
on their labeling the number of USP H eparin Units of activity contained per milliliter.
Although heparin is a treatment option for acute venous thromboembolism, its use
carries with it the risk of hemorrhage. Patients especially at risk include elderly patients,
postsurgical patients, patients with a history of peptic ulcers, severe renal, or hepatic failure,
and patients who recently have taken other medications that affect blood clotting time.1
W hen heparin sodium is administered in therapeutic amounts, its dosage is adjusted
according to the results of tests measuring the patient’s level of blood coagulation, or activated partial thromboplastin time (aPT T ). T hese tests are performed before each intravenous injection and approximately every 4 to 6 hours when administered by intravenous
infusion or subcutaneously. In general, the aPT T value should be maintained at 1.5 to
2 times the patient’s pretreatment aPT T value or, when the whole-blood clotting time is
evaluated, approximately 2 to 3 times the control value.1,2
T he dose varies depending on the circumstances. Bolus doses, given by direct intravenous injection, may be followed by intravenous infusion as a heparin drip. For prevention
of thromboembolism following surgery (also known as low-dose heparin therapy), patients
receive 5000 units given by deep subcutaneous injection 2 hours before surgery and an
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

c al ula h par n do	from m d a on ord r and andard z d pro o ol .
U l z	qu analg	do	har u .	o d	rm n appropr a do	of nar o	analg
a d on pr ou nar o
c al ula c al ula	ma d r a n n	l aran	ra	and apply n do d	rm na on .
d al	ody w gh and ad u	d	ody w gh and apply n do
d	rm na on .
c al ula	ar ou	hol	rol ra o and hol	rol r du on p r n from l n al
la ora ory da a.
c on r lood	rum h m ry alu	from mg/dL o mmol/L ( n rna onal y m).

10
Selected Clinical
Calculations
168 Pharma euti al c al ulations
additional 5000 units every 8 to 12 hours thereafter as required. H eparin is also used in
higher doses to treat patients with active phlebitis or with pulmonary emboli.3
In pediatric use, the initial dose may be 50 units/kg by intravenous infusion, followed by maintenance doses of 100 units/kg every 4 hours or 20,000 units/m2/24 hours, infused continuously.3
Figure 10.1 presents a hospital form for an adult weight–based heparin protocol. T he
form allows physicians’ orders for bolus doses, as well as protocols for intravenous heparin
infusions. T he values given in this figure may differ from heparin protocols at other institutions. Pharmacists must follow those used within their institutions of practice.
Low-molecular-weight heparins (LMW H s) are also used as antithrombotic agents and
are the agents of choice in treating deep vein thrombosis and pulmonary embolus. T he
CITY HOSPITAL
ADULT WEIGHT-BASED HEPARIN PROTOCOL
Standard Heparin IV Premixed Solution is 25,000 units in 250 mL (100 units per mL)
Initial laboratory tests (draw before starting heparin): aPTT, PT, CBC with platelet count
Day 2 and every 3 days thereafter: CBC with platelet count
aPTT six (6) hours after heparin infusion is started
aPTT six (6) hours after every change in heparin administration rate or bolus dose of heparin
Once a therapeutic aPTT level is reached, do an aPTT six (6) hours later
After two (2) consecutive therapeutic aPTT levels are obtained, do an aPTT daily at 0600
Discontinue all IM medications and other IM injections
Patient _______ MAY ______ MAY NOT receive drugs containing aspirin.
Patient _______ MAY ______ MAY NOT receive drugs containing non-steroidal
antiinflammatory agents.
Bolus Dos e
__________ None
Continuous infus ion rate
__________ Other (specify: __________ units)
__________ 80 units/kg (limit 8,000 units)
__________ Other (specify: __________ units/h)
__________ 18 units/kg/h
aPTT Value Heparin Dos e Adjus tments
Bolus with 80 units/kg and increase infusion rate by 4 units/kg/h
Bolus with 80 units/kg and increase infusion rate by 2 units/kg/h
No change in infusion rate
Decrease infusion rate by 2 units/kg/h
< 35 seconds
35 to 45 seconds
46 to 70 seconds
71 to 90 seconds
Hold infusion for 1 hour; when restarted, decrease infusion rate
by 3 units/kg/h
> 90 seconds
DATE TIME
M.D.
FIGURE 10.1 •  Example of hospital form for adult weight–based heparin protocol. (Courtesy of Nina Morris,
Southwestern Oklahoma State University, Weatherford, OK.)
10 • s ele ted c lini al c al ulation 169
products currently on the market in the United States are enoxaparin sodium (LOVEN OX)
and dalteparin sodium (FRAGMIN ). H eparin has a molecular weight ranging from 3000 to
30,000 daltons, whereas LMW H s are fragments of heparin with mean molecular weights
of 4000 to 6000 daltons.4 T hese shorter compounds may be administered subcutaneously
(rather than intravenously, as is heparin), they interfere less with platelet function, and they
generally have a more predictable anticoagulant response that does not require monitoring
of clotting times.
Special Considerations in Heparin Management
H eparin is a very useful but potentially dangerous agent. It is administered only when necessary and with extreme caution. H emorrhage is a distinct risk with heparin use, requiring
patients to be closely monitored. Pediatric patients and seniors are among those who require
particular care in dosing. H eparin-dosing errors can result from miscommunication (as with
the use of the abbreviation “u” for units), from miscalculation of the appropriate dose, or
from the administration of a product of incorrect strength. To reduce the likelihood of the
latter, products are available in which the strengths are made distinctive by use of stark
color-coding and bold, tall-letter labeling.
Example Calculations of Heparin Dosing
(1) An intravenous in usion contained 20,000 units o heparin sodium in 1000 mL o D5W. The
rate o in usion was set at 1600 units/h or a 160-lb patient. Calculate (a) the concentration o
heparin sodium in the in usion, in units/mL; (b) the length o time the in usion would run, in
hours; and (c) the dose o heparin sodium administered to the patient, on a unit/kg/min basis.
(a) 20 000
1000
, units 20 /
mL
= units mL
(b) 20 000
1600
, 12 5
/
.
units
units h
= hours
(c) 160 72 7
12 5 750
20 000
750
pounds kg
hours minutes
units
minutes
=
=
=
.
.
, 226 67 . / units min
(d) 26 67
72 7
0 37
. /
.
units min . / / min
kg
= units kg
(2) A patient weighing 80 kg was given an initial bolus dose o heparin and a heparin drip or
the f rst 6 hours. Using Figure 10.1, what was the total amount o heparin administered
in this period?
Bolus dose [80 units/kg]:
80
units 80 6400
kg
× = kg units
H eparin infusion [18 units/kg/h]:
18
80 6 8640
units
kg/h
× kg hour × = s units
6400 8640 units units + = 15 040 units ,
170 Pharma euti al c al ulations
(3) A ter 6 hours, the aPTT or the patient in example problem 2 is 102 seconds. Use
Figure 10.1 to determine any changes necessary in his heparin therapy, and calculate a new
f ow rate or the in usion in mL/h using the standard heparin IV solution.
According to Figure 10.1, the infusion for a patient with an aPT T of greater
than 90 seconds should be stopped for 1 hour and then decreased by 3 units/kg/h
when resumed. T he new infusion rate would then be calculated as follows:

18 units	3 units	15 units
kg h /	kg h /	kg h /
–	=

15
80
1200
units
kg h
kg uni
/
× =
tts
h
mL
units
× =
250
25 000 ,
12 mL h /
(4) Heparin sodium may be administered to children by intermittent intravenous in usion
every 4 hours at doses ranging rom 50 to 100 units/kg o body weight. Using an injection
containing heparin, 5000 units/mL, calculate the daily dosage range, in milliliters, or a
50-lb child.

50 100 to units	1 kg
×	×

 

2 2 lb .	kg dose /
to units doses 1136 36 2272 73 6 . .
dose .
day × .	=	,

50 1136 36 2272 73
lb to units do
= . . / sse
to u
6818 18 13 636 36 . , . nnits day
to units
day
mL
units
/
. .
6818 18 13 636 36 1
5000
× = 1 36 to 2 73mL day /
(5) The pediatric maintenance dose o heparin sodium is stated in the literature as 20,000
units/m2/24 hours. Using the BSA nomogram in Chapter 8, and a heparin sodium injection containing heparin sodium, 1000 units/mL, calculate the daily volume o injection to
administer to a 25-lb child measuring 22 inches in height.
BSA = 0.37 m2

20 000
,	2	units

0 37 7400
7400
1
1000
2
.
.
m
m units
units mL
units
× =
× = 7 4 mL injection
Example Calculations of Low-Molecular-Weight Heparin Dosing
The recommended dose o dalteparin sodium (FRAGMIN) or patients undergoing hip replacement
surgery is 2500 international units within 2 hours be ore surgery, 2500 units 4 to 8 hours a ter surgery, and 5000 units daily or 5 to 10 days, starting on the postoperative day. How many milliliters
rom a vial containing 10,000 units/mL should be administered (a) be ore surgery, (b) a ter surgery,
and (c) the day ollowing surgery?

(a)

1 10 000 mL units , ×

= .

2500 0 25
units mL
(b) Same as (a) = 0.25 mL

(c)	1 10 000 mL units ,

5000 0 5
units mL
× = .
10 • s ele ed c l n al c al ula on 171
Use of Equianalgesic Dosing Charts
N arcotic analgesics, also termed opioid analgesics, are widely prescribed to relieve moderate to severe pain. T hey are used in cases o acute pain, such as due to an injury or
surgery, and in cases o chronic pain due to cancer, musculoskeletal conditions, and other
illnesses. In cases o chronic pain, when the patient will most likely be on a narcotic analgesic or an extended period o time, the goal o therapy is usually to relieve the patient’s
pain enough that he or she can continue a normal li estyle but without overmedicating
the patient and causing unwanted side e ects o constant drowsiness, lethargy, and constipation. Once a patient is established on a chronic narcotic analgesic therapy, changes
o ten need to be made to manage the patient’s pain without overly sedating the patient.
Furthermore, the patient may be switched to a di erent narcotic analgesic medication i
he or she has developed a tolerance to the current medication regimen, cannot tolerate
the adverse e ects o the current medication, or desires a more convenient ormulation
or dosing schedule. In these cases, an equianalgesic dosing chart, such as in Table 10.1, is
used to determine the appropriate dose o the new medication to ensure that the patient
receives adequate pain relie with minimal adverse e ects. An equianalgesic dosing chart
is used to estimate the dose o the new narcotic analgesic to be used, and the patient
should still be monitored or pain relie and presence o side e ects. Most o the published charts are limited to adult patients weighing greater than 50 kg, and recommend
a reduced dosage or elderly patients and patients with renal or hepatic insu f ciency. In
addition, clinicians may reduce the stated equivalent dose due to the potential or incomplete cross-tolerance between opioid analgesics. To use the equianalgesic dosing chart,
the daily dose o the current medication is determined rom the dose and dosage regimen,
compared to the daily dose in the chart, and then converted to the dose and dosage regimen or new medication.
W hereas Table 10.1 provides equianalgesic dosing or opioids acting as ull agonists
at the mu opioid receptor, a di erent chart is utilized or opioid analgesics with di erent
pharmacological pro iles (Table 10.2). T hese include buprenorphine (a partial agonist at
mu opioid receptors), nalbuphine and butorphanol (opioid agonist–antagonists, which

CASE IN POINT 10.1 a A 198-l ho p al zed pa en	pla ed on hepar n herapy
o rea a pulmonary em ol m. t he pa en requ re a olu nje on ollowed y a hepar n n u on. t he ho p al ollow he pro o ol hown n F gure 10.1.
t he ho p al pharma	ha hepar n ava la le or olu do e	on a n ng 5000

un /mL n 5-mL v al and hepar n or n ravenou n u on n 250-mL n u on

ag ea h on a n ng 25,000 un	o hepar n.
(a) How many m ll l er o he 5000 un /mL nje on hould he pharma
re ommend a a olu do e?
( ) How many m ll l er per hour o he hepar n n u on hould he pharma he nur e o del ver, a ed on he andard n u on pro o ol?	n ru
( ) i he n ravenou e	programmed o del ver 60 drop per m ll l er, wha hould

e he f ow ra e, n drop per m nu e, o del ver he mL/h requ red n an wer ( )?
(d) How long w ll he 250-mL n u on ag la , n hour ?
a
c a e n Po n our e y o Flynn Warren, b hop, GA.
172 Pharma euti al c al ulations
block mu receptors and stimulate kappa opioid receptors), and pentazocine (an agonist at
kappa receptors and weakly blocking at mu receptors). T he dosing chart for these opioids
determines a dose equivalent to 10 mg of parenteral morphine. T he clinician may then use
this morphine dose to convert to another opioid analgesic by consulting the equianalgesic
dosing chart in Table 10.1.
Drug-specific conversion charts are available for certain opioid analgesics. For
example, Table 10.3 provides equivalent dosing for conversion from an existing narcotic
analgesic to the highly potent fentanyl transdermal system. Table 10.4 lists ratios to guide
conversion from hydrocodone, oxycodone, methadone, or morphine to oxymorphone
extended-release tablets. If a patient is changing to or from one of these narcotic analgesic
medications, it is important for the clinician to consult these drug-specific charts to guide
accurate and appropriate dosing.
Tab e 10.2 •  OPIOId AGONIST–ANTAGONIST ANAl GESICS:
APPROxImATE Eq UIANAl GESIC d OSES FOR Ad Ul TSa
Agonist–Antagonist
d ose E uiva ent to 10 g
Parentera morphine
Buprenorphine IM 0.3 mg
IV
Sublingual
Transdermal
Butorphanol IM 2 mg
IV
Nasal

Nalbuphine	SC/IM IV SC/IM IV	10 mg
Pentazocine	30 mg

aAdapted with permission from Drug Facts & Comparisons. Facts & Comparisons
eAnswers [database online]. St. Louis, MO: Clinical Drug Information LLC; 2015.
Tab e 10.1 •  OPIOId ANAl GESICS: APPROxImATE
Eq UIANAl GESIC d OSES FOR Ad Ul TSa
Opioi
E uiana gesic d ose

Ora	Parentera
200 mg NA	NA 0.1 mg

 

30–45 mg 7.5 mg

NA 1.5 mg

Levorphanol 4 mg (acute);
1 mg (chronic)
NA

Meperidine Morphine Oxycodone Oxymorphone

300 mg 30 mg 20 mg 10 mg

75 mg 10 mg NA 1 mg

aAdapted with permission from Drug Facts & Comparisons. Facts & Comparisons
eAnswers [database online]. St. Louis, MO: Clinical Drug Information LLC; 2015.
10 • s ele ted c lini al c al ulation 173
Example Calculations Using Equianalgesic Dosing Charts
(1) A patient is taking LORTAB 7.5-mg tablets containing 7.5 mg of hydrocodone bitartrate and 325 mg of acetaminophen to manage his chronic back pain. His current dosage
is two tablets every 6 hours, but his pain management doctor would like to switch him
to hydromorphone hydrochloride tablets to better alleviate his pain. Hydromorphone
hydrochloride tablets are available in strengths of 2, 4, and 8 mg and should be administered every 4 to 6 hours. Determine the dose of hydromorphone hydrochloride for this
patient.

7 5 . mg hydrocodone	2 tablets	4 doses
60 × × = mg hydrocodoone day /
tablet	dose	day

According to the chart in Table 10.1, 30 mg of hydrocodone is equivalent to
7.5 mg of hydromorphone taken orally.
60 7 5
30
15
mg hydrocodone
day
mg hydromorphone
mg hydrocodone
× . = mg hyydromorphone day /
Ta e 10.3 •  FENTANyl TRANSd ERmAl d OSAGE CONvERSION GUId El INESa,b

Current Ana gesic	d ai d osage ( g/ a )
Oral morphine IM/IV morphine Oral oxycodone Oral codeine Oral hydromorphone IV hydromorphone IM meperidine Oral methadone	60–134 10–22 30–67 150–447 8–17 1.5–3.4 75–165 20–44	135–224 23–37 67.5–112	225–314 38–52 112.5–157	315–404 53–67 157.5–202
17.1–28 3.5–5.6 166–278 45–74	28.1–39 5.7–7.9 279–390 75–104	39.1–51 8–10 391–503 105–134
Recommended fentanyl transdermal system dose
Fentanyl transdermal system	25 mcg/h	50 mcg/h	75 mcg/h	100 mcg/h

aAdapted with permission from Drug Facts & Comparisons. Facts & Comparisons eAnswers [database online]. St. Louis, MO:
Clinical Drug Information LLC; 2015.
bThis table should not be used to convert fentanyl transdermal to other therapies because the conversion to fentanyl transdermal is conservative. Use of this table for conversion to other analgesic therapies can overestimate the dose of the new agent.
Overdosage of the new analgesic agent is possible.
Ta e 10.4 •  CONvERSION FACTORS TO
OxymORPh ONE ER TAb l ETSa
Prior Ora Opioi
Appro i ate Ora
Con ersion Factor

Oxymorphone Hydrocodone	1 0.5
Oxycodone	0.5
Methadone	0.5
Morphine	0.333

aAdapted with permission from Drug Facts & Comparisons.
Facts & Comparisons eAnswers [database online].
St. Louis, MO: Clinical Drug Information LLC; 2015.
174 Pharma euti al c al ulations
Since the patient is accustomed to taking the current medication every 6 hours,
this dosage regimen would probably be most effective for him.
15 1
4
mg hydromorphone
day
day
doses
× = 3 75 mg dose . /
T he patient should begin with hydromorphone hydrochloride 4-mg tablets every
6 hours and monitored for relief of pain symptoms as well as for adverse effects.
(2) CR is a 57-year-old male patient who is 6 feet 1 inch tall and weighs 212 lb. He is receiving
a 20-mg intravenous injection of pentazocine lactate every 4 hours to control his pain after
an injury due to a motorcycle accident. His physician wishes to switch him to an oral dose of
meperidine hydrochloride so that he can move into a rehabilitation facility. W hat would be
the equivalent dose of meperidine hydrochloride for this patient?
According to Table 10.2, a 30-mg injection of pentazocine is equivalent to a
10-mg injection of morphine; therefore, the amount of morphine represented by a
20-mg injection of pentazocine can be calculated as:
10
30
20 6 67
mg morphine
mg pentazocine
× mg pentazocine mg morphine = .
According to Table 10.1, a 10-mg injection of morphine is equivalent to 300 mg
of meperidine given orally. T he oral dose of meperidine for this patient can be
calculated as:
300
10
6 67
mg meperidine
mg morphine
× . mg morphine = 200 mg meperidine
T he patient can take two 100-mg meperidine hydrochloride tablets every
4 hours to manage his pain.
(3) A cancer patient is taking one 20-mg oxycodone tablet q.i.d. to manage her pain. (a) W hat is the
total daily oxycodone dose for this patient? (b) The patient’s pain management physician decides to
switch her to fentanyl transdermal patches. W hat strength of fentanyl patch should he prescribe?5
(a) 20 4 mg
tablet
tablets
day
× = 80 mg day /
(b) According to Table 10.3, a patient receiving an oral oxycodone dose of 67.5 to
112 mg/day of oral oxycodone should begin with a 50 mcg/h fentanyl patch.
(4) A patient with a spinal injury is taking one 15-mg tablet of immediate-release morphine
sulfate every 4 hours for pain. His physician wants to switch him to oxymorphone hydrochloride extended-release tablets to better manage his pain, and reserve the immediate-release
morphine tablets for breakthrough pain. The oxymorphone hydrochloride extended-release
(ER) tablets should be given every 12 hours. Calculate the appropriate dose for this patient.
First, the daily dose of morphine sulfate must be calculated:
15 6
90
mg
dose
doses
day
× = mg day /
According to Table 10.4, a conversion factor of 0.333 should be used to convert
an oral dose of morphine to oxymorphone ER tablets.
90
0 333 29 97 30
mg morphine
day
× . . = mg mg oxymorphone ER day ≈ /
10 • s ele ed c lini al c al ula ion 175
Since the oxymorphone ER tablets are to be given every 12 hours, the single
dose can be calculated as:
30 1
2
mg oxymorphone ER
day
day
doses
× = 15 mg oxymorphone ER day /
T herefore, one 15-mg oxymorphone ER tablet should be given to this patient
every 12 hours.
CASE IN POINT 10.2 6 t he u ual re ommended do e of bu orphanol ar ra e na al
pray i one pray on aining 1 mg of drug, and he na al pray olu ion on ain he
drug a a on en ra ion of 10 mg/mL. c al ula e (a) he volume of olu ion delivered
wi h ea h do e; (b) he number of do e on ained in he 2.5-mL manufa urer’
on ainer; and ( ) he number of able , on aining 5 mg of hydro odone bi ar ra e
and 300 mg of a e aminophen, needed o produ e he 1-mg do e of bu orphanol
ar ra e.
Dosage Calculations Based on Creatinine Clearance
T he two major mechanisms by which drugs are eliminated from the body are through
hepatic (liver) metabolism and renal (kidney) excretion. W hen renal excretion is the major
route, a loss of kidney function will dramatically affect the rate at which the drug is cleared
from the body.
With many drugs, it is important to reach and maintain a specific drug concentration in the blood to realize the proper therapeutic effect. T he initial blood concentration
attained from a specific dose depends, in part, on the weight of the patient and the volume
of body fluids in which the drug is distributed.
T he kidneys receive about 20% of the cardiac output (blood flow) and filter
approximately 125 mL of plasma per minute. As kidney function is lost, the quantity of
plasma filtered per minute decreases, with an accompanying decrease in drug clearance.
T he filtration rate of the kidney can be estimated by a number of methods. O ne of the
most useful, however, is the estimation of the creatinine clearance rate (CrCl) through
the use of the following empiric formulas based on the patient’s age, weight, and serum
creatinine (Scr) value. Creatinine, which is a breakdown product from creatine produced
in muscle metabolism, is generally produced at a constant rate and in quantities that
depend on the muscle mass of the patient. Females usually have a lower serum creatinine than males due to less muscle mass. Because creatinine is eliminated from the body
essentially through renal filtration, reduced kidney performance results in a reduced
CrCl. T he normal adult value of serum creatinine is 0.6 to 1.3 mg/dL (the range varies
with the laboratory used as the reference source). T he CrCl represents the volume of
blood plasma that is cleared of creatinine by kidney filtration and usually expressed in
milliliters per minute.
In addition to the Jelliffe and Cockcroft-G ault equations, other equations are used to
estimate creatinine clearance for special patient populations such as pediatric patients and
elderly patients.10
176 Pharma euti al c al ulations
By the Jelliffe equation7,8:
For males:
CrCl (Patient s age in years
Serum creatinine in mg/dL
=
98 0 8 – . ) × ’ – 20
For females:
CrCl = 0.9 × CrCl determined using formula for males
By the Cockcroft-Gault equation9:
For males:
CrCl Patient s age in years Body weight in kg
Serum creat
=
– ×
×
( ) 140
72
’
iinine in mg/dL
For females:
CrCl = 0.85 × CrCl determined using formula for males
Example Calculations of Creatinine Clearance
(1) Determine the creatinine clearance rate for an 80-year-old male patient weighing 70 kg and
having a serum creatinine of 2 mg/dL. Use both the Jelliffe and Cockcroft-Gault equations.
By the Jelliffe equation:
CrCl
mg dL
mg dL mg
=
– × –
=
– ×
=
–
98 0 8 80 20
2
98 0 8 60
2
98 48
2
. ( )
( / )
( . )
( / ) ( / dL mg dL ) ( / )
=
=
50
2
25 mL/min
By the Cockcroft-Gault equation:
CrCl
mg dL
=
– ×
×
=
×
= =
( )
( / )
.
140 80 70
72 2
60 70
144
4200
144
29 2 mL/min
(2) A 70-year-old gentleman and his 68-year-old wife have their annual physical exams. He
weighs 160 lb and she 126 lb. His blood work reveals a serum creatinine of 1.3 mg/dL and
hers is 1.1 mg/dL. Using the Cockcroft-Gault equation, calculate their respective creatinine
clearance rates.
H is CrCl
H er CrCl
=

– × × ) . .

(

=
= ×
–
.
.
(
140 70 72 7
72 1 3
0 85 140 68
54 4 mL/min
)) .
.
.
×
×
=
57 3
72 1 1
44 3 mL/min
10 • s l c l al c al ula o 177
Ad j Us t in G c r e At in in e c Le Ar An c e FOr b Od y s Ur FAc e Ar e A
It is sometimes desirable to adjust the calculated creatinine clearance for body surface area to
account for this possible variable in determining drug dosage. T hisadjustment is accomplished
through the use of a nomogram or equation to determine body surface area (BSA), as
described previously in Chapter 8, and the following formula:
BSA
CrCl Adjusted CrCl
1 73 .
× =
If a patient weighing 120 lb and measuring 60 inches in height has a calculated creatinine
clearance of 40 mL/min, adjust the CrCl based on body surface area.
Using the nomogram in Chapter 8, the patient’s BSA is determined to be 1.50 m2.
1 50
1 73
40
2 2
. .
m / min . ,
m
× mL = 34 68 mL adjusted CrCl /min
N ormal CrCl may be considered 100 mL/min. T hus, in the preceding example, the
patient would exhibit about 35% of normal creatinine clearance.
Us e OF c r e At in in e c Le Ar An c e in d e t e r min in G d Os e s
T he CrCl method for determining drug dose is used with various drugs in which renal function is a factor. Meperidine, for example, is dosed based on creatinine clearance as follows:
CrCl = 10 – 50 mL/min, give 75% of usual dose
CrCl < 10 mL/min, give 50% of usual dose
The patient in example problem 2 on page 174 has a serum creatinine of 2.4 mg/dL. Using
the Cockcroft-Gault equation, determine if the meperidine dose should be adjusted for kidney
function.
212
1
2 2
96 36
140 57 96 36
72 2 4
46 29
lb kg
lb
kg
CrCl mL
× =
=
– ×
×
=
.
.
( ) .
.
. / min
According to the dosing information, 75% of the dose should be given. Since the
dose calculated in example problem 2 on page 174 is 200 mg, the patient should receive
200 mg × 75% = 150 mg based on his renal function.
For certain drugs, tables of dosage guidelines may be presented in the labeling/
literature to adjust for impaired renal function. For example, the usual dose of the antiinfective drug ceftazidime is 1 g every 8 to 12 hours, with dosage adjusted based on the
location and severity of the infection and the patient’s renal function. For adult patients
with impaired renal function, guidelines for dosage based on creatinine clearance are
given in Table 10.5.
Using Table 10.5, determine the dose and daily dose schedule for a 62-year-old female patient
weighing 70 kg with a serum creatinine of 1.8 mg/dL.
CrCl = × – × mL
×
0 85 =
140 62 70
72 1 8
. 35 81
( )
.
. / min
According to the table, a patient with a creatinine clearance of 31 to 50 mL/min should
receive a dose of 1 g every 12 hours.
178 Pharma euti al c al ulations
Tab e 10.5 •  CREATININE Cl EARANCE d OSING GUId El INES FOR
CEFTAzId ImE (Iv OR Im)a
Rena Function
Creatinine

C earance ( l / in) 100–51 50–31 30–16 15–6 <5

d ose 1 g 1 g 1 g 500 mg 500 mg

Frequency q8–12 h q12h q24h q24h q48h

Normal to mild impairment Moderate impairment Severe impairment Very severe impairment Essentially none

aAdapted from product literature for FORTAZ (ceftazidime). Available at http://www.accessdata.fda.gov/drugsatfda_docs/label/2014/050578s055,050634s023lbledt.pdf. Accessed
February 23, 2015.
CAl CUl ATIONS CAPSUl E
Creatinine Clearance Equations7–9
Jelliffe equation
For males:
CrCl
98 0.8 (Patient’s age in years 20)
Serum creatinine in mg/dL
=
– × –
For females:
CrCl 0.9 CrCl determined by equation for males = ×
Cockcroft-Gault equation
For males:
CrCl
(140 Patient’s age in years) pt. wt., kg
72 Serum creatinine
=
– ×
× iin mg/dL
For females:
CrCl 0.85 CrCl determined using for males = ×
Adjusting CrCl for body surface area
BSA
1.73
× CrCl Adjusted CrCl =
Dosage Calculations Based on Ideal Body Weight and Adjusted
Body Weight
T he ideal body weight (IBW ) provides an excellent estimation of the distribution volume,
particularly for some polar drugs that are not well distributed in adipose (fat) tissue. T he
IBW may be calculated through the use of the following formulas based on the patient’s
height and gender.
10 • s ele ted c lini al c al ulation 179
For males:
IBW = 50 kg + 2.3 kg for each inch of patient height over 5 feet
or in pounds
110 lb + 5 lb for each inch over 5 feet
For females:
IBW = 45.5 kg + 2.3 kg for each inch of patient height over 5 feet
or in pounds
100 lb + 5 lb for each inch over 5 feet
Adjusted body weight may be used in calculating dosages for obese patients using the
following equation:11
Adjusted body weight = [(ABW – IBW ) × 0.25] + IBW,
where ABW is the patient’s actual body weight.
Clinical controversy exists over the use of actual body weight, IBW, or an adjusted
body weight to determine dosages, and specific references should be consulted to determine
the most appropriate dose for a patient.12–14
Example Calculations of Ideal Body Weight and Adjusted Body Weight
(1) Calculate the ideal body weight in pounds and kilograms for a male patient weighing 164 lb
and measuring 5 feet 8 inches in height.
IBW = 110 lb + (8 × 5 lb) = 110 lb + 40 lb = 150 lb
IBW = 50 kg + (8 × 2.3 kg) = 50 kg + 18.4 kg = 68.4 kg
(2) Calculate the ideal body weight, in kilograms, for a female patient weighing 60 kg and
measuring 160 cm in height.
160
1
2 54
cm 62 99 5 3
i
cm
× = nch in feet inches ches ≈
.
.
IBW = 45.5 kg + (3 × 2.3 kg) = 45.5 kg + 6.9 kg = 52.4 kg
(3) Calculate the ideal body weight and adjusted body weight, in kilograms, for a male patient
who is 6 feet 1 inch tall and weighs 255 lb.
IBW = 50 kg + (13 × 2.3 kg) = 50 kg + 29.9 kg = 79.9 kg
ABW lb kg
lb
= 255 × 1 = kg
2 2
115 91
.
.
Adjusted body weight = [(115.91 kg – 79.9 kg) × 0.25] + 79.9 kg = 9 kg + 79.9 kg = 88.9 kg
Drug-Specific Clinical Equations
For certain clinical conditions, there are equations that are useful for determining patient
requirements. For example, the following is used in determining the amount of iron required
to bring hemoglobin (H b) values to normal levels:
Iron required mg
Body weight lb
H b g/dL
g/
( ) =
× × –
( ) ×
( ) .
.
0 3 100
100
14 8 dL
180 Pha ma ut al c al ulat on
In the equation, 14.8 g/dL is the normal value o hemoglobin in adults and the actor
0.3 is its iron content (percent).15
Using the equation for determining iron deficiency, calculate the number of milliliters of an
iron dextran solution containing 50 mg/mL of iron to be administered to a 150-lb patient with a
hemoglobin value of 10 g/dL.
Iron required mg ( ) .
.
. .
= × × –
×
= × ×
150 0 3 100
10 100
14 8
150 0 3 32 4
== 1458 mg
by proportion mg
mg
mL
x mL
x
,
50
1458
1
= =
29 mL iron dextran solution
Therapeutic Drug Monitoring
Also termed dr ug therapy monitoring, this process o ten includes the analysis o blood
serum samples to ensure optimum drug therapy. T his is especially important or categories o drugs in which the margin between sa e and toxic levels is narrow. Data are available indicating these levels.16 T he drugs presented in this chapter are but a ew o those
requiring specif c types o dosing. Many other drugs, including aminoglycoside antibiotics
(gentamicin, tobramycin, amikacin), theophylline, digoxin, and war arin, require dosing
based on plasma levels o the drug, specif c laboratory values, creatinine clearance, and
IBW. Clinical re erence sources should be consulted when dosing drugs with specif c and
complex dosing parameters.

CASE IN POINT 10.3 a A 35-y a -ol mal pat nt w gh ng 180 l an	tan ng lam –
5 f t 8 n h	tall ha	n agno	w th Aid s . H phy	an p
u n (e Pivir ) a a ompon nt of h t atm nt p og am an know that th	o
of th	ug mu t	a ju t	a um	on th pat nt’	nal fun t on. La o ato y t t
n l	at that th pat nt’	at n n	2.6 mg/ L an ha h l at th	am
l fo 5 ay .
(a) c al ulat th pat nt’ ib W an u	n u	qu nt al ulat on f th ib W low
than th pat nt’ a tual w ght.
( ) c al ulat th pat nt’ c c l y th c o k oft-Gault quat on.
( ) s l t th app op at	o of lam u n f om th	o ng h ul :

Creatinine Clearance Initial d ose maintenance d ose

<5 mL/m n 5–14 mL/m n 15–29 mL/m n 30–49 mL/m n

50 mg 150 mg 150 mg 150 mg

25 mg on 50 mg on 100 mg on 150 mg on

a ly a ly a ly a ly

a
c a n Po nt ou t y of Flynn Wa n, b hop, GA.
10 • s ele ted c lini al c al ulation 181
Clinical Laboratory Tests
It is common practice in assessing health status to analyze biologic f uids, especially blood
and urine, or speci c chemical content. T he clinical laboratory tests used, known as chemistries, analyze samples or such chemicals as glucose, cholesterol, total lipids, creatinine,
blood urea nitrogen (BUN ), bilirubin, potassium, sodium, calcium, carbon dioxide, and
other substances, including drugs ollowing their administration. Blood chemistries are
per ormed on plasma (the f uid part o the blood) or serum (the watery portion o clotted
blood). Depending on the laboratory equipment used as well as patient actors (such as age
and gender), the “usual” amount o each chemical substance varies, with no single “normal”
value, but rather a common range. For example, the re erence range o glucose in serum is,
by some laboratories, 65 to 115 mg/dL and that or creatinine is 0.5 to 1.7 mg/dL.
Table 10.6 presents examples o the normal ranges o serum chemistry values or some commonly analyzed blood components. T he “conversion actors” shown are used to convert the units
most o ten used in the United States to those o the international system. For example, a cholesterol reading o 180 (mg/dL) may be recorded as 4.65 millimoles per liter (mmol/L or mM).
Low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein (H DL-C),
and total cholesterol (T C) are each measured in assessing a patient’s risk or atherosclerosis.17 T he greatest risk comes rom the non–high-density lipoprotein cholesterol (non–
H DL-C), particularly in patients with high serum levels o triglycerides (T G or T GR). In
addition, certain accompanying patient actors are considered added risk actors and a ect
the LDL-C goal or a particular patient. T hese include personal and/or amilial history o
coronary heart disease, atherosclerotic disease, diabetes, hypertension, and cigarette smoking. Table 10.7 presents categories o cholesterol and triglyceride blood levels. Furthermore,
total cholesterol is calculated by adding triglyceride level divided by ive, H DL, and LDL
levels (i.e., T C = T G/5 + H DL + LDL).
T here are two “cholesterol ratios” that are considered clinically relevant to risk assessment or cardiovascular disease. One is the ratio o total cholesterol to H DL cholesterol,
the target being 5:1 or less. T he other ratio used in assessing risk is LDL:H DL with the
target being 3:1 or less.18 Greater proportions o H DL are considered to lower risk o cardiovascular disease. In addition, the percent reduction required to achieve a goal level o
LDL cholesterol may be calculated as the di erence in values as a percent o the current
level. T he di erence in values is calculated by subtracting the patient’s desired LDL rom
the current measured LDL level, then dividing it by the current LDL level.
Tab e 10.6 •  ExAmPl ES OF NORmAl RANGES OF SERUm Ch EmISTRy vAl UESa
l aborator Test
Nor a va ues (Range,
in US Units)
Con ersion Factor
(mu tip )
Internationa
S ste b

Albumin Calcium Cholesterol, total HDL cholesterol LDL cholesterol Glucose Triglycerides Creatinine Urea nitrogen (BUN)

3.6–5 g/dL 8.6–10.3 mg/dL <200 mg/dL ≥60 mg/dL <130 mg/dL 65–115 mg/dL <150 mg/dL 0.5–1.7 mg/dL 8–25 mg/dL

10 0.25 0.026 0.026 0.026 0.055 0.011 88.4 0.357

36–50 g/L 2.2–2.6 mmol/L <5.2 mmol/L ≥1.56 mmol/L <3.38 mmol/L 3.58–6.39 mmol/L <1.65 mmol/L 44.2–150.28 mmol/L 2.86–8.93 mmol/L

aNormal values shown may vary between test laboratories and may be referred to as “reference,” “healthy,” or “goal” values.
bThe international system is generally expressed in mmol (or other units) per liter.
182 Pharma euti al c al ulations
Example Calculations Involving Clinical Laboratory Tests
(1) If a patient is determined to have a serum cholesterol level of 200 mg/dL, what is the
equivalent value expressed in terms of millimoles (mmol) per liter?
Molecular W eight m w of cholesterol

mmol cholesterol 1 mg dL 200 /

= 387 mg mg L 2000 /

( . . ) =
387
mg
mg
millimole
x millimol
387
2000
1
( )
( )
( )
(
= =
ees
x
)
= 5 17 mmol L . /
(2) Calculate the TC:HDL ratio when the total cholesterol is 240 mg/dL and the HDL
cholesterol is 60 mg/dL, and identify if the ratio is within the desirable range.
240 mg/dL:60 mg/dL = 4:1
T he ratio is less than the maximum desired level of 5:1.
(3) If 160 mg/dL is a patient’s current LDL level and the desired level is 100 mg/dL, calculate
the percent reduction required.

Difference in values: Difference as a p

mg dL

mg dL

mg dL 100 × = % . 37 5%

160 100 60 / / / – =
eercent of current level: mg dL
mg dL
60
160
/ /
Ta e 10.7 •  CATEGORIES OF Ch Ol ESTEROl ANd TRIGl yCERId E
b l OOd l EvEl Sa

b oo l e e (Fasting) Total cholesterol (TC) levels: <200 mg/dL	C inica Categor
Desirable
200–239 mg/dL	Borderline high
240 mg/dL and above Low-density cholesterol (LDL): <100 mg/dL	High
Optimal
100–129 mg/dL	Near optimal
130–159 mg/dL	Borderline high
160–189 mg/dL	High

 

190 mg/dL and above High-density cholesterol (HDL): <40 mg/dL	Very high
Low level/increased risk

40–50 mg/dL (men); 50–59 mg/dL
(women)
Average level/average risk

60 mg/dL and above Triglycerides (TRG): <150 mg/dL	High level/less than average risk
Desirable
150–199 mg/dL	Borderline high

 

200–499 mg/dL	High
500 mg/dL and above	Very high

aNational Heart, Lung, and Blood Institute; National Institutes of Health; Public Health Service;
U.S. Department of Health and Human Services. NIH Publication No. 05–3290. Available at
http://www.nhlbi.nih.gov/health/public/heart/chol/wyntk.htm. Accessed March 2, 2011.
10 • s ele ted c lini al c al ulation 183
PRACTICE PROb l EmS
Heparin-Dosing Calculations
1. A hospital pharmacy order calls for 5000 units of heparin to be administered
to a patient, twice daily, subcutaneously, for the prevention of thrombi. T he
pharmacist has on hand a vial containing 10,000 H eparin Units/mL. H ow many
milliliters of the injection should be administered for each dose?
2. A physician orders 1500 units of heparin to be administered by intravenous
infusion per hour. T he pharmacy provides a heparin intravenous bag containing 25,000 units of heparin in 250 mL of D5W. H ow many milliliters should be
administered per minute?
3.19 A male patient weighing 76 kg is placed on heparin therapy for the prevention
of deep vein thrombosis after surgery.
(a) H ow many milliliters of a heparin injection containing 5000 units/mL
should be administered for a loading dose of 80 units/kg?
(b) W hat should be the infusion rate, in mL/h, using a solution that contains
heparin 25,000 units/500 mL, to administer 18 units/kg/h?
(c) Six hours after heparin therapy is initiated, the patient’s aPT T is found to
be 75 seconds. Adjust the infusion rate, in mL/h, according to the heparin
protocol (Fig. 10.1).
4.19 A blood sample taken from a 113-lb patient 6 hours after heparin therapy is
initiated shows an aPT T of 24 seconds. Calculate (a) the bolus dose and (b) the
infusion rate, in mL/h, according to the heparin protocol (Fig. 10.1).
5. Enoxaparin sodium (LOVEN OX) injection, a low-molecular-weight heparin,
contains 150 mg/mL in 0.8-mL prefilled syringes. T he recommended dose for
knee replacement surgery is 30 mg every 12 hours. H ow many milliliters of the
injection should be administered per dose?
Equianalgesic Dosing Calculations
6. A patient has been taking acetaminophen 300 mg with codeine 30 mg
(T YLEN OL with CODEIN E #3) tablets and wishes to switch to acetaminophen/hydrocodone tablets due to nausea and constipation caused by the
codeine. T he patient has been taking one tablet every 4 to 6 hours. W hat would
be the most appropriate dose and dosage regimen for the acetaminophen/
hydrocodone tablets?
(a) One 2.5-mg hydrocodone/325-mg acetaminophen tablet every 4 to 6 hours
(b) One 5-mg hydrocodone/300-mg acetaminophen tablet every 4 to 6 hours
(c) One 7.5-mg hydrocodone/300-mg acetaminophen tablet every 6 hours
(d) One 10-mg hydrocodone/325-mg acetaminophen tablet every 6 hours
7. T C is a 52-year-old female patient who is receiving 0.5 mL of a 50 mcg/mL injection
of fentanyl citrate (SUBLIMAZE) every 2 hours following surgery to manage her
pain. H er physician wants to change to oral oxycodone hydrochloride given every
4 hours so she can be discharged from the hospital. W hat strength of oxycodone
hydrochloride tablets should be used for this patient?
(a) 20-mg tablets
(b) 15-mg tablets
(c) 10-mg tablets
(d) 5-mg tablets
184 Pharma euti al c al ulations
8. IH is a 42-year-old male patient suffering from chronic back pain due to a
workplace injury. H e is currently taking one-half of a 2-mg levorphanol tartrate
tablet every 6 hours to manage his pain but consults his doctor about switching to BUT RAN S weekly buprenorphine transdermal patches for convenience.
BUT RAN S transdermal delivery systems are available in strengths of 5, 7.5, 10,
15, and 20 mcg/h. W hat strength of patch should be used for this patient?
9. N T is taking two PERCOCET tablets each containing 7.5 mg of oxycodone
and 325 mg of acetaminophen every 4 hours to manage his pain. H is physician
wants to switch him to oxymorphone extended-release tablets (OPAN A ER) for
improved pain control. Oxymorphone extended-release tablets are available in
strengths of 5, 7.5, 10, 15, 20, 30, and 40 mg to be given every 12 hours. W hat
should be the dose and dosage regimen for this patient?
10. A patient is receiving morphine sulfate intravenously via a patient controlled
analgesia (PCA) pump. T he concentration of the solution is 15 mg/mL and is
being infused at a rate of 0.1 mL/h. T he patient may access a 2-mg bolus dose
every hour for breakthrough pain and is currently using an average of 8 doses per
day. T he patient’s caregiver requests that the patient be converted to a fentanyl
transdermal patch (DURAGESIC) for a “more safe dosage form”. W hat strength
of fentanyl patch would be most effective for this patient?
Creatinine Clearance Calculations
11. Use both the Jelliffe equation and the Cockcroft-Gault equation to calculate the
creatinine clearance rate for a 24-year-old male patient weighing 70 kg with a
serum creatinine of 1 mg/dL.
12. If the patient in problem 11 is 5 feet 8 inches tall, adjust the creatinine clearance
calculated by the Cockcroft-Gault equation based on body surface area.
13. T he usual adult dose of levofloxacin is a 500-mg initial dose followed by subsequent doses of 250 mg every 24 hours for 10 days. For patients with a CrCl
of less than 19 mL/min, doses following the initial dose are administered every
48 hours. H ow many 250-mg levofloxacin tablets should be dispensed to a
75-year-old, 160-lb female patient with a serum creatinine of 1.32 mg/dL? (Use
the Cockcroft-Gault equation to determine creatinine clearance.)
14. Using Table 10.5, what would be the dose and dosage schedule of ceftazidime for
an 84-year-old male patient weighing 60 kg, measuring 66 inches in height, and
having a serum creatinine level of 4.22 mg/dL? (Use the Cockcroft-Gault equation to determine creatinine clearance.)
Ideal Body Weight and Adjusted Body Weight Calculations
15. Calculate the ideal body weight in pounds and kilograms for an 87-year-old
female patient who is 5 feet 1 inch tall and weighs 111 lb.
16. Calculate the adjusted body weight in kilograms for a 50-year-old male patient
who is 5 feet 11 inches tall and weighs 288 lb.
17. T he initial dose for atracurium besylate is 0.4 mg/kg and should be dosed based on
IBW for obese patients.12 H ow much of a 10-mg/mL injection should be administered to a 42-year-old male patient who is 6 feet 2 inches tall and weighs 262 lb?
18. DT is a 61-year-old female patient with primary humoral immunodeficiency. She
is 5 feet 6 inches tall and weighs 303 lb. T he dosing range for human immune
globulin (BIVIGAM) is 300 to 800 mg/kg given intravenously every 3 to 4 weeks,
and the patient’s adjusted body weight should be used for dosing this drug since
she is obese.12 W hat would be the dose range for this patient?
10 • s ele ted c lini al c al ulation 185
Clinical Laboratory Test Calculations
19. If a serum sample is determined to contain 270 mg/dL of cholesterol, what is the
concentration of cholesterol (m.w. 386) in terms of millimoles per liter?
20. T he normal blood level of theophylline is 0.055 to 0.11 mmol/L. Determine the
amount range, in micrograms, of theophylline that would be contained in a 5-mL
blood sample to fall within this range. (m.w. theophylline = 180.17)
21. Among clinical recommendations to prevent cardiovascular disease in women
is the maintenance of lipid levels as follows: low-density lipoproteins (LDL)
<100 mg/dL; high-density lipoproteins (H DL) >50 mg/dL; and triglycerides
(T G) <150 mg/dL.20 W hich of the following meet these criteria?
(a) LDL <2.6 mmol/L
(b) H DL >1.3 mmol/L
(c) T G <1.65 mmol/L
(d) All of the above
22. If a patient is instructed by her physician to reduce her LDL cholesterol level
from 130 mg/dL to 100 mg/dL, calculate the percent reduction required.
23. A patient has an H DL of 50 mg/dL, an LDL of 150 mg/dL, and a T G of 85 mg/dL.
Calculate the (a) T C:H DL ratio and (b) LDL percent reduction required for a
goal of 100 mg/dL.
24. On the basis of the information in Table 10.6, calculate the mmol/L of glucose
equivalent to a value of 140 mg/dL.
(a) 7.7 mmol/L
(b) 2.5 mmol/L
(c) 5.4 mmol/L
(d) 6.2 mmol/L
CAl Cq UIz
10.A. When a PTT was performed on the patient described in “Case in Point 10.1,” the
patient’s value was 40 seconds. Based on the protocol in Figure 10.1, calculate
(a) the needed bolus dose, in units, and (b) the new infusion rate, in mL/h, using
heparin injection, 25,000 units/250 mL.
10.B. A patient has been receiving an intravenous infusion of fentanyl citrate (SUBLIMAZE)
at a rate of 15 mcg/h for pain management during an extended 4-day hospital stay.
His physician wishes to prescribe oxymorphone ER (OPANA ER) tablets to be
administered every 12 hours to allow the patient to return home. Should 15-, 20-,
30-, or 40-mg oxymorphone ER tablets be prescribed for this patient to receive an
equivalent dose for his pain?
10.C. Based on creatinine clearance, the dose of a drug is:
CrCl = 8–10 mL/min; dose = 2.43 mg/kg every 24 hours, divided into two doses
CrCl = 11–20 mL/min; dose = 3.58 mg/kg every 24 hours, divided into two doses
CrCl = 21–40 mL/min; dose = 5.87 mg/kg every 24 hours as a single dose.
For a 52-year-old male patient weighing 155 lb and measuring 69 inches with a
serum creatinine of 2.6 mg/dL, calculate the per-dose volume to administer of an
injection containing drug, 80 mg/mL.
186 Pharma euti al c al ulations
ANSwERS TO “CASE IN POINT” ANd PRACTICE PROb l EmS
Case in Point 10.1
(a) Patient’s weight in kg:
198
1
2 2
lb kg 90
lb
× = kg
.
Bolus dose: 80 units heparin/kg
80
90 7200
7200
1
5000
units
kg
kg units
units mL
units
× =
× = 1.44 mL
(b) Infusion rate: 18 units/kg/h
18 90 1620
250
25 000
1620
1
units kg h kg units h
mL
units
units
h
/ / /
,
× =
× = 116 2 . / mL h
(c) 16 2
1
60
1
1
60
16 2 16
.
min
mL . / min
h
drops
mL
h
× × = or drops

(d) 250 mL	1
16 2

15 43
h
mL
× = h
.
.
Case in Point 10.2

(a)	0 1 = . / mL dose	×
1 mg	1 mL
10 mg	dose

(b) 2 5 1
0 1
. 25
.
mL
dose
mL
× = doses
10.D. A hospital order for midazolam for maintenance of sedation at a rate of 0.05 mg/kg/h
is received for a patient. The patient is a 33-year-old female patient who is 5 feet
4 inches tall and weighs 164 lb. Because she is obese, the patient should receive a
dose based on her ideal body weight.12 Calculate the infusion rate for an IV solution
with a midazolam concentration of 0.5 mg/mL.
10.E. Calculate the total cholesterol in a patient with a HDL of 87 mg/dL, LDL of 152 mg/dL,
and a TRG of 50 mg/dL. Also, which of the following are correct?
(a) HDL:LDL ratio ≈ 1:1.7
(b) TC:HDL ratio ≈ 2.9:1
(c) HDL = high risk
(d) LDL = low risk
(e) TRG = low risk
(f) After being placed on a statin drug, the patient’s LDL dropped to 106 mg/dL,
equivalent to a 30% reduction.
10 • s ele ted c lini al c al ulation 187
(c) According to Table 10.2, a 2-mg intranasal dose of butorphanol tartrate is
equivalent to 10 mg of parenteral morphine.
1
10
2
mg butorphanol mg morphine 5
mg butorphanol
× = mg morphine
According to Table 10.1, a 10-mg parenteral dose of morphine is equivalent
to 30 mg of hydrocodone given orally.
5
30
10
15
15
mg morphine mg hydrocodone
mg morphine
mg hydrocodone
m
× =
gg hydrocodone tablet
mg hydrocodone
× 1 = tablets
5
3
Case in Point 10.3

(a)	IBW kg inches Patient s actual weight 180 lb 1 = + × = = × 50 2 3 8 68 4 ( . ) . ’ kg/2.2 lb kg= 81 8 .
(b) CrCl kg = – × = = [( ) . ] 140 35 68 4 7182	mL
mg dL × . / 72 2 6	. 187 2

. /min
38 37
(c) Dose = 150 mg initially and 150 mg maintenance dose once daily
Practice Problems
1. 0.5 mL heparin injection
2. 0.25 mL/min
3. (a) 1.22 mL heparin injection
(b) 27.36 mL/h
(c) 24.32 mL/h
4. (a) 4109.09 units
(b) 11.3 mL/h
5. 0.2 mL enoxaparin sodium
injection
6. (b) One 5-mg hydrocodone/
300-mg acetaminophen tablet
every 4 to 6 hours
7. (c) 10-mg tablets
8. 10-mcg/h transdermal patch
9. 20-mg tablet every 12 hours
10. 75-mcg/h transdermal patch
11. 94.8 mL/min (Jelliffe)
112.78 mL/min (Cockcroft-Gault)
12. 118.64 mL/min
13. 12 levofloxacin tablets
14. 500 mg ceftazidime every 24 hours
15. 105 lb
47.8 kg
16. 89.2 kg
17. 3.29 mL atracurium besylate
injection
18. 23.67 to 63.13 g human immune
globulin
19. 6.99 mmol/L
20. 49.55 to 99.09 mcg
21. (d) All of the above
22. 23.08%
23. (a) 4.34:1 = T C:H DL ratio
(b) 33.33%
24. (a) 7.78 mmol/L
188 Pharma euti al c al ulations
References
1. H eparin dosing. Available at: http://www.rxkinetics.com/heparin.html. Accessed June 25, 2014.
2. H eparin Sodium Injection, USP. Available at: http://www.hospira.com/Images/EN -3340_32-92402_1.pdf.
Accessed July 16, 2014.
3. H eparin Sodium. Drug Facts & Comparisons. Facts & Comparisons [database online]. St. Louis, MO: Wolters
Kluwer H ealth, Inc.; 2014.
4. Bontempo FA, H assett AC. Low molecular weight heparin. Available at: http://www.itxm.org/tmu/tmu1996/
tmu6-96.htm. Accessed July 16, 2014.
5. Stockton SJ. Calculations. International Journal of Pharmaceutical Compounding 2014;18:320.
6. Stockton SJ. Calculations. International Journal of Pharmaceutical Compounding 2009;13:239.
7. Jelliffe RW. Estimations of creatinine clearance when urine cannot be collected. Lancet 1971;1:975.
8. Jelliffe RW. Creatinine clearance bedside estimate. Annals of Internal Medicine 1973;79:604.
9. Cockcroft DW, Gault MH . Prediction of creatinine clearance from serum creatinine. Nephron 1976;16:31.
10. Dowling T C. Evaluation of kidney function. In: DiPiro JT, Talbert RL, Yee GC, et al., eds. Pharmacotherapy:
A Pathophysiologic Approach, 9th Ed. [book online]. N ew York, N Y: McGraw-H ill; 2014.
11. Chessman KH , Kumpf VJ. Assessment of nutrition status and nutrition requirements. In: DiPiro JT, Talbert
RL, Yee GC, et al., eds. Pharmacotherapy: A Pathophysiologic Approach, 9th Ed. [book online]. N ew York, N Y:
McGraw-H ill; 2014.
12. D rug D osing in O besity Reference Table. Available at: http://clincalc.com/kinetics/obesitydosing.aspx.
Accessed February 22, 2015.
13. N g JK, Schulz LT, Rose W E, et al. Daptomycin dosing based on ideal body weight versus actual body weight:
comparison of clinical outcomes. Antimicrobial Agents in Chemotherapy 2014;58(1):88–93. Available at: http://
www.ncbi.nlm.nih.gov/pubmed/24145531. Accessed February 22, 2015.
14. ASCO Guideline Recommends the Use of Actual Body Weight to Calculate Appropriate Dose of Chemotherapy
Drugs for Obese Patients. Available at: http://www.asco.org/press-center/asco-guideline-recommends- useactual-body-weight-calculate-appropriate-dose. Accessed February 22, 2015.
15. Alldredge BK, Corelli RL, Ernst ME, et al., eds. Koda-Kimble & Young’s Applied Therapeutics: The Clinical Use of
Drugs. 10th Ed. Baltimore, MD: Wolters Kluwer H ealth/Lippincott Williams & Wilkins; 2013:238.
16. Drug levels. Drug Facts & Comparisons. Facts & Comparisons [Database Online]. St. Louis, MO: Wolters
Kluwer H ealth, Inc.; 2015.
17. N ational Cholesterol Education Program Report. Circulation 2004;110:227–239. Available at: http://www.
circulationaha.org. Accessed March 1, 2011.
18. H errier RN , Apgar DA, Boyce RW, et al. Dyslipidemia. In: H errier RN , Apgar DA, Boyce RW, et al., eds.
Patient Assessment in Pharmacy [book online]. N ew York, N Y: McGraw-H ill; 2015.
19. Ansel H C, Prince SJ. Pharmaceutical calculations. In: The Pharmacist’s Handbook. Baltimore, MD: Lippincott
Williams & Wilkins; 2004:236–240.
20. Women’s health: W hat’s hot. Pharmacy Today 2007;13(9):28.
189
W hen a solvent passes through a semipermeable membrane rom a dilute solution into
a more concentrated one, the concentrations become equalized and the phenomenon is
known as osmosis. T he pressure responsible or this phenomenon is termed osmotic pressure and varies with the nature o the solute.
I the solute is a nonelectrolyte, its solution contains only molecules and the osmotic
pressure varies with the concentration o the solute. I the solute is an electrolyte, its solution contains ions and the osmotic pressure varies with both the concentration o the solute
and its degree o dissociation. T hus, solutes that dissociate present a greater number o
particles in solution and exert a greater osmotic pressure than do undissociated molecules.
Two solutions that have the same osmotic pressure are termed isosmotic. Many solutions intended to be mixed with body luids are designed to have the same osmotic pressure or greater patient com ort, e icacy, and sa ety. A solution having the same osmotic
pressure as a specific body luid is termed isotonic (meaning o equal tone) with that speci ic
body luid.
Solutions o lower osmotic pressure than that o a body luid are termed hypotonic,
whereas those having a higher osmotic pressure are termed hypertonic. Pharmaceutical dosage orms intended to be added directly to the blood or mixed with biological luids o the
eye, nose, and bowel are o principal concern to the pharmacist in their preparation and
clinical application.
Special Clinical Considerations of Tonicity
It is generally accepted that or ophthalmic and parenteral administration, isotonic solutions
are better tolerated by the patient than those at the extremes o hypo- and hypertonicity. With the administration o an isotonic solution, there is a homeostasis with the body’s
intracellular f uids. T hus, in most instances, preparations that are isotonic, or nearly so, are
pre erred. H owever, there are exceptions, as in instances in which hypertonic solutions are
used to “draw” f uids out o edematous tissues and into the administered solution.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

c al ula c al ula D mon ra	h d o a on fa or (i) of a h m al ag n .
h	od um hlor d	qu al n (E- alu ) of a h m al ag n .
y al ula on wh h r a olu on	hypo on , o on , or hyp r on .
P rform al ula on r qu r d n h pr para on of o on	olu on .
c al ula	h pH of a uff r olu on.
D rm n h amoun of ompon n n d d o pr par a uff r a a p	f pH.

Isotonic and Buffer Solutions
11
190 Pharma euti al c al ulations
Most ophthalmic preparations are ormulated to be isotonic, or approximately isotonic, to duplicate ophthalmic tears or the com ort o the patient. T hese solutions are also
prepared and bu ered at an appropriate pH , both to reduce the likelihood o irritation to
the eye’s tissues and to maintain the stability o the preparations.
Injections that are not isotonic should be administered slowly and in small quantities to minimize tissue irritation, pain, and cell luid imbalance. T he tonicity o smallvolume injections is generally inconsequential when added to large-volume parenteral
in usions because o the presence o tonic substances, such as sodium chloride or
dextrose in the large-volume in usion, which serve to adjust the tonicity o the smaller
added volume.1
Intravenous in usions, which are hypotonic or hypertonic, can have pro ound adverse
e ects because they generally are administered in large volumes.1 Large volumes o hypertonicin usions containing dextrose, or example, can result in hyperglycemia, osmotic diuresis, and excessive loss o electrolytes. Excess in usions o hypotonic luids can result in the
osmotic hemolysis o red blood cells and surpass the upper limits o the body’s capacity to
sa ely absorb excessive luids. Even isotonic luids, when in used intravenously in excessive
volumes or at excessive rates, can be deleterious due to an overload o luids placed into the
body’s circulatory system.
Physical/Chemical Considerations in the Preparation of Isotonic
Solutions
T he calculations involved in preparing isotonic solutions may be made in terms o data
relating to the colligative properties o solutions. T heoretically, any one o these properties
may be used as a basis or determining tonicity. Practically and most conveniently, a comparison o reezing points is used or this purpose. It is generally accepted that -0.52°C is
the reezing point o both blood serum and lacrimal f uid.
W hen 1g molecular weight o any nonelectrolyte, that is, a substance with negligible dissociation, such as boric acid, is dissolved in 1000 g o water, the reezing
point o the solution is about 1.86°C below the reezing point o pure water. By
simple proportion, there ore, we can calculate the weight o any nonelectrolyte that
should be dissolved in each 1000 g o water i the solution is to be isotonic with body
luids.
Boric acid, or example, has a molecular weight o 61.8; thus (in theory), 61.8 g in
1000 g o water should produce a reezing point o -1.86°C. T here ore:

1 86 0 52 . ( ) . ( )

61 8 17 3 . ( ) ( ) .

° °
= =
C C
g
x g
x g
In short, 17.3 g o boric acid in 1000 g o water, having a weight-in-volume strength o
approximately 1.73%, should make a solution isotonic with lacrimal luid.
W ith electrolytes, the problem is not so simple. Because osmotic pressure depends
more on the number o particles, substances that dissociate have a tonic e ect that
increases with the degree o dissociation; the greater the dissociation, the smaller the
quantity required to produce any given osmotic pressure. I we assume that sodium
chloride in weak solutions is about 80% dissociated, then each 100 molecules yields 180
particles, or 1.8 times as many particles as are yielded by 100 molecules o a nonelectrolyte. T his dissociation actor, commonly symbolized by the letter i, must be included in
11 • i oton c and b uffer s olut on 191
the proportion when we seek to determine the strength of an isotonic solution of sodium
chloride (m.w. 58.5):

1 86 1 8 0 52 . ( ) . . ( ) ° × °

58 5 9 09 . ( ) ( ) .

= =
C
C
g
x g
x g
H ence, 9.09 g of sodium chloride in 1000 g of water should make a solution isotonic
with blood or lacrimal fluid. In practice, a 0.9% w/v sodium chloride solution is considered
isotonic with body fluids.
Simple isotonic solutions may then be calculated by using this formula:
0 52
1 86
1000
.
. ( )
×
×
=
molecular weight
dissociation
g of solute per g
i
oof water
T he value of i for many medicinal salts has not been experimentally determined. Some
salts are exceptional (such as zinc sulfate, with only 40% dissociation and an i value therefore of
1.4), but most medicinal salts approximate the dissociation of sodium chloride in weak solutions.
If the number of ions is known, we may use the following values, lacking better information:
N onelectrolytes and substances of slight dissociation: 1.0
Substances that dissociate into 2 ions: 1.8
Substances that dissociate into 3 ions: 2.6
Substances that dissociate into 4 ions: 3.4
Substances that dissociate into 5 ions: 4.2
A special problem arises when a prescription directs us to make a solution isotonic by
adding the proper amount of a tonicity agent (such as sodium chloride or boric acid) to the
solution containing the active ingredient. Given a 0.5% w/v solution of sodium chloride,
we may easily calculate that 0.9 g – 0.5 g = 0.4 g of additional sodium chloride that should
be contained in each 100 mL if the solution is to be made isotonic with a body fluid. But
how much sodium chloride should be used in preparing 100 mL of a 1% w/v solution of
atropine sulfate, which is to be made isotonic with lacrimal fluid? T he answer depends on
how much sodium chloride is in effect represented by the atropine sulfate.
T he relative tonic effect of two substances—that is, the quantity of one that is equivalent in tonic effects to a given quantity of the other—may be calculated if the quantity of
one having a certain effect in a specified quantity of solvent is divided by the quantity of the
other having the same effect in the same quantity of solvent. For example, we calculated
that 17.3 g of boric acid per 1000 g of water and 9.09 g of sodium chloride per 1000 g of
water are both instrumental in making an aqueous solution isotonic with lacrimal fluid. If,
however, 17.3 g of boric acid are equivalent in tonicity to 9.09 g of sodium chloride, then
1 g of boric acid must be the equivalent of 9.09 g ÷ 17.3 g or 0.52 g of sodium chloride.
Similarly, 1 g of sodium chloride must be the “tonicic equivalent” of 17.3 g ÷ 9.09 g or 1.9 g
of boric acid.
We have seen that one quantity of any substance should in theory have a constant tonic
effect if dissolved in 1000 g of water: 1 g molecular weight of the substance divided by its
i or dissociation value. H ence, the relative quantity of sodium chloride that is the tonicic
equivalent of a quantity of boric acid may be calculated by these ratios:
58 5 1 8
61 8 1 0
58 5 1 0
61 8 1 8
. .
. .
. .
. .
÷ ÷
××
or
and we can formulate a convenient rule: quantities of two substances that are tonicic equivalents are proportional to the molecular weights of each multiplied by the i value of the other.
192 Pharma euti al c al ulations
To return to the problem involving 1 g of atropine sulfate in 100 mL of solution:
Molecular weight of sodium chloride = 58.5; i = 1.8
Molecular weight of atropine sulfate = 695; i = 2.6
695 1 8
58 5 2 6
××
=
.
. .
( )
( )
l g
x g
x = 0.12 g of sodium chloride represented by
1 g of atropine sulfate
T herefore, the sodium chloride equivalent, or E-value, of atropine sulfate is 0.12.
Because a solution isotonic with lacrimal fluid should contain the equivalent of 0.9 g
of sodium chloride in each 100 mL of solution, the difference to be added must be
0.9 g – 0.12 g = 0.78 g of sodium chloride.
Rearranging the information for calculating the E-value of boric acid or atropine sulfate, the following equation can be used to calculate the sodium chloride equivalent of any
substance:

Molecular weight of sodium chloride Factor of sodium chloride i

fa i cctor of the substance Molecular weight of the substance = Sodium chlooride equivalent

×
Table 11.1 gives the sodium chloride equivalents (E-values) of each of the substances
listed. T hese values were calculated according to the rule stated previously using the
general dissociation factors listed on page 191 or adapted from tables listing experimental values. If the amount of a substance included in a pr escription is multiplied by its
sodium chloride equivalent, the amount of sodium chloride r epr esented by that substance
is determined.
T b 11.1 •  So d Iu m Ch l o r Id e e q u Iva l e n TS (E-va l u e S)
S bst c m c W ig t I s

S i (e –	C )a	i	e i	t	Antipyrine	188	1
0.17
Atropine sulfate·H2O	695	3	0.12
Benoxinate hydrochloride	345	2	0.17
Benzalkonium chloride	360	2	0.16
Benzyl alcohol	108	1	0.17
Boric acid	61.8	1	0.52
Brimonidine tartrate	442	2	0.13
Chlorobutanol	177	1	0.24
Cocaine hydrochloride	340	2	0.17
Cromolyn sodium	512	2	0.14
Cyclopentolate hydrochloride	328	2	0.18
Demecarium bromide	717	3	0.12
Dextrose (anhydrous)	180	1	0.18
Dextrose·H2O	198	1	0.16
Ephedrine hydrochloride	202	2	0.29
Ephedrine sulfate	429	3	0.2
Epinephrine bitartrate	333	2	0.18
Fluorescein sodium	376	3	0.31

11 • i oton c and b uffer s olut on 193
S bst c m c W ig t I s

S i (e –	C )a	i	e i	t	Glycerin	92	1
0.35
Homatropine hydrobromide Hydroxyamphetamine hydrobromide	356 232	2 2	0.17 0.25
Idoxuridine	354	1	0.09
Lidocaine hydrochloride	289	2	0.2
Mannitol	182	1	0.18
Morphine sulfate·5H2O	759	3	0.11
Moxifloxacin hydrochloride	438	2	0.13
Naphazoline hydrochloride	247	2	0.27
Oxymetazoline hydrochloride	297	2	0.22
Penicillin G potassium	372	2	0.18
Phenobarbital sodium	254	2	0.24
Phenylephrine hydrochloride	204	2	0.32
Physostigmine salicylate	413	2	0.16
Pilocarpine hydrochloride	245	2	0.24
Potassium chloride	74.5	2	0.76
Potassium iodide	166	2	0.34
Potassium nitrate Potassium phosphate, monobasic Procaine hydrochloride	101 136 273	2 2 2	0.58 0.43 0.21
Proparacaine hydrochloride	331	2	0.15
Scopolamine hydrobromide·3H2O	438	2	0.12
Silver nitrate	170	2	0.33
Sodium bicarbonate	84	2	0.65
Sodium borate·10H2O	381	5	0.42
Sodium carbonate·H2O	124	3	0.6
Sodium chloride	58	2	1
Sodium citrate·2H2O	294	4	0.31
Sodium iodide	150	2	0.39
Sodium lactate Sodium phosphate, dibasic, anhydrous Sodium phosphate, dibasic·7H2O Sodium phosphate, monobasic, anhydrous Sodium phosphate, monobasic·H2O	112 142 268 120 138	2 3 3 2 2	0.52 0.53 0.29 0.49 0.42
Tetracaine hydrochloride	301	2	0.18
Tetracycline hydrochloride	481	2	0.12
Tetrahydrozoline hydrochloride	237	2	0.25
Timolol maleate	432	2	0.14
Tobramycin	468	1	0.07
Tropicamide	284	1	0.09
Urea	60	1	0.53
Xylometazoline hydrochloride	281	2	0.21
Zinc chloride	136	3	0.62
Zinc sulfate·7H2O	288	2	0.16

aCalculated based on general dissociation constant or adapted from Allen LV, ed. Remington: The Science and Practice of
Pharmacy. London, UK: Pharmaceutical Press; 2013:652–662 and O’Neil MJ, ed. The Merck Index. Vol. 13. Whitehouse
Station, NJ: Merck & Co., Inc.; 2001:MISC-32–MISC-42.
T b 11.1 •  So d Iu m Ch l o r Id e e q u Iva l e n TS (E-va l u e S) (Continued)
194 Pharma euti al c al ulations
T he procedure for the calculation of isotonic solutions with sodium chloride equivalents may
be outlined as follows:
St ep 1. Calculate the amount of sodium chloride represented by each ingredient in a prescription by multiplying the amount of each ingredient by its sodium chloride equivalent.
St ep 2. Calculate the amount of sodium chloride, alone, that would be contained in
an isotonic solution of the volume specified in the prescription, namely, the amount
of sodium chloride in a 0.9% solution of the specified volume.
St ep 3. Subtract the amount of sodium chloride represented by the ingredients in
the prescription (Step 1) from the amount of sodium chloride, alone, that would
be represented in the specific volume of an isotonic solution (Step 2). T he answer
represents the amount of sodium chloride to be added to make the solution isotonic.
St ep 4. If an agent other than sodium chloride, such as boric acid, dextrose, or mannitol, is to be used to make a solution isotonic, divide the amount of sodium chloride
(Step 3) by the sodium chloride equivalent of the other substance.
Example Calculations of the i Factor
(1) Zinc sulfate is a 2-ion electrolyte, dissociating 40% in a certain concentration. Calculate its
dissociation (i) factor.
On the basis of 40% dissociation, 100 particles of zinc sulfate will yield:
40 zinc ions
40 sulfate ions
60 undissociated particles
or 140 particles
Because 140 particles represent 1.4 times as many particles as were present before dissociation, the dissociation (i) factor is 1.4.
(2) Zinc chloride is a 3-ion electrolyte, dissociating 80% in a certain concentration. Calculate
its dissociation (i) factor.
On the basis of 80% dissociation, 100 particles of zinc chloride will yield:
80 zinc ions
80 chloride ions
80 chloride ions
20 undissociated particles
or 260 particles
Because 260 particles represents 2.6 times as many particles as were present before
dissociation, the dissociation (i) factor is 2.6.
Example Calculations of the Sodium Chloride Equivalent (E-values)
(1) Papaverine hydrochloride (m.w. 376) is a 2-ion electrolyte, dissociating 80% in a given
concentration. Calculate its sodium chloride equivalent.
Because papaverine hydrochloride is a 2-ion electrolyte, dissociating 80%, its i factor is 1.8.
58 5
1 8
1 8
376
.
.
.
× = 0 16 .
(2) Calculate the sodium chloride equivalent for glycerin, a nonelectrolyte with a molecular
weight of 92.2
Glycerin, i factor = 1.0
58 5
1 8
1 0
92
.
.
.
× = 0 35 .
11 • i oton c and b uffer s olut on 195
(3) Calculate the sodium chloride equivalent or timolol maleate (TIMOPTIC), which dissociates into two ions and has a molecular weight o 432.2
T imolol maleate, i actor = 1.8
58 5
1 8
1 8
432
.
.
.
× = 0 14 .
(4) Calculate the sodium chloride equivalent or f uorescein sodium, which dissociates into three
ions and has a molecular weight o 376.2
Fluorescein sodium, i actor = 2.6
58 5
1 8
2 6
376
.
.
.
× = 0 22 .
N ote that the calculated value di ers rom the value in Table 11.1 (0.31). T his is
most likely due to using the general dissociation actor o 2.6 rather than the speci ic
dissociation actor or luorescein sodium. T he value reported in Table 11.1 is an
experimentally determined value.
(5) The agent brimonidine tartrate (ALPHAGAN P) has a molecular weight o 442 and dissociates into two ions when in solution. It is used as a 0.1% ophthalmic solution in the treatment o glaucoma. Calculate (a) the sodium chloride equivalent o brimonidine tartrate
and (b) whether, without additional ormulation agents, a 0.1% solution would be isotonic,
hypotonic, or hypertonic with tears.
(a) 58 5
1 8
1 8
442
.
.
.
× = 0 13 sodium chloride equivalent .
(b) Arbitrarily select a volume o solution as a basis or the calculation. T he commercial
product is available in 10-mL containers, so that volume would be a good choice.
For isotonicity, a 10-mL volume would require the ollowing amount o
sodium chloride or its equivalent:
10 mL × 0.9% w/v = 0.09 g sodium chloride or its equivalent
A 10-mL volume o a 0.1% w/v solution o brimonidine tartrate would contain
10 mL × 0.1% w/v = 0.01 g brimonidine tartrate
Applying the sodium chloride equivalent (0.13):
0.01 g brimonidine tartrate × 0.13 = 0.0013 g o sodium chloride equivalence
T hus, this solution would be hypotonic.
(6) I 1 g o epinephrine bitartrate, when dissolved in water, prepares 20 mL o an isotonic solution, calculate its sodium chloride equivalent.
20 mL o an isotonic sodium chloride solution would be calculated by
20 mL × 0.9% w/v = 0.18 g sodium chloride (in 20 mL o solution)
T here ore, 1 g o epinephrine bitartrate is equal in tonic e ect to 0.18 g sodium
chloride, and thus, its sodium chloride equivalent is 0.18.
Example Calculations of Tonicic Agent Required
(1) How many grams o sodium chloride should be used in compounding the ollowing prescription?

H omatropine hydrobromide Sodium chloride Purif ed water ad Make isoton. sol. Sig. or the eye

0.6 g qs 30 mL

196 Pharma euti al c al ulations
St ep 1.
0 6
1000
1
0 17 11 1
102
. . ( . ) g mg
g
from T able
mg of sodium chloride rep
× ×
= rresented by the homatromine H Br
St ep 2.
30
0 9
100
1000
1
270 30
mL
g
mL
mg
g
mg of sodium chloride in mL of an iso
× ×
=
.
ttonic sodium chloride solution
St ep 3. 270 mg ( rom Step 2) – 102 mg ( rom Step 1) = 168 mg of sodium chloride
to be used
(2) How many grams of boric acid should be used in compounding the following prescription?
St ep 1. Proparacaine H Cl:
0.
.
5
100
1000
1
60 300 0 15 45
g
mL
mg
g
mL mg mg of sodium
chloride rep
× × = × =
rresented
Pilocarpine H Cl:
2
100
1000
1
60 1200 0 24 288
g
mL
mg
g
mL mg mg of sodium
chloride rep
× × = × = .
rresented
Total: 45 mg + 288 mg = 333 mg o sodium chloride represented by both
ingredients
St ep 2.
0 9
100
1000
1
60
540 60
. g
mL
mg
g
mL
mg of sodium chloride in mL of an iso
× ×
= ttonic sodium chloride solution
St ep 3. 540 mg ( rom Step 2) – 333 mg ( rom Step 1) = 207 mg o sodium chloride
required to make the solution isotonic
But because the prescription calls or boric acid:
St ep 4. 207 mg ÷ 0.52 = 398.08 mg of boric acid to be used
(3) How many grams of potassium nitrate should be used to make the following prescription
isotonic?
Proparacaine hydrochloride 0.5%
Pilocarpine hydrochloride 2%
Boric acid qs
Purif ed water ad 60 mL
Make isoton. sol.
Sig. one drop in each eye
Sol. silver nitrate 60 mL
1:500 w/v
Make isoton. sol.
Sig. or eye use
11 • i oton c and b uffer s olut on 197
St ep 1.
1
500
1000
1
60 120 0 33
39 6
g
mL
mg
g
mL mg silver nitrate
mg of sodi
× × = ×
=
.
. um chloride represented
St ep 2.
0 9
100
1000
1
60
540 60
. g
mL
mg
g
mL
mg of sodium chloride in mL of an iso
× ×
= ttonic sodium chloride solution
St ep 3. 540 mg ( rom Step 2) – 39.6 mg ( rom Step 1) = 500.4 mg o sodium chloride required to make solution isotonic
Because, in this solution, sodium chloride is incompatible with silver nitrate,
the tonicity agent o choice is potassium nitrate. T here ore,
St ep4. 500.4 mg ÷ 0.58 (sodium chloride equivalent o potassium nitrate) = 862.76 mg
of potassium nitrate to be used
(4) How many grams of sodium chloride should be used in compounding the following
prescription?
Let us assume that ingredient X is a new substance or which no sodium chloride
equivalent is to be ound in Table 11.1 and that its molecular weight is 295 and its i actor is 2.4. T he sodium chloride equivalent o ingredient X may be calculated as ollows:
58 5
1 8
2 4
295
. 0 26
.
.
× = . , the sodium chloride equivalent for ingredient X
T hen,
St ep 1.
0 5
1000
1
. . g 0 26 130
mg
g
mg of sodium chloride represented by
ingre
× × =
ddient X
St ep 2.
0 9
100
1000
1
50
450 50
. g
mL g
mL
mg of sodium chloride in mL of an iso
× ×
=
mg
ttonic sodium chloride solution
St ep 3. 450 mg ( rom Step 2) – 130 mg ( rom Step 1) = 320 mg of sodium chloride
to be used
Preparing Isotonic Solutions by Volume Adjustment
As a convenience in compounding, a method o preparing isotonic solutions by volume
adjustment may be employed. T he method, once described in the United States Pharmacopeia–
National Formulary,3 is based on the ollowing:
Ingredient X 0.5 g
Sodium chloride qs
Purif ed water ad 50 mL
Make isoton. sol.
Sig. eyedrops
198 Pharma euti al c al ulations
By adding puri ied water to a 1-g quantity o a drug with a known E-value, a calculated
volume o an isotonic solution may be prepared. Then, by diluting this volume o solution with an
isotonic vehicle, the drug strength may be reduced while maintaining the solution’s isotonicity.
For example, 1 g of tetracaine hydrochloride (E = 0.18) can prepare 20 mL of an isotonic solution, calculated as follows:
0 18 . [ ( .)] 0 9
( )
g sodium chloride equiv . (
x mL isotonic solution
g so
=
ddium chloride
mL isotonic solution
x mL
)
( )
;
100
= 20
T his isotonic solution would contain 5% w/v tetracaine hydrochloride (1 g/20 mL).
If a solution of lesser strength is desired, a calculated quantity of an isotonic vehicle,
such as 0.9% sodium chloride, may be added. For example, if a 1% w/v solution of
tetracaine hydrochloride is desired, a total volume of 100 mL (1 g tetracaine hydrochloride/100 mL) may be prepared by adding 80 mL of isotonic vehicle to the 20 mL of the
5% w/v solution.
(1) I pilocarpine hydrochloride has a sodium chloride equivalent o 0.24, (a) how many
milliliters o isotonic solution may be prepared rom 1 g o the drug, and (b) how many
milliliters o 0.9% w/v sodium chloride solution may be added to the resultant solution to prepare an isotonic solution having a 1.5% w/v concentration o pilocarpine
hydrochloride?
(a) 0 24 . [ ( .)] 0 9
( )
g sodium chloride equiv . (
x mL isotonic solution
g so
=
ddium chloride
mL isotonic solution
x
)
( )
;
100
= 26.67 mL
(b) Although there are a number of ways to solve this problem, use of the equation
in Chapter 15 is perhaps the most convenient method:
1st quantity (Q1) ¥ 1st concentration (C1) = 2nd quantity (Q2) × 2nd
concentration (C2)
First, one must calculate the concentration of pilocarpine hydrochloride in 26.67 mL
of solution:
1
26 67
100 3 75
g
mL
w v
.
× = % . % /
T hen, applying the above equation:
26.67 mL (Q 1) × 3.75% (C1) = x mL (Q 2) × 1.5% (C2)
x
mL
= mL
×
=
26 67 3 75
1 5
66 68
. . %
. %
.
T hus, 66.68 mL of solution may be prepared, and 40.01 mL (66.68 mL – 26.67 mL)
of 0.9% sodium chloride solution should be added.
Proof that the concentration of pilocarpine hydrochloride is 1.5%:
1
66 68
100 1 4997 1 5
g pilocarpine H Cl
mL
or w v pilocarpine H Cl
.
× = % . . % /
Other examples of calculated volumes of isotonic solutions that may be prepared from
1 g of drug are given in Table 11.2 and available from other references.3,4
(2) Determine the volume o purif ed water and 0.9% w/v sodium chloride solution needed to
prepare 20 mL o a 1% w/v solution o hydromorphone hydrochloride (E = 0.22).
St ep 1. 20 mL × 1% w/v = 0.2 g hydromorphone hydrochloride needed
St ep 2. 0.2 g (hydromorphone hydrochloride) × 0.22 (E-value) = 0.044 g (sodium
chloride equivalence)
11 • i oton c and b uffer s olut on 199
0 044 0 9

100 mL

x mL

hydrochloride may be prepared by the addition o a su f cient quantity (qs) o purif ed water.

. . g
g N aCl
= ; x = 4.89 mL o an isotonic solution o hydromorphone
St ep 3. 20 mL – 4.89 mL = 15.11 mL 0.9% w/v sodium chloride solution required
Proof : . % .
.
20 0 9 0 18
0 2
mL g sodium chloride or equivalent required × =
×× 0 22 0 044 = . . ( g sodium chloride represented by g 0 2 .
hydromorphone hydrochloride
mL g sodium chloride present
)
. . % .
.
15 11 0 9 0 136
0 0
× =
444 0 136 0 18 g g g sodium chloride required for isotonicity + = . .
Use of Freezing Point Data in Isotonicity Calculations
Freezing point data (DT ) can be used in isotonicity calculations when the agent has a tonicic
e ect and does not penetrate the biologic membranes in question (e.g., red blood cells). As
stated previously, the reezing point o both blood and lacrimal f uid is -0.52°C. T hus, a
pharmaceutical solution that has a reezing point o -0.52°C is considered isotonic.
Representative data on reezing point depression by medicinal and pharmaceutical
substances are presented in Table 11.3. Although these data are or solution strengths o 1%
( ) DT f 1% , data or other solution strengths and or many additional agents may be ound in
physical pharmacy textbooks and in the literature.
Freezing point depression data may be used in isotonicity calculations as shown by the
ollowing.
Example Calculations Using Freezing Point Data
How many milligrams each of sodium chloride and lidocaine hydrochloride are required to prepare
30 mL of a 1% solution of lidocaine hydrochloride isotonic with tears?
To make this solution isotonic, the reezing point must be lowered to -0.52°C. From
Table 11.3, it is determined that a 1% solution o lidocaine hydrochloride has a reezing
point lowering o 0.063°C. T hus, su icient sodium chloride must be added to lower the
reezing point an additional 0.457°C (0.52°C – 0.063°C).
Also rom Table 11.3, it is determined that a 1% solution o sodium chloride lowers
the reezing point by 0.58°C. By proportion:
1 0 58
0 457
% %
.
.
N aCl
x N aCl
=
°C°C
x = 0.79% sodium chloride needed to lower the reezing point by 0.457°C and, thereore, required to make the solution isotonic

T b	11.2• e xa mpl e S o f ISo To n IC So l u TIo n S Th aT may Be
pr e pa r e d f r o m 1	q u a n TITIe S o f d r u g Sa
d	, 1	v	Is t ic S 57.8 22.2 35.6 26.7 20.0	ti , l
Boric acid Ephedrine sulfate
Phenylephrine hydrochloride
Pilocarpine hydrochloride Tetracaine hydrochloride

  

Zinc sulfate·7H2O aCalculated from the E-values in Table 11.1.

17.8

200 Pharma euti al c al ulations
T hus, to make 30 mL of solution,
30 mL × 1% = 0.3 g = 300 mg lidocaine hydrochloride, and
30 mL × 0.79% = 0.24 g = 236.68 mg sodium chloride
N OT E: Should a prescription call for more than one medicinal and/or pharmaceutic
ingredient, the sum of the freezing points is subtracted from the required value in determining the additional lowering required by the agent used to provide isotonicity.
T b 11.3 •  f r e e zIn g po In T d aTa f o r Se l e CT a g e n TS

a	t	f	i	p i t d	ssi , 1% S	ti s (DT 1%)
Atropine sulfate Boric acid Chlorobutanol Dextrose Ephedrine sulfate Epinephrine bitartrate Glycerin Homatropine hydrobromide Lidocaine hydrochloride Lincomycin Morphine sulfate Naphazoline hydrochloride Physostigmine salicylate Sodium bisulfite Sodium chloride Sulfacetamide sodium Zinc sulfate	0.07 0.29 0.14 0.09 0.13 0.10 0.20 0.11 0.063 0.09 0.08 0.16 0.09 0.36 0.58 0.14 0.09

Ca l Cu l aTIo n S Ca pSu l e
Isotonicity
To calculate the “equivalent tonic effect” to sodium chloride represented by an ingredient
in a preparation, multiply its weight by its E-value:
g E value g equivalent tonic effect to sodium chloride × – , =
To make a solution isotonic, calculate and ensure the quantity of sodium chloride and/
or the equivalent tonic effect of all other ingredients to total 0.9% w/v in the preparation:
g NaCl g NaCl tonic equivalents
mL preparation
w v
( ) ( )
( )
+ × 100 0 9 = . % /
To make an isotonic solution from a drug substance, add sufficient water by the equation:
g drug substance E value drug substance
( ) ( ) mL water
.
×
=
–
0 009
This solution may then be made to any volume with isotonic sodium chloride solution
to maintain its isotonicity.
The E-value can be derived from the same equation, given the grams of drug substance and the milliliters of water required to make an isotonic solution.
11 • i o on and b uffer s olu on 201

Ca Se In po In T 11.1 a A lo al oph halmolog	rea ng one of h pa en for a
po -LAs iK eye nfe on ha	no re pond ng o op al profloxa n. t he e nfe –
on , al hough rare, an o ur af er la er n	u kera om leu	(LAs iK) urgery for
v on orre on.
t op al am ka n ulfa e ha	een hown o e effe ve for he rea men of eye an Pseudomonas,5,6 Burkholderia ambifaria,7
nfe on due o profloxa n-re
Mycobacterium chelonae, and Mycobacterium fortuitum.8–10
t he oph halmolog	pre r e 60 mL of a 2.5% am ka n ulfa e o on	olu
on, wo drop n he affe ed eye every 2 hour .
Am ka n ulfa e Us P (c 22H43N5O13·2H2s O2), m.w., 781.76,	an am nogly o
de- ype an	o	on a n ng hree on .

(a) De erm ne he we gh n gram of am ka n ulfa e needed o prepare he
olu on.
( ) c al ula e he od um hlor de equ valen (E-value) for am ka n ulfa e.
( ) c al ula e he amoun of od um hlor de needed o make he prepared oluon o on .
(d) How many m ll l er of 23.5% od um hlor de nje on hould e u ed o
o a n he needed od um hlor de?
a
c a e n Po n our e y of W. b ea h, A hen , GA.

Ca Se In po In T 11.2 11 A formula for a ompounded oph halm	olu on	hown
elow:
t o ramy n ulfa e	300 mg 100 mg 806 mg 100 mL
D lofena	od um
s od um hlor de
s er le wa er for nje on q
t h formula om ne he an a er al a on of o ramy n ulfa e w h he an –
nflamma ory and analge	proper e of d lofena	od um. i hould e prepared n
an a ep	env ronmen u h a a lam nar flow hood and ha a eyond-u e da e of up
o 3 day f ored n he refr gera or.
(a) t o ramy n ulfa e [(c 18H37N5O9)2·5H2s O4]	a 7- on ele roly e and ha a d o a e 80% a a er
mole ular we gh of 1425.45. A um ng ha
a n on en ra on, al ula e he d o a on fa or (i) and od um hlor de
equ valen (E-value) for o ramy n ulfa e.
( ) t he po en y of o ramy n ulfa e	634 o 739 m g of o ramy n a v y per
m ll gram. Wha	he amoun range of o ramy n a v y n h formula on?
( ) D lofena	od um (c 14H10c l2NNaO2)	a 2- on ele roly e w h an average
d o a on fa or of 1.8 and a mole ular we gh of 318.13. c al ula e he
E-value for d lofena	od um.

(d) i he amoun of od um hlor de l ed n he formula on orre o make
he olu on o on ?
(e) How mu h of ea h ngred en would e needed o prepare 20 mL of he
ompounded olu on?
(f) How mu h of a o ramy n ulfa e nje a le olu on w h a on en ra on of
80 mg/2 mL would e needed o prepare 20 mL of he ompounded olu on?
202 Pharma euti al c al ulations
Buffers and Buffer Solutions
W hen a minute amount o hydrochloric acid is added to pure water, a signif cant increase in
hydrogen-ion concentration occurs immediately. In a similar manner, when a minute amount
o sodium hydroxide is added to pure water, it causes a correspondingly large increase in the
hydroxide-ion concentration. T hese changes take place because water alone cannot neutralize
even traces o acid or base, that is, it has no ability to resist changes in hydrogen-ion concentration or pH . A solution o a neutral salt, such as sodium chloride, also lacks this ability.
T here ore, it is said to be unbuffered.
T he presence o certain substances or combinations o substances in aqueous solution
imparts to the system the ability to maintain a desired pH at a relatively constant level, even
with the addition o materials that may be expected to change the hydrogen-ion concentration. T hese substances or combinations o substances are called buffers, and solutions o
them are called buffer solutions. By de inition, then, a buffer solution is a system, usually an
aqueous solution, that possesses the property o resisting changes in pH with the addition
o small amounts o an acid or base.
Bu ers are used to establish and maintain an ion activity within rather narrow
limits. In pharmacy, the most common bu er systems are used in (i) the preparation o
such dosage orms as injections and ophthalmic solutions, which are placed directly into
pH -sensitive body luids; (ii) the manu acture o ormulations in which the pH must be
maintained at a relatively constant level to ensure maximum product stability; and (iii)
pharmaceutical tests and assays requiring adjustment to or maintenance o a speci ic pH
or analytic purposes.
A bu er solution is usually composed o a weak acid and a salt o the acid, such as
acetic acid and sodium acetate, or a weak base and a salt o the base, such as ammonium
hydroxide and ammonium chloride. Typical bu er systems that may be used in pharmaceutical ormulations include the ollowing pairs: acetic acid and sodium acetate, boric
acid and sodium borate, and sodium phosphate monobasic and sodium phosphate dibasic. Formulas or standard bu er solutions or pharmaceutical analysis are given in the
United States Pharmacopeia.12
In the selection o a bu er system, due consideration must be given to the dissociation
constant o the weak acid or base to ensure maximum bu er capacity. T his dissociation
constant, in the case o an acid, is a measure o the strength o the acid; the more readily
the acid dissociates, the higher its dissociation constant and the stronger the acid. Selected
dissociation constants, or Ka values, are given in Table 11.4.
T bl 11.4 •  d ISSo CIaTIo n Co n STa n TS o f So me
We a k a CId S aT 25°C

a ci Acetic	k 1.75 × 10-5
Barbituric	1.05 × 10-4
Benzoic	6.30 × 10-5
Boric	6.4 × 10-10
Formic	1.76 × 10-4
Lactic	1.38 × 10-4
Mandelic	4.29 × 10-4
Salicylic	1.06 × 10-3

11 • i o on and b u s olu on 203
T he dissociation constant, or Ka value, of a weak acid is given by the equation:
K
H A
H A

where A ( + ) ( ) – –	salt
H A acid	(	)

a =
= =
Because the numeric values of most dissociation constants are small numbers and may
vary over many powers of 10, it is more convenient to express them as negative logarithms:
pK K a = – log a
W hen equation K
H A
a H A
=
( + ) ( ) –
( )
is expressed in logarithmic form, it is written:
pK H salt
a acid
= – –
log ( ) log +
and because pH = -log (H +):
then pK pH salt
acid
and pH pK salt
acid
a
a
= –
= +
log
log
Buffer Equation
T he equation just derived is the H enderson-H asselbalch equation for weak acids, commonly known as the buffer equation.
Similarly, the dissociation constant, or Kb value, of a weak base is given by the equation:
K
B OH
BOH
in which B salt
b = and BOH base
= =

( + ) ( (	)
and the buffer equation for weak bases, which is derived from this relationship, may
be expressed as:
pH pK pK base = – + log
w	b	salt

) – +
T he buffer equation is useful for calculating (1) the pH of a buffer system if its composition is known and (2) the molar ratio of the components of a buffer system required to
give a solution of a desired pH . T he equation can also be used to calculate the change in pH
of a buffered solution with the addition of a given amount of acid or base.
pKA vALUe Of A We AK Ac iD Wit H KNOWN Dis s Oc iAt iON c ONs t ANt
Calculating the pKa value of a weak acid, given its dissociation constant, Ka:
The dissociation constant of acetic acid is 1.75 × 10–5 at 25°C. Calculate its pKa value.
pK K a = – log log( . ) . a = – 1 75 10 × = -5 4 76
pH vALUe Of A s ALt /Ac iD b Uf f e r s ys t e m
Calculating the pH value:
W hat is the pH of a buffer solution prepared with 0.05 M sodium borate and 0.005 M boric
acid? The pKa value of boric acid is 9.24 at 25°C.
N ote that the ratio of the components of the buffer solution is given in molar
concentrations.
204 Pha a u al c al ula on
Using the buffer equation for weak acids:
pH pK salt
a acid
= +
= +
= +
= +
=
log
. log .
.
. log
.
.
9 24 0 05
0 005
9 24 10
9 24 1
10 24
pH vALUe Of A b As e /s ALt b Uf f e r s ys t e m
Calculating the pH value:
W hat is the pH of a buffer solution prepared with 0.05 M ammonia and 0.05 M ammonium
chloride? The Kb value of ammonia is 1.80 × 10-5 at 25°C.
Using the buffer equation for weak bases:
pH pK pK base
= w – b + log salt
Because the K
w value for water is 1014 at 25°C, pKw = 14.
pK K
pH
b = – b = – × =
= – + =
log log( . ) . –
. log .
.
1 80 10 4 74
14 4 74 0 05
0 05
5
9.26
mOLAr r At iO Of s ALt /Ac iD f Or A b Uf f e r s ys t e m Of De s ir e D pH
Calculating the molar ratio of salt/acid required to prepare a buffer system with a desired pH value:
W hat molar ratio of salt/acid is required to prepare a sodium acetate–acetic acid buffer solution
with a pH of 5.76? The pKa value of acetic acid is 4.76 at 25°C.
Using the buffer equation:

pH pK	salt acid log	a
salt acid	a

pH pK
antilog of
= +
= –
= – =
log
5 76 4 76 1 . .
1 ==
=
10
ratio or 10 1 / : 10 1
QUANt it y Of c OmPONe Nt s iN A b Uf f e r s OLUt iON t O yie LD A s Pe c if ic vOLUme
Calculating the amounts of the components of a buffer solution required to prepare a desired
volume, given the molar ratio of the components and the total buffer concentration:
The molar ratio of sodium acetate to acetic acid in a buffer solution with a pH of 5.76 is 10:1.
Assuming the total buffer concentration is 0.022 mol/L, how many grams of sodium acetate (m.w. 82)
and how many grams of acetic acid (m.w. 60) should be used in preparing a liter of the solution?
Because the molar ratio of sodium acetate to acetic acid is 10:1,
the mole fraction of sodium acetate or
and the mole fract
=
+
10
1 10
10
11
iion of acetic acid or =
1+
1 10
1
11
11 • i o on and b u s olu on 205
If the total buffer concentration = 0.022 mol/L,
Concentration of sodium acetate mol L mol L
Conc
= × =
10
11
0 022 0 02 . / . /
eentration of acetic acid mol L mol L
Amount of so
= × =
1
11
0 022 0 002 . / . /
ddium acetate mol L g mol L g
Amount of acetic acid
= × × =
=
0 02 82 1 1 64 . / / .
00 002 60 1 0 12 . / / . mol L g mol L g × × =
T he efficiency of buffer solutions—that is, their specific ability to resist changes in
pH—is measured in terms of buffer capacity; the smaller the pH change with the addition of
a given amount of acid or base, the greater the buffer capacity of the system. Among other
factors, the buffer capacity of a system depends on (1) the relative concentration of the buffer components and (2) the ratio of the components. For example, a 0.5-M acetate buffer at
a pH of 4.76 would have a higher buffer capacity than a 0.05-M buffer.
If a strong base such as sodium hydroxide is added to a buffer system consisting of
sodium acetate and acetic acid, the base is neutralized by the acetic acid forming more
sodium acetate, and the resulting increase in pH is slight. Actually, the addition of the base
increases the concentration of sodium acetate and decreases by an equal amount the concentration of acetic acid. In a similar manner, the addition of a strong acid to a buffer system
consisting of a weak base and its salt would produce only a small decrease in pH .
c HANGe iN pH Wit H ADDit iON Of AN Ac iD Or b As e
Calculating the change in pH of a buffer solution with the addition of a given amount of
acid or base:
Calculate the change in pH after adding 0.04 mol of sodium hydroxide to a liter of a buffer
solution containing 0.2 M concentrations each of sodium acetate and acetic acid. The pKa value of
acetic acid is 4.76 at 25°C.
T he pH of the buffer solution is calculated by using the buffer equation as follows:
pH pK salt
a acid
= +
= +
= +
=
log
. log .
.
. log
.
4 76 0 2
0 2
4 76 1
4 76
T he addition of 0.04 mol of sodium hydroxide converts 0.04 mol of acetic acid to 0.04 mol
of sodium acetate. Consequently, the concentration of acetic acid is decreased and the concentration of sodium acetate is increased by equal amounts, according to the following equation:
pH pK salt base
acid base
pH pK
pK
a a a
= +
+-
= +
+-
=
log
log . .
. .
0 2 0 04
0 2 0 04
++
= + =
log .
.
. . . .
0 24
0 16
4 76 0 1761 4 9361 4 94 or
Because the pH before the addition of the sodium hydroxide was 4.76, the change in
pH = 4.94 – 4.76 = 0.18 unit.
206 Pharma euti al c al ulations
pr a CTICe pr o Bl e mS
Calculations of Tonicity
1. Isotonic sodium chloride solution contains 0.9% w/v sodium chloride. I the
E-value o boric acid is 0.52, calculate the percentage strength (w/v) o an isotonic
solution o boric acid.
2. Sodium chloride is a 2-ion electrolyte, dissociating 90% in a certain concentration. Calculate (a) its dissociation actor and (b) the reezing point o a molal
solution.
3. A solution o anhydrous dextrose (m.w. 180) contains 25 g in 500 mL o water.
Calculate the reezing point o the solution.
4. Procaine hydrochloride (m.w. 273) is a 2-ion electrolyte, dissociating 80% in a
certain concentration.
(a) Calculate its dissociation actor.
(b) Calculate its sodium chloride equivalent.
(c) Calculate the reezing point o a molal solution o procaine hydrochloride.
5. T he reezing point o a molal solution o a nonelectrolyte is -1.86°C. W hat is the
reezing point o a 0.1% solution o zinc chloride (m.w. 136), dissociating 80% ?
(For lack o more de inite in ormation, assume that the volume o the molal solution is approximately 1 liter.)

6.

Ephedrine sul ate Sodium chloride Purif ed water ad Make isoton. sol. Sig. use as directed

0.3 g qs 30 mL

H ow many milligrams o sodium chloride should be used in compounding the
prescription?
7.

H ow much sodium chloride should be used in compounding the prescription?
8.	Zinc sul ate	0.06 g
Fluorescein sodium Sodium chloride Purif ed water qs Make isoton. sol. Sig. use in the eye	0.25% w/v qs 30 mL

 

H ow much boric acid should be used in compounding the prescription?
9.	Cromolyn sodium Benzalkonium chloride Bu er solution (pH 5.6) Water or injection ad Sig. one (1) drop in each eye b.i.d.	4% (w/v) 1:10,000 (w/v) qs 10 mL
Boric acid Purif ed water ad Make isoton. sol. Sig. drop in eyes	qs 30 mL

H ow many milliliters o the bu er solution (E = 0.30) should be used to render
the solution isotonic? (For lack o more de inite in ormation, assume that the
speci ic gravity o the bu er solution is 1.)
Benoxinate hydrochloride 0.4% w/v

11 • i oton c and b uffer s olut on 207
10.
H ow many grams o sodium chloride should be used in preparing the solution?
11. A sterile ophthalmic preparation contains 0.6% besi loxacin (E = 0.08) in a 5-mL
container. Calculate the quantity o sodium chloride required or isotonicity.
12. Calculate the effective quantity (g) of sodium chloride related to tonicity in 100 mL o
an intravenous luid labeled “5% dextrose in 0.45% sodium chloride,” and indicate whether the solution is isotonic, hypotonic, or hypertonic.

13.	Brimonidine tartrate T imolol maleate	30 mg 75 mg
Chlorobutanol Sodium chloride Purif ed water qs Make isoton. sol. Sig. or the eye	50 mg qs 15 mL

H ow many milligrams o sodium chloride should be used in compounding the
prescription?
14.

H ow much boric acid should be used in compounding the prescription?
15.	Sol. homatropine hydrobromide 1% Make isoton. sol. with boric acid	15 mL
Zinc sul ate	0.05 g
Boric acid Purif ed water ad Make isoton. sol. Sig. drop in eye	qs 30 mL

H ow many milligrams o boric acid should be used in compounding the
prescription?

16.	Procaine H ydrochloride Sodium Chloride	1% qs
Sterile Water or Injection ad Make isoton. sol. Sig. For injection.	100

17.
H ow many milliliters o a 0.9% solution o sodium chloride should be used in
compounding the prescription?

Dextrose, anhydrous Sodium chloride	2.5% qs
Sterile water or injection ad Label: Isotonic dextrose and saline solution	1000 mL

Tetracaine hydrochloride 0.1 g
Sig. or the eye
H ow many grams o sodium chloride should be used in compounding the
prescription?

Phenylephrine hydrochloride	1%
Chlorobutanol Sodium chloride Purif ed water ad Make isoton. sol. Sig. use as directed	0.5% qs 15 mL

208 Pharma euti al c al ulations
18.
H ow many milliliters o a 5% solution o boric acid should be used in compounding the prescription?

19.	Ephedrine hydrochloride	0.5 g
Chlorobutanol Dextrose, monohydrate Rose water ad Make isoton. sol. Sig. nose drops	0.25 g qs 50 mL

H ow many grams o dextrose monohydrate should be used in compounding the
prescription?

20.	N aphazoline hydrochloride	1%
Sodium chloride	qs
Purif ed water ad Make isoton. sol. Sig. use as directed in the eye	30 mL

H ow many milligrams o sodium chloride should be used in compounding the
prescription? Use the reezing point depression method or the sodium chloride
equivalent method.

21.	Moxi oxacin hydrochloride	110 mg
Chlorobutanol	50 mg
Sodium chloride	qs
Purif ed water ad Make isoton. sol. Sig. eye drops	20 mL

H ow many milligrams o sodium chloride should be used in compounding the
prescription?
22. H ow many milligrams o sodium chloride may be used in the preparation o
15 mL o an eye drop containing 1% tropicamide and 0.5% chlorobutanol to
render the solution isotonic with tears?
(a) 18 mg
(b) 31.5 mg
(c) 103.5 mg
(d) 135 mg

23.	Monobasic sodium phosphate, anhydrous Dibasic sodium phosphate, anhydrous Sodium chloride	5.6 g 2.84 g qs
Purif ed water ad Label: Isotonic bu er solution, pH 6.5	1000 mL

H ow many grams o sodium chloride should be used in preparing the solution?
24. H ow many grams o anhydrous dextrose should be used in preparing 1 liter o a
½% isotonic ephedrine sul ate nasal spray?

Oxymetazoline hydrochloride	½%
Boric acid solution	qs
Purif ed water ad Make isoton. sol. Sig. or the nose, as decongestant	15 mL

11 • i oton c and b uffer s olut on 209
25.
You have on hand an isotonic bu ered solution, pH 6.5. H ow many milliliters o
puri ied water and how many milliliters o the bu ered solution should be used
in compounding the prescription?

26.	Tobramycin Tetracaine hydrochloride Sol. 2% Sodium chloride	0.75% 15 mL qs
Purif ed water ad Make isoton. sol. Sig. or the eye	30 mL

T he 2% solution o tetracaine hydrochloride is already isotonic. H ow many milliliters o a 0.9% solution o sodium chloride should be used in compounding the
prescription?
27. Determine i the ollowing commercial products are hypotonic, isotonic, or
hypertonic:
(a) An ophthalmic solution containing 40 mg/mL o cromolyn sodium and
0.01% o benzalkonium chloride in puri ied water.
(b) A parenteral in usion containing 20% (w/v) o mannitol.
(c) A 500-mL large volume parenteral containing D5W (5% w/v o anhydrous
dextrose in sterile water or injection).
28. For agents having the ollowing sodium chloride equivalents, calculate the percentage concentration o an isotonic solution:
(a) 0.20
(b) 0.32
(c) 0.61
29. H ow many milliliters each o puri ied water and an isotonic sodium chloride solution should be used to prepare 30 mL o a 1% w/v isotonic solution o entanyl
citrate (E = 0.11)?
30. Using the E-values in Table 11.1, calculate the number o milliliters o water
required to make an isotonic solution rom 0.3 g o each o the ollowing:
(a) Antipyrine
(b) Chlorobutanol
(c) Ephedrine sul ate
(d) Silver nitrate
(e) Zinc sul ate
31. Calculate the E-values or each o the ollowing, given that the number o milliliters o water shown will produce an isotonic solution rom 0.3 g o drug
substance.
(a) Apomorphine hydrochloride, 4.7 mL water
(b) Aminocaproic acid, 8.7 mL water
(c) Prilocaine hydrochloride, 7.7 mL water
(d) Procainamide hydrochloride, 7.3 mL water
(e) Gentamicin sul ate, 1.7 mL water
Xylometazoline hydrochloride 0.8% w/v
Chlorobutanol 0.5% w/v
Purif ed water qs 100 mL
Make isoton. sol. and bu er to pH 6.5
Sig. nose drops

210 Pharma euti al c al ulations
32. COSOPT ophthalmic solution contains dorzolamide hydrochloride 22.26 mg/mL,
timolol maleate 6.83 mg/mL, benzalkonium chloride 0.0075% w/v, and mannitol
for tonicity.13 Dorzolamide hydrochloride has a molecular weight of 360.91 and is
a 2-ion electrolyte that dissociates 78% in a certain concentration. T he E-values
for the other ingredients can be found in Table 11.1. H ow much of each ingredient
would be needed to prepare enough solution to fill five hundred 10-mL bottles?
Calculations of Buffer Solutions
33. T he dissociation constant of ethanolamine is 2.77 × 10-5 at 25°C. Calculate its
pKb value.
34. W hat is the pH of a buffer solution prepared with 0.055 M sodium acetate and
0.01 M acetic acid? T he pKa value of acetic acid is 4.76 at 25°C.
35. W hat molar ratio of salt to acid would be required to prepare a buffer solution
with a pH of 4.5? T he pKa value of the acid is 4.05 at 25°C.
36. W hat is the change in pH on adding 0.02 mol of sodium hydroxide to a liter of
a buffer solution containing 0.5 M of sodium acetate and 0.5 M acetic acid? T he
pKa value of acetic acid is 4.76 at 25°C.
37. T he molar ratio of salt to acid needed to prepare a sodium acetate–acetic acid
buffer solution is 1:1. Assuming that the total buffer concentration is 0.1 mol/L,
how many grams of sodium acetate (m.w. 82) should be used in preparing 2 liters
of the solution?
38. W hat is the change in pH with the addition of 0.01 mol hydrochloric acid to a
liter of a buffer solution containing 0.05 M of ammonia and 0.05 M of ammonium
chloride? T he Kb value of ammonia is 1.80 × 10-5 at 25°C.
39. Calculate the pH of the following buffer:

Sodium phosphate, dibasic Sodium phosphate, monobasic Water qs

6.2 g 4.5 g 1000 mL

T he pKa value of sodium phosphate monobasic is 7.21 at 25°C and serves as an
acid in this buffer because it is more acidic than sodium phosphate dibasic. T he
molecular weight of sodium phosphate monobasic is 120 and of sodium phosphate dibasic is 142.
40. W hat is the pH change in the buffer in problem 39 if 3 mL of a 5-M hydrochloric
acid solution are added to the buffer? Assume negligible volume displacement by
the hydrochloric acid solution.
Ca l Cq u Iz
11.A. A 3-mL container o a 0.5% ophthalmic solution o moxi loxacin hydrochloride (m.w.
401; i = 1.8) is prepared in an aqueous solution o 0.45% sodium chloride. Calculate
the quantity, in milligrams, o boric acid required to render the solution isotonic.
11.B. How many grams o boric acid should be used to render this prescription isotonic?

Tetracaine hydrochloride 0.1% Epinephrine bitartrate in NSS Boric acid, qs Purif ed water, ad	0.5% 10 mL
30 mL

11 • i oton c and b uffer s olut on 211
a n SWe r S To “Ca Se In po In T” a n d pr a CTICe pr o Bl e mS
Case in Point 11.1
(a) 60 mL × 2.5% w/v = 1.5 g amikacin sulfate
(b) Sodium chloride m.w. = 58.5
Amikacin m.w. = 781.76
i
E
E
=
× =
=
2 6
58 5
1 8
2 6
781 76
0 108
.
.
.
.
.
.
(c) 60 mL × 0.9% w/v = 0.54 g sodium chloride
1.5 g (amikacin sulfate) × 0.108 (N aCl equivalent) = 0.162 g
0.54 g – 0.162 g = 0.378 g sodium chloride required for isotonicity
(d) 23 5
100

. g	. 0 378
;	=

mL
g
x mL
x = 1.61 mL sodium chloride injection
11.C. A ormulation pharmacist has developed an injection or dental local anesthesia that
contains the ollowing agents:

Lidocaine hydrochloride Epinephrine bitartrate	1% 1:50,000
Sodium chloride Potassium metabisulf te	6.5 mg/mL 1.2 mg/mL
Edetate disodium Sterile purif ed water, ad	0.25 mg/mL 1.7 mL

Using the ollowing data, determine the total tonic effect, expressed in terms o
percent strength o “sodium chloride” or its equivalent.
Lidocaine hydrochloride (E = 0.2)
Epinephrine bitartrate (E = 0.18)
Potassium metabisul ite (m.w. 222; i = 2.6)
Edetate disodium (m.w. 372; i = 2.6)
11.D. A FLEET saline enema delivers in each 118 mL 19 g monobasic sodium phosphate
(monohydrate) and 7 g dibasic sodium phosphate (heptahydrate). Calculate the
product’s percent strength in terms o “sodium chloride or its equivalent,” and
indicate whether the enema is hypotonic, isotonic, or hypertonic.
11.E. What would be the pH o a bu er solution prepared with 0.5 M dibasic sodium
phosphate and 1 M monobasic sodium phosphate? The pKa o monobasic sodium
phosphate is 7.21 at 25°C.
212 Pharma euti al c al ulations
Case in Point 11.2
(a) On the basis of 80% dissociation, 100 particles of tobramycin sulfate will yield:
80 × 2 = 160 tobramycin ions
80 × 5 = 400 sulfate ions
20 undissociated particles
580 total particles
i = =
= × =
580
100
5 8
58 5
1 8
5 8
1425 45
0
particles
particles
E value
.
.
.
.
.
– .132
(b)
Amount range = 190.2 to 221.7 mg tobramycin activity
(c) E-value = 58 5 × =
1 8
1 8
318 13
. 0 184
.
.
.
.
(d) 300 mg tobramycin sulfate × 0.132 = 39.6 mg sodium chloride equivalent
100 mg diclofenac sodium × 0.184 = 18.4 mg sodium chloride equivalent
39.6 mg + 18.4 mg + 806 mg = 864 mg sodium chloride equivalent
Since 100 mL of an isotonic solution would contain 0.9 g or 900 mg of sodium
chloride, the solution is slightly hypotonic. According to the calculations
of E-values for the ingredients, an additional 900 mg – 864 mg = 36 mg of
sodium chloride should be added.
(e)
Formula conversion factor mL
mL
= =
20
100
0 2 .
Tobramycin sulfate: 300 mg × 0.2 = 60 mg
Diclofenac sodium: 100 mg × 0.2 = 20 mg
Sodium chloride: 806 mg × 0.2 = 161.2 mg
Sterile water for injection: qs 20 mL
(f) 60 2
80
mg 1 5
mL
mg
× = . mL of injectable solution
300
634
1
mg tobramycin sulfate mcg tobramycin
mg tobramycin sulfac
×
ee
mg
mcg
mg tobramycin
mg tobramycin sulfate m
×
= ×
1
1000
190 2
300
739
.
ccg tobramycin
mg tobramycin sulfate
mg
mcg
mg tobram
1
1
1000
221 7
×
= . ycin
Practice Problems
1. 1.73% w/v
2. (a) 1.9
(b) -3.53°C
3. -0.52°C
4. (a) 1.8
(b) 0.21
(c) -3.35°C
5. -0.036°C
6. 210 mg sodium chloride
7. 226.35 mg sodium chloride
8. 500.77 mg boric acid
9. 0.113 mL buffer solution
10. 4.5 g sodium chloride
11. 42.6 mg sodium chloride
12. 1.35 g sodium chloride, hypertonic
13. 108.6 mg sodium chloride
14. 469.23 mg boric acid
15. 210.58 mg boric acid
11 • i oton c and b uffer s olut on 213
References
1. Ingham A, Poon CY. Tonicity, osmoticity, osmolality, and osmolarity. In: Allen LV, ed. Remington: The Science
and Practice of Pharmacy. Vol. 22. Philadelphia, PA: Pharmaceutical Press; 2013:641–646.
2. Ansel H C, Prince SJ. Pharmaceutical Calculations: T he Pharmacist’s Handbook. Baltimore, MD: Lippincott
Williams & Wilkins; 2004:111.
3. Pharmaceutical Dosage Forms. US Pharmacopeial Convention, Inc. United States Pharmacopeia 21–National
Formulary 16. Rockville, MD: US Pharmacopeial Convention, Inc.; 1985.
4. Allen LV, Ansel H C. Ansel’s Pharmaceutical Dosage Forms and Drug Delivery Systems. Vol. 10. Baltimore, MD:
Lippincott Williams & Wilkins; 2014:612.
5. T itcomb LC. Topical ocular antibiotics: part 2. Pharmaceutical Journal 2000;264:441–445.
6. G arg P, Sharma S, Rao G N . C iprofloxacin-resistant pseudomonas keratitis. Ophthalmology 1999;106:
1319–1323.
7. Matoba AY. Polymicrobial keratitis secondary to Burholderia ambifaria, enterococcus, and staphylococcus aureus
in a patient with herpetic stromal keratitis. American Journal of Ophthalmology 2003;136:748–749.
8. Chung MS, G oldstein MH , D riebe W T, et. al. M ycobacterium chelonae keratitis after laser in situ keratomileusis successfully treated with medical therapy and flap removal. American Journal of Ophthalmology
2000;129:382–384.
9. Chandra N S, Torres MF, Winthrop KL, et. al. Cluster of Mycobacterium Chelonae keratitis cases following laser
in-situ keratomileusis. American Journal of Ophthalmology 2001;132:819–830.
10. Ford JG , H uang AJW, Pflugfelder SC, et. al. N ontuberculous mycobacterial keratitis in south Florida.
Ophthalmology 1998;105:1652–1658.
11. Allen LV. Tobramycin sulfate 0.3% and diclofenac sodium 0.1% ophthalmic solution. International Journal of
Pharmaceutical Compounding 2010;14:74.
12. Buffer Solutions. US Pharmacopeial Convention, Inc. United States Pharmacopeia 37-National Formulary 32
[book online]. Rockville, MD: US Pharmacopeial Convention, Inc.; 2014.
13. Cosopt (dorzolamide hydrochloride-timolol maleate ophthalmic solution) [product label information]. U.S.
Food and Drug Administration. Department of H ealth and H uman Services. [U.S. Food and Drug Administration
Website.] Available at: http://www.accessdata.fda.gov/drugsatfda_docs/label/2010/020869s036lbl.pdf.
Accessed January 9, 2015.
16. 0.69 g sodium chloride
17. 7.67 mL sodium chloride solution
18. 4.56 mL boric acid solution
19. 1.53 g dextrose monohydrate
20. 186.21 mg sodium chloride (freezing point method) or 189 mg
sodium chloride (sodium chloride
equivalent method)
21. 153.7 mg sodium chloride
22. (c) 103.5 mg sodium chloride
23. 4.751 g sodium chloride
24. 44.44 g anhydrous dextrose
25. qs 32 mL purified water
68 mL buffered solution
26. 13.25 mL sodium chloride solution
27. (a) H ypotonic
(b) H ypertonic
(c) Isotonic
28. (a) 4.5%
(b) 2.81%
(c) 1.48%
29. 3.67 mL purified water
26.33 mL sodium chloride solution
30. (a) qs 5.67 mL water
(b) qs 8 mL water
(c) qs 6.67 mL water
(d) qs 11 mL water
(e) qs 5.33 mL water
31. (a) 0.14
(b) 0.26
(c) 0.23
(d) 0.22
(e) 0.051
32. 111.3 g dorzolamide hydrochloride, 34.15 g timolol maleate,
375 mg benzalkonium chloride,
127.89 g mannitol
33. 4.56
34. 5.5
35. 2.82:1
36. 0.03 unit
37. 8.2 g
38. 0.18 unit
39. 7.28
40. 0.33 unit
214
As noted in Chapter 11, the molecules o chemical compounds in solution may remain
intact, or they may dissociate into particles known as ions, which carry an electric charge.
Substances that are not dissociated in solution are called nonelectrolytes and those with
varying degrees o dissociation are called electrolytes. Urea and dextrose are examples o
nonelectrolytes in body water; sodium chloride in body luids is an example o an electrolyte.
Electrolyte ions in the blood plasma include the cations N a+, K+, Ca2+, and Mg2+ and
the anions Cl–, H CO 3-, H PO 42-, SO 42-, organic acids, and protein. Electrolytes in body
luids play an important role in maintaining the acid–base balance. T hey also play a part in
controlling body water volumes and help regulate metabolism.
Applicable Dosage Forms
Electrolyte preparations are used in the treatment o disturbances o the electrolyte and f uid
balance in the body. T hey are provided by the pharmacy as oral solutions, syrups, tablets,
capsules, and, when necessary, intravenous in usions.
Milliequivalents
A chemical unit, the milliequivalent (mEq), is used almost exclusively in the United States
by clinicians, physicians, pharmacists, and manu acturers to express the concentration
o electrolytes in solution. T his unit o measure is related to the total number o ionic
charges in solution, and it takes note o the valence o the ions. In other words, it is a unit o
measurement o the amount o chemical activity o an electrolyte.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

D rm n h mol ular w gh of an l	roly from a om or formula w gh a w ll
a h	al n	and h num r of on produ d upon d o a on.
c al ula	pro l m n ol ng m ll qu al n and apply h	pr n pl	o produ
u d for l	roly r pla m n .
c al ula pro l m n ol ng m ll mol	and m romol	and und r and h r u	n
pharma y pra	.

 

c al ula pro l m n ol ng m ll o mol and o molar y and apply h olu on pr mar ly u d for n ra nou nfu on .

pr n pl

o

Electrolyte Solutions:
Milliequivalents, Millimoles,
and Milliosmoles
12
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 215
Under normal conditions, blood plasma contains 154 mEq of cations and an equal
number of anions (Table 12.1). H owever, it should be understood that normal laboratory
values of electrolytes vary, albeit within a rather narrow range, as shown in Table 12.2. T he
total concentration of cations always equals the total concentration of anions. Any number
of milliequivalents of N a+, K+, or any cation always reacts with precisely the same number
of milliequivalents of Cl–, H CO 3-, or any anion. For a given chemical compound, the milliequivalents of cation equals the milliequivalents of anion equals the milliequivalents of
the chemical compound.
In preparing a solution of K+ ions, a potassium salt is dissolved in water. In addition to
the K+ ions, the solution will also contain negatively charged ions. T hese two components
will be chemically equal, in that the milliequivalents of one are equal to the milliequivalents
of the other. Dissolving 40 mEq of potassium chloride in water results in a solution that
contains 40 mEq of K+ per liter and 40 mEq of Cl–. Interestingly, the solution will not contain the same weight of each ion.
A milliequivalent represents the amount, in milligrams, of a solute equal to 1 1000 / of
its gram equivalent weight, taking into account the valence of the ions. T he milliequivalent
expresses the chemical activity or combining power of a substance relative to the activity of
1 mg of hydrogen. T hus, based on the atomic weight and valence of the species, 1 mEq is
represented by 1 mg of hydrogen, 20 mg of calcium, 23 mg of sodium, 35.5 mg of chlorine,
39 mg of potassium, and so forth.
A key element in converting between the weight of an electrolyte (i.e., milligrams) and
its chemical activity (i.e., milliequivalents) is the valence of the substance, and the total valence
of the cation or anion in the compound must be taken into account. Sodium chloride, for
example, has a total valence of one because there is one sodium cation with a +1 charge and
T b e 12.1 •  Bl o o d Pl a SMa El Ec Tr o l yTES
in Mil l iEq u iva l En TS PEr l iTEr (mE /l )

c t	s	mE /l	a	s	mE /l
Na+ K+ Ca2+ Mg2+	142	HCO3-	24
5	Cl–	105
5	HPO42-	2
2	SO42-	1
Org. Ac.– Proteinate–	6 16
154	154

T b e 12.2 • u Su a l r Ef Er En c E r a n g E o f
Bl o o d SEr u M va l u ES f o r So ME El Ec Tr o l yTESa

c t	/a	mE /l	Si u ts (mm /l )
Sodium Potassium Calcium Magnesium Chloride Carbon dioxide Phosphorus	135–145 3.5–5.5 4.6–5.5 1.5–2.5 96–106 24–30 2.5–4.5	135–145 3.5–5.5 2.3–2.75 0.75–1.25 96–106 24–30 0.8–1.5

aReference ranges may vary slightly between clinical laboratories
based, in part, on the analytical methods and equipment used.
216 Pharma euti al c al ulations
one chloride anion with a -1 charge in the compound. H owever, sodium citrate has a total
valence of three because there are three sodium ions with a +1 charge (for a total of +3)
and one citrate ion with a -3 charge. Knowing the valence of various compounds is essential in the calculation of milliequivalents. Important values for some ions are presented in
Table 12.3, and a complete listing of atomic weights is provided on the back pages of this text.
Example Calculations of Milliequivalents
T he following conversion can be used to convert milligrams to milliequivalents and vice
versa:
Molecular weight
Valence
mg
mEq
=
(1) A physician prescribes 10 mEq of potassium chloride for a patient. H ow many
milligrams of KCl would provide the prescribed quantity?

Molecular weight of KCl	K	Cl . ( )	.
Valence

Convers
= + =
=
39 35 5 74 5 + –
1
iion mg
mEq
mEq
mg
mEq
=
× =
74 5
1
10
74 5
1
.
.
745 mg
T b e 12.3 •  va l u ES f o r So ME iMPo r Ta n T io n S
i f m v e ce
a t m c
f m We ght

Eq	e t
We ghta
27	9

 

Aluminum	A13+
Ammonium	NH4+
Calcium	Ca2+
Ferric	Fe3+
Ferrous	Fe2+
Lithium	Li+
Magnesium	Mg2+
Potassium	K+
Sodium	Na+
Acetate	C2H3O2-
Bicarbonate	HCO3-
Carbonate	CO32-
Chloride	Cl–
Citrate	C6H5O73-
Gluconate	C6H11O7-
Hydroxide	OH–
Lactate	C6H5O3-
Phosphate, monobasic H2PO4-
Phosphate, dibasic Sulfate	HPO42- SO42-

3 1 18 18
2 40 20
3 56 18.7
2 56 28
1 7 7
2 24 12
1 39 39
1 23 23
1 59 59
1 61 61
2 60 30
1 35.5 35.5
3 189 63
1 195 195
1 17 17
1 89 89
1 97 97
2 96 48
2 96 48

a	Atomic or formula weight
Equivalent weight =	Valence

12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 217
(2) If a patient is prescribed 300 mg of potassium chloride, what is the corresponding mEq?
See example problem 1 for molecular weight and conversion for KCl.
300
1
74 5
mg
mEq
mg
× =
.
4 03 mEq .
(3) A physician prescribes 3 mEq/kg of NaCl to be administered to a 165-lb patient. How many
milliliters of a half–normal saline solution (0.45% NaCl) should be administered?
Molecular weight of N aCl N a Cl
Valence
Conve
= + =
=
23 35 5 58 5 + –
1
( ) . ( ) .
rrsion mg
mEq

mEq kg 3

kg lb 1 2 2

lb mEq
mEq
mg
=
× × =
×
58 5
1
165 225
225
58 5
.
.
.
11
1
1000
13 16
13 16
100
0 45
0 45
mEq
g
mg
g
g
mL
g
of N aCl so
× =
× =
.
.
.
2925 mL . % llution
(4) W hat is the concentration, in milligrams per milliliter, of a solution containing 2 mEq of
potassium chloride (KCl) per milliliter?
See example problem 1 for molecular weight and conversion for KCl.
2 74 5
1
mEq
mL
mg
mEq
× =
.
149 mg mL /
(5) W hat is the concentration, in grams per milliliter, of a solution containing 4 mEq of calcium
chloride (CaCl2 · 2H 2O) per milliliter?
Molecular weig t of CaCl H O Ca Cl
H
h [ 2 2 2 40 2 35 5 2
2 18
• = + × +
×
( + ) . ( )] –
[ ( 22 147
2
147
2
O
Valence
Conversion mg
mEq
)] =
= =
N OT E: T he water of hydration molecules should be accounted for in the
molecular weight but does not interfere in determination of valence.
4 147
2
1
1000
mEq
mL
mg
mEq
g
mg
× × = 0 29 g mL . /
(6) W hat is the percent (w/v) concentration of a solution containing 100 mEq of ammonium
chloride per liter?
Molecular weight of N H Cl N H Cl
Valence
Con
4 18 35 5 53 5 4
1
= + =
=
( + ) . ( ) . –
vversion mg
mEq
mEq
L
mg
mEq
g
mg
L
mL
=
× × × ×
53 5
1
100 53 5
1
1
1000
1
1000
10
.
.
00 = 0 54 w v . / %
218 Pharma euti al c al ulations
(7) A solution contains 10 mg/100 mL of K+ ions. Express this concentration in terms of
milliequivalents per liter.
Molecular weight of K
Valence
Conversion mg
mEq
mg
m
+
= = =
39
1
39
1
10
100 L
mEq
mg
mL
L
× × =
1
39
1000
2 56 mEq L . /
(8) A solution contains 10 mg/100 mL of Ca2+ ions. Express this concentration in terms of
milliequivalents per liter.
Molecular weight of Ca
Valence
Conversion mg
mEq
mg
2 40
2
40
2
10
10
+
= = =
00
2
40
1000
mL
mEq
mg
mL
L
× × = 5 mEq L /
(9) A magnesium (Mg2+) level in blood plasma is determined to be 2.5 mEq/L. Express this
concentration in terms of milligrams per liter.
Molecular weight of Mg
Valence
Conversion mg
mEq
mEq
2 24
2
24
2
2 5
+
= = =
.
LL
mg
mEq
× =
24
2
30 mg L /
(10) An aluminum hydroxide gel suspension contains 320 mg of aluminum hydroxide in each
teaspoonful dose. How many milliequivalents of aluminum would a patient receive each day
if he is ingesting two teaspoonfuls of the suspension four times daily?
Molecular weight of Al(OH ) Al OH
Valence
C
3
27 3 3 17 78
3
= + × =
=
( + ) [ ( )] –
oonversion mg
mEq
mg Al(OH )
tsp
tsp
dose
doses
day
=
× × =
78
3
320 2 4
3 2560 mmg Al(OH ) day
mg Al(OH )
day
mEq
mg
mEq Al(OH ) da
3
3
3
2560 3
78
98 46
/
× = . / yy
=
98 46 mEq Al day . 3+/
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 219
(11) How many milliequivalents of magnesium are represented in an 8-mL dose of an injectable
solution containing 50% w/v magnesium sulfate heptahydrate?
Molecular weight of MgSO H O Mg SO
H O
4 2
2
4
2
2
7 24 96
7 18
• = + +
×
( + ) ( ) –
[ ( )] ==
= =
× ×
246
2
246
2
8
50 7
100
1
4 2
Valence
Conversion mg
mEq
mL
g MgSO H O
mL
• 0000
1
4000 7
4000 7
2
246
32 52
4 2
4 2
mg
g
mg MgSO H O
mg MgSO H O
mEq
mg
m
=
× =
•
•
. Eq MgSO H O 4 • 7 2
=
32.52 mEq Mg 2+
(12) How many milliequivalents of Na+ would be contained in a 30-mL dose of the following solution?

Sodium phosphate, dibasic, heptahydrate Sodium phosphate, monobasic, monohydrate Purif ed water ad Each salt is considered separately in solving the problem. Sodium phosphate, dibasic, heptahydrate:

18 g 48 g 100 mL

Molecular weight of N a H PO H O N a
H PO
2 4 2
2
7 2 23
96 4 7 18
• = × +
+ ×
+
–
[ ( )]
( ) [ ()] H O
Valence
Conversion mg
mEq
g N a H PO H O
2
2 4 2
268
2
268
2
18 7
100
== =
•
mmL
mL
dose
g N a H PO H O dose
g N a H PO H O
dose
× =
×
30
5 4 7
5 4 7 100
2 4 2
2 4 2
. /
.
•
• 00
1
2
268
40 3 7
40 3
2 4 2
mg
g
mEq
mg
mEq N a H PO H O dose
mEq N a dose
× =
=
+
. /
. /
•
Sodium phosphate, monobasic, monohydrate:
Molecular weight of N aH PO H O N a H PO
H O
2 4 2 2 4
2
23 97
18 13
• = + +
=
( + ) ( ) –
( ) 8
1
138
1
48
100
30
2 4 2
Valence
Conversion mg
mEq
g N aH PO H O
mL
mL
dos
= =
×
•
ee
= g N aH PO H O dose
× ×
14 4
14 4 1000
1
1
2 4 2
2 4
. /
.
•
g N aH PO H O •
dose
mg
g
2 mEq

1138 mg

104 35 4 mEq + / N a dose

2

104 35
40
mEq N aH PO H O/dose
= 2
=
=
.
. •
T otal ./ . / . / 3 104 35 mEq mEq N a dose N a dose + + + + = 144 65 mEq N a dose
220 Pharma u al c al ula ons
Millimoles and Micromoles
Molar concentrations [as millimoles per liter (mmol/L) and micromoles per liter (mmol/L or
mcmol/L)] are used in the International System (SI), which is employed in European countries and in many others throughout the world. Milliequivalents are used almost exclusively
in the United States to express concentrations of electrolyte ions in a solution; however,
millimoles and micromoles are sometimes used in expressions of clinical laboratory values.
In some electrolyte solutions, determining the valence of the ions can be quite complicated,
such as in the case of the phosphate ion, which can exist in a monovalent (H 2PO 4-), divalent
(H PO 42-), or trivalent (PO 43-) form. Millimoles are often used to express concentrations in
these types of solutions as well.
A mole is the molecular weight of a substance in grams. A millimole is one-thousandth
of a mole and is, therefore, the molecular weight of a substance in milligrams. Similarly,
a micromole is one-millionth of a mole, which is the molecular weight of a substance in
micrograms. For example, the molecular weight of sodium chloride is 58.5 g/mol but can
be converted to milligrams and millimoles as follows:

58 5 .	1000 mg	1 mol
1000 mmol	g
58 5 . / × × = mg mmol

g mol
Similarly, the molecular weight can also be converted to micrograms and micromoles.
N otice that millimolar conversions do not take into account the valence of an electrolyte as
do milliequivalent conversions. T herefore, for monovalent species, the numeric values of
the milliequivalent and millimole are identical. Similar to milliequivalents, the millimoles of
the compound are equal to the millimoles of the cation, which are equal to the millimoles
of the anion, but this does not hold true for the actual weights of the ions.

c a SE in Po in T 12.1 a A hosp al pharma s r	s a m d a on ord r all ng
for 10 me q of al um o n ra nous flu d s o	add d o a 500-mL ag of normal sal n solu on. t h adm n s r d a a ra of 0.5 me q of al um p r hour.
t h pharma s has a a la l 10-mL als of a 10% nj	on of al um hlor d
d hydra . (a) How many m ll l rs of h s nj	on should	add d o h	ag of iv

flu d o mak h d s r d produ ? ( ) if h nurs adm n s r ng h iv flu d us s
an n ra nous s ha d l rs 12 drops/mL, how many drops p r m nu should
d l r d o pro d h d s r d dos ?
aPro l m our sy of Flynn Warr n, b shop, GA.

c a SE in Po in T 12.2 A pa n s o r	0.12 me q of f rrous glu ona p r
k logram of ody w gh a h day d d d n o hr	dos s. (a) if h pa n w ghs
132 l , how many m ll l rs of a ompound d syrup on a n ng 300 mg of f rrous
glu ona p r aspoonful should	adm n s r d for a h dos ? ( ) How mu h f r
rous glu ona would	n d d o pr par 6 fl. oz. of h ompound d syrup?

12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 221
Example Calculations of Millimoles and Micromoles
T he following conversion can be used to convert milligrams to millimoles and vice versa:
molecular weight mg
mmol
=
T he following conversion can be used to convert micrograms to micromoles and
vice versa:
molecular weight mcg
mcmol
=
(1) How many millimoles of monobasic sodium phosphate monohydrate (m.w. 138) are present
in 100 g of the substance?
100
1000 1
138
g
mg
g
mmol
mg
× × = 724 64 mmol .
(2) W hat is the weight, in milligrams, of 5 mmol of potassium phosphate dibasic?
Molecular weight of K H PO K H PO
mmol
2 4 4
2 39 96 174 2
5 174
= × + =
×
[ ( )] ( ) + –
mmg
1 mmol
= 870 mg
(3) Convert the trough plasma range of 0.5 mg/mL to 2 mg/mL for tobramycin (m.w. = 467.52)
to mmol/L.1

0 5 . m	1000 m mol mL
1	1 L	. m g
1 07 . / m mol L = 4 28 m	×	×
2 1 1 467 . m m mol m g

1
467 52
g
mL
g
mL
×
552
1000
1
mL
L
× = . / mol L
Range = 1.07 to 4.28 mmol/L
(4) If lactated Ringer’s injection contains 20 mg of calcium chloride dihydrate (CaCl2 · 2H 2O)
in each 100 mL, calculate the millimoles of calcium present in 1 L of lactated Ringer’s
injection.
Molecular weight of CaCl H O Ca Cl
H
2 2
2 40 2 35 5 2
2 18
• = + × +
×
( + ) [ . ( )] –
[ ( 22

2 2 20 2 100 mg CaCl H O mL × •	1000 L	mL × =	•
2 2 1 200 2 L mg CaCl H O

147
200
O
)] =
mmg CaCl H O mmol
mg CaCl H O
mmol CaCl H O
2 2
2 2
2 1 2 2
147 2
• 1 36 2
•
× = •
=
. .
1 36 mmol Ca2+
(5) How many micromoles of calcium are present in each milliliter of lactated Ringer’s
injection?

1 36 .	1	1000
1000

mmol . /
L
L
mL
mcmol
mmol
× × = 1 36 mcmol mL
222 Pharma euti al c al ulations
(6) A patient is receiving a slow intravenous in usion containing 40 mEq o potassium chloride
in 1000 mL o f uid. I , a ter 12 hours, 720 mL o in usion had been in used, how many
millimoles o potassium chloride were administered?
Molecular weight of KCl K Cl
mL
mEq
m
= + =
×
39 35 5 74 5 + –
720
40
1000
( ) . ( ) .
LL
mEq of KCl administered

mEq 28 8 .	228 8 mmol .
mg 74 5 .	mmol
mEq 1	mg

=
× × =
28 8
1
74 5
.
.
N OT E: Since potassium chloride is monovalent, the amount in milliequivalents
and the amount in millimoles are the same.
(7) A medication order calls or 1.8 g o potassium chloride in 60 mL o solution. How many
millimoles o KCl are contained in each milliliter?
See example problem 6 or molecular weight o KCl.
1 8
60
1000 1
74 5
.
.
g . /
mL
mg
g
mmol
mg
× × = 0 403 mmol mL
(8) Calculate the concentrations in mmol/L or each o the ollowing in usion solutions:
(a) 5% NaCl, (b) 3% NaCl, (c) 0.9% NaCl (NSS), (d) 0.45% NaCl (hal -NSS), and
(e) 0.2% NaCl.
(a) Molecular weight of N aCl N a Cl
g
mL
mg
= + =
×
23 35 5 58 5 + –
5
100
1000
( ) . ( ) .
gg
mL
L
mmol
mg
× × =
1000 1
58 5 .
854 7 mmol L . /

(b)	3
100

1000 1000 1
58 5
g
mL
mg
g
mL
L
mmol
mg
× × × =
.
512 82 mmol L . /
(c) 0 9
100
1000 1000 1
58 5
.
.
g . /
mL
mg
g
mL
L
mmol
mg
× × × = 153 85 mmol L
(d) 0 45
100
1000 1000 1
58 5
.
.
g . /
mL
mg
g
mL
L
mmol
mg
× × × = 76 92 mmol L
(e) 0 2
100
1000 1000 1
58 5
.
.
g . /
mL
mg
g
mL
L
mmol
mg
× × × = 34 19 mmol L
Osmolarity
As indicated in Chapter 11, osmotic pressure is important to biologic processes that involve
the di usion o solutes or the trans er o f uids through semipermeable membranes. T he
labels o solutions that provide intravenous replenishment o f uid, nutrients, or electrolytes,
and the osmotic diuretic mannitol are required to state the osmolar concentration. T his
in ormation indicates to the practitioner whether the solution is hypoosmotic, isoosmotic,
or hyperosmotic with regard to biologic f uids and membranes.
Osmotic pressure is proportional to the total number o particles in solution. T he
unit used to measure osmotic concentration is the milliosmole (mOsmol). For dextrose, a
nonelectrolyte, 1 mmol (1 ormula weight in milligrams) represents 1 mOsmol. T his relationship is not the same with electrolytes, however, because the total number o particles
in solution depends on the degree o dissociation o the substance in question. Assuming
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 223
complete dissociation, 1 mmol of N aCl represents 2 mOsmol (N a+ + Cl–) of total particles,
1 mmol of CaCl2 represents 3 mOsmol (Ca2+ + 2Cl–) of total particles, and 1 mmol of
sodium citrate (N a3C 6H 5O 7) represents 4 mOsmol (3N a+ + C 6H 5O 7-) of total particles.
T he milliosmolar value of separate ions of an electrolyte may be obtained by dividing
the concentration, in milligrams per liter, of the ion by its atomic weight. T he milliosmolar
value of the whole electrolyte in solution is equal to the sum of the milliosmolar values of the
separate ions. According to the United States Pharmacopeia, the ideal osmolar concentration
may be calculated according to the equation2:
mOsmol L Concentration of substance g L
Molecular weight g
/ ( / ) N
( )
= × uumber of species × 1000
Furthermore, the osmolar concentration is the total of the osmotic concentration of all
solutes in a solution, so each solute must be included in the calculation of osmolarity of a
particular solution as example problem 6 demonstrates.
In practice, as the concentration of the solute increases, physicochemical interaction
among solute particles increases and actual osmolar values decrease when compared to
ideal values. Deviation from ideal conditions is usually slight in solution within the physiologic range and for more dilute solutions, but for highly concentrated solutions, the actual
osmolarities may be appreciably lower than ideal values. For example, the ideal osmolarity
of 0.9% sodium chloride injection is:
mOsmol L g L
g
/ / mOsmol L
.
= 9 × × × . /
50 5
2 1000 307 69
Because of bonding forces, however, the number of species is slightly less than 2 for
solutions of sodium chloride at this concentration, and the actual measured osmolarity of
the solution is about 286 mOsmol/L.
Some pharmaceutical manufacturers label electrolyte solutions with ideal or
stoichiometric osmolarities calculated by the equation just provided, whereas others list
experimental or actual osmolarities. T he pharmacist should be aware of this distinction.
A distinction also should be made between the terms osmolarity and osmolality. W hereas
osmolarity is the milliosmoles of solute per liter of solution, osmolality is the milliosmoles of solute
per kilogram of solvent. For dilute aqueous solutions, osmolarity and osmolality are nearly
identical. For more concentrated solutions, however, the two values may be quite dissimilar.
T he pharmacist should pay particular attention to a product’s label statement regarding
osmolarity versus osmolality.
N ormal serum osmolality is considered to be within the range of 275 to 300 mOsmol/kg.
T he contribution of various constituents to the osmolality of normal serum is shown in
Table 12.4. Osmometers are commercially available for use in the laboratory to measure
osmolality.3 Abnormal blood osmolality that deviates from the normal range can occur in
association with shock, trauma, burns, water intoxication (overload), electrolyte imbalance,
hyperglycemia, or renal failure.3
Example Calculations of Milliosmoles
T he equation adapted from the USP used in the previous example can be used to determine
osmolarity, or the following conversion can be used to convert milligrams to milliosmoles
and vice versa:
Molecular weight
N umber of species produced by dissociation
mg
mOs
=
mmol
224 Pharma euti al c al ulations
(1) A solution contains 10% of anhydrous dextrose in water for injection. How many
milliosmoles per liter are represented by this concentration?
Molecular weight of anhydrous dextrose = 180
Dextrose does not dissociate, therefore the “number of species” = 1
Conversion mg
mOsmol
g
mL
mg
g
mL
L
mOsmol
=
× × ×
180
1
10
100
1000 1000 1
180 mg
= 555 56 mOsmol L . /
Or, utilizing the equation:
10
100
1000
100
100
180
1 1000
g
mL
mL
L
g L
g L
× =
× × =
/
/
555 56 mOsmol L . /
(2) A solution contains 156 mg of K+ ions per 100 mL. How many milliosmoles are represented
in a liter of the solution?
Molecular weight of K+ = 39
N umber of species = 1

Conversion	mg mOsmol 39 1
mg mL L mOsmol × 1000 1 1 40 mOsmol
mL	L	mg 39

=
× × =
156
100
T b e 12.4 •  Th E c o n Tr iBu Tio n o f va r io u S c o n STiTu En TS o f n o r Ma l
h u Ma n SEr u M To Th E To Ta l SEr u M o SMo Tic Pr ESSu r Ea
c st t e t
Me c e t t
(mEq/l )
o sm t P ess e
(mo sm /kg w te )b

Pe e t ge	T t
o sm t P ess e
Sodium Potassium Calcium Magnesium Chloride Bicarbonate Proteinate Phosphate Sulfate Organic anions Urea Glucose	142.0 5.0 2.5 2.0 102.0 27.0 16.0 2.0 1.0 3.5 30 (mg/100 mL) 70 (mg/100 mL)	139.0 4.9 1.2 1.0 99.8 26.4 1.0 1.1 0.5 3.4 5.3 4.1	48.3 1.7 0.4 0.3 34.7 9.2 0.3 0.4 0.2 1.2 1.8 1.4
Totals	287.7 mOsmol/kg	99.9%
Observed normal mean	289.0 mOsmol/kg

aFrom Chughtai MA, Hendry EB. Serum electrolytes, urea, and osmolality in cases of chloride depletion. Clinical
Biochemistry 1967;1:91. Adapted from Fluid and Electrolytes. Chicago, IL: Abbott Laboratories, 1970.
bWater content of normal serum taken as 94 g/100 mL.
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 225
(3) Calculate the osmolarity of a 3% hypertonic sodium chloride solution. Assume complete
dissociation.
Molecular weight of N aCl N a Cl
N umber of specie
= + = 23 ( ) . ( ) . 35 5 58 5 + –
ss N a and Cl
Conversion mg
mOsmol
g
mL
mg
g
= =
× ×
2 + –
58 5
2
3
100
1000 100
( )
.
00 2
58 5
mL
L
mOsmol
mg
× =
.
1025 64 mOsmol L . /
(4) Calcium chloride dihydrate injection is a 10% solution of CaCl2 · 2H 2O. How many
milliosmoles are present in a 10-mL vial? Assume complete dissociation.
Molecular weight of CaCl H O Ca Cl
H
2 2
2 40 2 35 5 2
2 18
• = + × +
×
( + ) [ . ( )] –
[ ( 22
2
147
3 2
147
3
O
N umber of species Ca and Cl
Conversion mg
mO
)]
( )
=
= =
+ –
ssmol
g
mL
mg
g
mL
mOsmol
mg
10
100
1000
10
3
147
× × × = 20 41 mOsmol .
(5) If a pharmacist wished to prepare 100 mL of a solution containing 50 mOsmol of calcium
chloride, how many grams of calcium chloride would be needed? Assume complete dissociation.
Molecular weight of CaCl Ca Cl
N umber of s
2
= + 40 ( 2 35 5 111 2+ ) [ . ( )] × = –
ppecies Ca and Cl
Conversion mg
mOsmol
mOsmol m
= =
×
3 + 2 –
111
3
50
111
( 2 )
gg
mOsmol
g
3 mg
1
1000
× = 1 85 g .
(6) W hat is the osmolarity of a solution containing 5% dextrose and 0.45% sodium chloride
(D5½NS)? Assume complete dissociation.
Because this solution contains two ingredients, the osmolarity of each must be
calculated then added to determine the total osmolarity of the solution. Molecular
weight, number of species, and conversion determinations for dextrose and sodium
chloride are shown in example problems 1 and 3.
Dextrose:
5
100
1000 1000 1
180
277 78
g
mL
mg
g
mL
L
mOsmol
mg
× × × = . / mOsmol L
Sodium chloride:
0 45
100
1000 1000 2
58 5
153 85
.
.
g . /
mL
mg
g
mL
L
mOsmol
mg
× × × = mOsmol L
T otal mOsmol L mOsmol L = + = 277 78 153 85 . / . / 431.62 mOsmol/ L
(7) PLASMA-LYTE 56 contains 32 mg of magnesium acetate tetrahydrate, 128 mg of
potassium acetate, and 234 mg of sodium chloride in each 100 mL of solution.4 W hat is the
osmolarity of this solution? Assume complete dissociation.
226 Pharma euti al c al ulations
Magnesium acetate tetrahydrate (Mg(C 2H 3O 2)2 · 4H 2O):
Molecular weight Mg C H O
H O
N u
= + × +
× =
24 2 59 + –
4 18 214
2
2 3 2
2
( ) [ ( )]
[ ( )]
mmber of species Mg and C H O
Conversion mg
mOsmol
= =
3 + 2 –
214
3
32
2
( 2 3 2 )
mmg
mL
mL
L
mOsmol
mg
mOsmol L
100
1000 3
214
× × = 4 49 . /
Potassium acetate (KC 2H 3O 2):
Molecular weight K C H O
N umber of species K a
= + =
=
+ –
+
39 59 98
2
( ) ( ) 2 3 2
( nd C H O
Conversion mg
mOsmol
mg
mL
mL
L
mOsmo
2 3 2
98
2
128
100
1000 2
–
=
× ×
)
ll
mg
mOsmol L
98
= 26 12 . /
Sodium chloride (N aCl):
234
100
1000 2
58 5
80
mg
mL
mL
L
mOsmol
mg
× × = mOsmol L
.
/
Total = 4.49 mOsmol/L + 26.12 mOsmol/L + 80 mOsmol/L = 110.61 mOsmol/L
(8) Calculate the milliequivalents o sodium, potassium, and chloride, the millimoles o anhydrous dextrose, and the osmolarity o the ollowing parenteral f uid. Assume complete
dissociation.

Dextrose, anhydrous Sodium chloride Potassium chloride Water for injection, ad

50 g 4.5 g 1.49 g 1000 mL

Sodium chloride:
4 5

1000 mg	1 mEq
58 5 . mg	g
× × =

76 92
76 92
.
.
.
g
mEq N aCl
and mE
76.92 mEq N a+
qq Cl
g
mL
mg
g

mL mOsmol 1000 2	1000
L	mg 58 5 .
× × × =

mOsmol
–
4 5
1000
153 85
.
. /L
Potassium chloride:

1 49 . g ×	20 20 mEq KCl and mEq Cl = = 20 mEq K + –	×
1000 mg	1 mEq
74 5 . mg	g

1 49
1
.
g
0000
1000 1000 2

74 5 40 mg × = mOsmol L . /

g

L

×

×

mL
mg
mL
mOsmol

12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 227
Dextrose:
50
1000 1

180 mg	g
g ×	×	=

50
1000
1000 1000
mg
mmol
g
mL
mg
g
mL
L
× ×
277.78 mmol
×× =
1
180
277 78
mOsmol
mg
. / mOsmol L
76.92 mEq N a+, 20 mEq K+, 76.92 mEq + 20 mEq = 96.92 mEq Cl–
277.78 mmol dextrose
Osmolarity = 153.85 mOsmol/L + 40 mOsmol/L + 277.78 mOsmol/L = 471.62 mOsmol/L
Clinical Considerations of Water and Electrolyte Balance
Maintaining body water and electrolyte balance is an essential component o good health.
Water provides the environment in which cells live and is the primary medium or the ingestion o nutrients and the excretion o metabolic waste products. N ormally, the osmolality o
body f uid is maintained within narrow limits through dietary input, the regulatory endocrine processes, and balanced output via the kidneys, lungs, skin, and the gastrointestinal
system.
In clinical practice, luid and electrolyte therapy are undertaken either to provide
maintenance requirements or to replace serious losses or de icits. Body losses o water
and/or electrolytes can result rom a number o causes, including vomiting, diarrhea, prouse sweating, ever, chronic renal ailure, diuretic therapy, surgery, and others. T he type
o therapy undertaken (i.e., oral or parenteral) and the content o the luid administered
depend on a patient’s speci ic requirements.
For example, a patient taking diuretics may simply require a daily oral potassium
supplement along with adequate intake o water. An athlete may require rehydration with
or without added electrolytes. H ospitalized patients commonly receive parenteral maintenance therapy o luids and electrolytes to support ordinary metabolic unction. In severe
cases o de icit, a patient may require the prompt and substantial intravenous replacement
o luids and electrolytes to restore acute volume losses resulting rom surgery, trauma,
burns, or shock.
T he composition o body luids generally is described with regard to body compartments: intr acellular (within cells), intr avascular (blood plasma), or interstitial (between
cells in the tissue). Intravascular and interstitial luids commonly are grouped together and
termed extr acellular luid. T he usual re erence ranges o electrolytes in blood plasma are
shown in Table 12.2. Although all electrolytes and nonelectrolytes in body luids contribute
to osmotic activity, sodium and chloride exert the principal e ect in extracellular luid, and
potassium and phosphate predominate in intracellular luid.
Since cell membranes generally are reely permeable to water, the osmolality o the
extracellular luid (about 290 mOsmol/kg water) is about equal to that o the intracellular
luid. T here ore, the plasma osmolality is a convenient and accurate guide to intracellular
osmolality and may be approximated by the ormula5:
Plasma osmolality mOsmol kg plasma N a ( / ) [ ] [ ] BUN Glucose
.
[ ]
= + + 2
2 8 18
where sodium (N a) concentration is in mEq/L, and blood urea nitrogen (BUN ) and
glucose concentrations are in mg/100 mL (mg/dL).
228 Pharma u al c al ula ons
Example Calculation of Plasma Osmolality
Estimate the plasma osmolality from the following data: sodium, 135 mEq/L; blood urea nitrogen,
14 mg/dL; and glucose, 90 mg/dL.
Plasma osmolality mEq L = + + = 2 135 14 mg dL mg dL m
2 8
90
18
[ / ] [ / ] 280
.
[ / ]
Osmol kg/

c a SE in Po in T 12.3 a A hosp al pharma s	lls a m d a on ord r all ng or an
n ra nous lu d o d x ros 5% n a 0.9% sod um hlor d nj	on and 40 me q o
po ass um hlor d n a o al olum o 1000 mL. t h n ra nous n us on s adm n
s r d hrough an iv s	ha d l rs 15 drops p r m ll l r. t h n us on has	n
runn ng a a ra o 12 drops p r m nu	or 15 hours.
Dur ng h 15-hour p r od: (a) How many me q o Kc l ha ( ) How many grams o Kc l ha ( ) How many m ll mol s o Kc l ha
n adm n s r d? n adm n s r d?
n adm n s r d?

(d) Wha s h o al osmolar y o h n ra nous f u d?
aPro l m our sy o Flynn Warr n, b shop, GA.
c a l c u l aTio n S c a PSu l E
Milliequivalents, Millimoles, and Milliosmoles
To calculate milliequivalents (mEq), use the following conversion:
Molecular weight
Valence
mg
mEq
=
where “valence” is the total valence of the cation or anion in the compound.
To calculate millimoles (mmol), use the following conversion:
Molecular weight mg
mmol
=
To calculate milliosmoles (mOsmol), use the following conversion:
Molecular weight
Number of species produced by dissociation
mg
mOs
=
mol
where “number of species produced by dissociation” is one for substances that do
not dissociate, two for substances that dissociate into two ions, three for substances that
dissociate into three ions, and so on.
Osmolarity (mOsmol/L) is the total number of milliosmoles of solute(s) per liter of
solution.
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 229
Pr a c Tic E Pr o Bl EMS
Calculations Based on Millimoles, Micromoles, and Milliequivalents
1. Convert blood plasma range of 11 to 25 mcmol/L of copper (m.w. = 63.55) to mcg/mL.
2. A preparation contains, in each milliliter, 236 mg of dibasic potassium phosphate
(m.w. = 174.18) and 224 mg of monobasic potassium phosphate (m.w. = 136.09).
Calculate the total concentration of phosphate, in mmol/mL, and potassium, in
mEq/mL, in the preparation.6
3. A 10-mL ampul contains 2.98 g of potassium chloride. W hat is the concentration
of the solution in milliequivalents per milliliter?
4. A 154-lb patient is to receive 36 mg/kg of ammonium chloride. H ow many
milliliters of an ammonium chloride (N H 4Cl—m.w. 53.5) injection containing
5 mEq/mL should be added to the patient’s intravenous infusion?
5. A sterile solution of potassium chloride contains 2 mEq/mL. If a 20-mL ampul of
the solution is diluted to 1 liter, what is the percentage strength of the resulting
solution?
6. A certain electrolyte solution contains, as one of the ingredients, the equivalent
of 4.6 mEq of calcium per liter. H ow many grams of calcium chloride dihydrate
(CaCl2 · 2H 2O—m.w. 147) should be used in preparing 20 liters of the solution?
7. Ammonium chloride injection contains 267.5 mg of N H 4Cl (m.w. 53.5) per
milliliter. H ow many mEq of ammonium chloride are present in a 20-mL vial?
8. A solution contains, in each 5 mL, 0.5 g of potassium acetate (C 2H 3KO 2—m.w.
98), 0.5 g of potassium bicarbonate (KH CO 3—m.w. 100), and 0.5 g of potassium
citrate monohydrate (C 6H 5K3O 7 · H 2O—m.w. 324). H ow many milliequivalents
of potassium (K+) are represented in each 5 mL of the solution?
9. H ow many grams of sodium chloride should be used in preparing 20 liters of a
solution containing 154 mEq/L?
10. Sterile solutions of potassium chloride containing 5 mEq/mL are available in
20-mL containers. Calculate the amount, in grams, of potassium chloride in the
container.
11. H ow many milliliters of a solution containing 2 mEq of potassium chloride per
milliliter should be used to obtain 2.98 g of potassium chloride?
12. A patient is given 125 mg of phenytoin sodium (C 15H 11N 2N aO 2—m.w. 274) three
times a day. H ow many milliequivalents of sodium are represented in the daily
dose?
13. If a 40-mL vial of sodium chloride is added to a 1-L container of water for injection, calculate the concentration of sodium chloride, in mEq/mL in the original
vial, if the resultant dilution is 0.56% in strength.
14. H ow many grams of sodium bicarbonate (N aH CO 3—m.w. 84) should be used in
preparing a liter of a solution to contain 44.6 mEq per 50 mL?
15. A liter of an electrolyte solution contains the following: 131 mEq N a+, 111 mEq
Cl–, 5 mEq K+ , 29 mEq C 3H 5O 3- (lactate), and 4 mEq Ca2+. Convert each of these
values to mmol/L.
16. Sterile sodium lactate solution is available commercially as a 1/ 6-molar solution
of sodium lactate in water for injection. H ow many milliequivalents of sodium
lactate (C 3H 5N aO 3—m.w. 112) would be provided by a liter of the solution?
17. A certain electrolyte solution contains 0.9% of sodium chloride in 10% dextrose solution. Express the concentration of sodium chloride (N aCl) in terms of
milliequivalents per liter.
230 Pharma euti al c al ulations
19. H ow many milliequivalents of potassium are in 5 million units of penicillin
V potassium (C 16H 17KN 2O 6S—m.w. 388)? One milligram of penicillin V potassium represents 1380 penicillin V units.
20. T he normal potassium level in the blood plasma is 17 mg% (17 mg/100 mL).
Express this concentration in terms of milliequivalents per liter.
21. H ow many grams of potassium citrate (C 6H 5K3O 7 · H 2O—m.w. 324) should be
used in preparing 500 mL of a potassium ion elixir so as to supply 15 mEq of K
in each 5-mL dose?
22. A potassium supplement tablet contains 2.5 g of potassium bicarbonate (KH CO 3—
m.w. 100). H ow many milliequivalents of potassium (K+) are supplied by the
tablet?
23. Ringer’s injection contains 0.86% of sodium chloride, 0.03% of potassium chloride, and 0.033% of calcium chloride dihydrate. Calculate the sodium, potassium,
calcium, and chloride content in mEq/L.
24. Calculate the mEq of N a+ in each gram of ampicillin sodium (C 16H 18N 3N aO 4S—
m.w. 371).
25. A 20-mL vial of concentrated ammonium chloride solution containing 5 mEq/mL
is diluted to 1 liter with sterile distilled water. Calculate (a) the total milliequivalent value of the ammonium ion in the dilution and (b) the percentage strength
of the dilution.
26. If a liter of an intravenous fluid contains 5% dextrose and 34 mEq sodium
(as N aCl), calculate the percent strength of sodium chloride in the solution.
27. H ow many milliequivalents of potassium would be supplied daily by the usual
dose (0.3 mL three times a day) of saturated potassium iodide solution? Saturated
potassium iodide solution contains 100 g of potassium iodide per 100 mL.
28. An intravenous solution calls for the addition of 25 mEq of sodium bicarbonate.
H ow many milliliters of 8.4% w/v sodium bicarbonate injection should be added
to the formula?
29. Calcium gluconate (C 12H 22CaO 14—m.w. 430) injection 10% is available in a
10-mL ampul. H ow many milliequivalents of Ca2+ does the ampul contain?
30. A flavored potassium chloride packet contains 1.5 g of potassium chloride. H ow
many milliequivalents of potassium chloride are represented in each packet?
31. H ow many milliequivalents of Li+ are provided by a daily dose of four 300-mg
tablets of lithium carbonate (LIT HOBID) (Li2CO 3—m.w. 74)?
32. Magnesium chloride is available as magnesium chloride hexahydrate in an
injectable solution that supplies 1.97 mEq of magnesium per milliliter. W hat is
the percent strength of magnesium chloride hexahydrate in this solution?
33. A patient is to receive 10 mEq of potassium gluconate (C 6H 11KO 7—m.w. 234) four
times a day for 3 days. If the dose is to be one teaspoonful in a cherry syrup vehicle,
(a) how many grams of potassium gluconate should be used and (b) what volume,
in milliliters, should be dispensed to provide the prescribed dosage regimen?
34. A physician wishes to administer 1,200,000 units of penicillin G potassium every
4 hours. If 1 unit of penicillin G potassium (C 16H 17KN 2O 4S—m.w. 372) equals 0.6
mcg, how many milliequivalents of K+ will the patient receive in a 24-hour period?
18. Potassium chloride 10%
Cherry syrup q.s. ad 480 mL
Sig. tablespoonful b.i.d.
H ow many milliequivalents of potassium chloride are represented in each
prescribed dose?
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 231
35. Five milliliters of lithium citrate syrup contain the equivalent of 8 mEq of Li+.
Calculate the equivalent, in milligrams, of lithium carbonate (Li2CO 3—m.w. 74)
in each 5-mL dose of the syrup.
36. H ow many milligrams of magnesium sulfate (MgSO 4—m.w. 120) should be
added to an intravenous solution to provide 5 mEq of Mg2+ per liter?
37. K-TAB, a slow-release potassium chloride tablet, contains 750 mg of potassium
chloride in a wax/polymer matrix. H ow many milliequivalents of potassium
chloride are supplied by a dosage of one tablet three times a day?
38. An electrolyte solution contains 222 mg of sodium acetate (C 2H 3N aO 2—m.w. 82)
and 15 mg of magnesium chloride (MgCl2—m.w. 95) in each 100 mL. Express
these concentrations in milliequivalents of N a+ and Mg2+ per liter.
39. MARBLEN LIQ UID contains 520 mg of calcium carbonate and 400 mg of magnesium carbonate in each teaspoonful dose. If a patient takes two teaspoonfuls
after every meal, how many milliequivalents of calcium and magnesium is she
receiving per day assuming that she eats three meals per day?
40. A patient has a sodium deficit of 168 mEq. H ow many milliliters of isotonic
sodium chloride solution (0.9% w/v) should be administered to replace the
deficit?
41. A normal 70 kg (154 lb) adult has 80 to 100 g of sodium. It is primarily distributed
in the extracellular fluid. Body retention of 1 g additional of sodium results in
excess body water accumulation of approximately 310 mL. If a person retains
100 mEq of extra sodium, how many milliliters of additional water could be
expected to be retained?
42. A patient receives 3 liters of an electrolyte fluid containing 234 mg of sodium
chloride (N aCl—m.w. 58.5), 125 mg of potassium acetate (C 2H 3KO 2—m.w. 98),
and 21 mg of magnesium acetate (Mg(C 2H 3O 2)2—m.w. 142) per 100 mL. H ow
many milliequivalents each of N a+, K+, and Mg2+ does the patient receive?
43. Magnesium citrate laxative solution (CIT ROMA) contains 1.745 g of magnesium
citrate per fluid ounce of solution. Express the concentration of magnesium in
this solution as milliequivalents per milliliter.
44. T he usual adult dose of calcium for elevating serum calcium is 7 to 14 mEq.
H ow many milliliters of a calcium gluceptate injection, each milliliter of which
provides 18 mg of elemental calcium, would provide the recommended dosage
range?
45. T he oral pediatric maintenance solution PEDIALYT E liquid has the following
electrolyte content per liter: sodium, 45 mEq; potassium, 20 mEq; chloride,
35 mEq; and citrate, 30 mEq. Calculate the equivalent quantities of each in terms
of milligrams.
46. Calculate the milliequivalents of chloride per liter of the following parenteral
fluid:

Sodium chloride Potassium chloride Calcium chloride, anhyd.	516 mg 89.4 mg 27.8 mg
Magnesium chloride, anhyd. 14.2 mg
Sodium lactate, anhyd. Water for injection ad	560 mg 100 mL

47. T he pediatric infusion rate for potassium is 5 mEq/h. If 9 mL of a 39.2% solution
of potassium acetate (KC 2H 3O 2) is diluted to 1 L of infusion solution, calculate
the proper infusion rate in mL/h.
232 Pharma euti al c al ulations
48. GOLYT ELY, a colon lavage preparation, contains the following mixture of dry
powder in each packet to prepare one gallon of solution:

Sodium sulfate Sodium chloride Potassium chloride Sodium bicarbonate Polyethylene glycol (3350)

21.5 g 5.53 g 2.82 g 6.36 g 227.1 g

Calculate the milliequivalents each of sodium and chloride present in the
prepared solution.
49. PH OSPH A 250 N EUT RAL tablets contain 852 mg dibasic sodium phosphate
anhydrous, 155 mg monobasic potassium phosphate, and 130 mg monobasic
sodium phosphate monohydrate in each tablet. Determine the amount, in
milliequivalents, of sodium and potassium in each tablet and the amount, in
millimoles, of phosphate in each tablet.
50. T PN ELECT ROLYT ES solution contains the electrolytes shown below.
Calcium chloride 16.5 mg/mL

Magnesium chloride Potassium chloride Sodium acetate Sodium chloride

25.4 mg/mL 74.6 mg/mL 121 mg/mL 16.1 mg/mL

(a) H ow many milliequivalents of sodium are contained in 5 mL of this solution?
(b) Express the concentration of magnesium chloride as mmol/mL.
Calculations Including Milliosmoles
51. At 3:00 P.M., a pharmacist received an order to add 30 mEq/L of potassium
chloride to the already running intravenous fluid for a patient. After checking the
medication order, the pharmacist found that the patient is receiving a 5% dextrose/0.9% sodium chloride infusion at a rate of 85 mL/h and that the patient’s
liter of fluid was started at 1:30 PM.7
(a) Assuming that it took 30 minutes to provide the needed potassium chloride
to the floor nurse, how many milliequivalents of potassium chloride should
have been added to the patient’s running IV fluid to achieve the ordered
concentration?
(b) H ow many milliliters of an injection containing 2 mEq of potassium chloride/mL should have been used to supply the amount of potassium chloride
needed?
(c) W hat was the osmolarity of the infusion with the potassium chloride
added? Assume complete dissociation of the sodium chloride and potassium
chloride.
52. A solution contains 322 mg of N a+ ions per liter. H ow many milliosmoles are
represented in the solution?
53. A solution of sodium chloride contains 77 mEq/L. Calculate its osmolar strength
in terms of milliosmoles per liter. Assume complete dissociation.
54. Calculate the osmolarity, in milliosmoles per liter, of a parenteral solution
containing 2 mEq/mL of potassium acetate (KC 2H 3O 2—m.w. 98).
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 233
55. Calculate (a) the milliequivalents per milliliter, (b) the total milliequivalents, and
(c) the osmolarity of a 500-mL parenteral fluid containing 5% w/v of sodium
bicarbonate.
56. W hat is the osmolarity of an 8.4% w/v solution of sodium bicarbonate?
57. A hospital medication order calls for the administration of 100 g of mannitol to
a patient as an osmotic diuretic over a 24-hour period. Calculate (a) how many
milliliters of a 15% w/v mannitol injection should be administered per hour and
(b) how many milliosmoles of mannitol (m.w. 182) would be represented in the
prescribed dosage.
58. W hat would be the osmolarity of 500 mL of a solution containing 5% w/v
dextrose, 0.3% w/v sodium chloride, and 30 mEq of potassium acetate?
59. Magnesium citrate laxative solution (CIT ROMA) contains 1.745 g of magnesium
citrate per fluid ounce of solution. Calculate the osmolarity of this solution.
60. W hat would be the osmolarity of 1000 mL of a solution containing 10% w/v
dextrose, 0.225% w/v sodium chloride, and 15 mEq of calcium gluconate?
61. H ow many (a) millimoles, (b) milliequivalents, and (c) milliosmoles of calcium
gluconate (Ca(C 6H 11O 7)2—m.w. 430) are represented in 15 mL of a 10% w/v
calcium gluconate solution?
62. T he information for a cardioplegic solution states that each 100 mL of solution contains calcium chloride dihydrate U SP 17.6 mg, magnesium chloride
hexahydrate U SP 325.3 mg, potassium chloride USP 119.3 mg, and sodium
chloride U SP 643 mg, in water for injection USP. T he information also gives
electrolyte content per liter (not including ions for pH adjustment) as sodium
(N a+) 110 mEq, magnesium (Mg2+) 32 mEq, potassium (K+) 16 mEq, calcium
(Ca2+) 2.4 mEq, and chloride (Cl–) 160 mEq. Osmolar concentration 304
mOsmol/liter (calc.).8 Calculate the labeled concentrations to determine their
accuracy.
63. N AUZEN E contains in each tablespoonful dose 4.17 g of fructose (m.w. = 180),
921 mg of sodium citrate dihydrate, and 4.35 g of dextrose. (a) W hat would be
the osmolarity of this solution? (b) If a patient ingests the maximum daily dose
of 120 mL of N AUZEN E, how many milliequivalents of sodium would he
ingest?
64. Estimate the plasma osmolality, in milliosmoles per kilogram, from the following data: sodium, 139 mEq/L; blood urea nitrogen, 26 mg/100 mL; and glucose,
100 mg/dL.
65. A patient undergoes a CH EM-7 blood test with the following results:
Sodium 146 mEq/L

Potassium Chloride Bicarbonate BUN Creatinine Glucose

4.8 mEq/L 108 mEq/L 28 mEq/L 23 mg/dL 1.1 mg/dL 134 mg/dL

Estimate the plasma osmolality for this patient.
234 Pharma euti al c al ulations
c a l c q u iz
NOTE: In solving the following problems, refer to Table 12.3 as needed.
12.A. A veterinarian ordered a liter of Hartmann’s Irrigation (lactated Ringer’s irrigation)
with the following formula:

Sodium chloride Sodium lactate Potassium chloride Calcium chloride, dihydrate Water for injection, ad

600 mg 310 mg 30 mg 20 mg 100 mL

Calculate the mEq/L of Na+, K+, Ca2+, Cl–, and C3H5O3-.
12.B. Calculate the content of Hartmann’s Irrigation in mOsmol/L.
12.C. A multiple electrolytes injection (PLASMA-LYTE 148) contains the following electrolytes in each 100 mL:

Sodium chloride Sodium gluconate Sodium acetate trihydrate Potassium chloride Magnesium chloride

526 mg 502 mg 368 mg 37 mg 30 mg

The formula for sodium gluconate is C6H11NaO7; for sodium acetate trihydrate,
C2H3NaO2 · 3H2O; and for magnesium chloride, MgCl2 · 6H2O.
Calculate the mEq/L of Na+ in the injection.
12.D.a A patient has been receiving lithium carbonate (Li2CO3) capsules but, due to difficulty in swallowing, needs to change to a liquid form. If the patient’s dose of lithium
carbonate is 300 mg three times a day, how many millimoles of lithium is the
patient receiving per day? If lithium citrate syrup contains 300 mg of lithium citrate
(C6H5Li3O7) per 5 mL, how many milliliters of syrup per day would be equivalent to
the lithium in the capsules?
12.E.a A patient is receiving an intravenous infusion containing 40 mEq of potassium chloride in 1000 mL of dextrose 5% in half–normal saline. The infusion has been running at a rate of 80 mL/h for the past 6.5 hours. Following a lab report showing the
patient’s serum potassium level to be 3.5 mEq/L, the physician decides to increase
the potassium dose while slowing the infusion flow rate to 40 mL/h. The physician
prescribes potassium chloride injection (14.9% KCl) to be added to the IV such that
the patient will receive a total of 80 mEq of potassium over the remaining time for
completion of the infusion. How many milliliters of the potassium chloride injection
should be added by the pharmacist?
aPro lem ourtesy of Flynn Warren, b ishop, GA.
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 235
a n SWEr S To “c a SE in Po in T” a n d Pr a c Tic E Pr o Bl EMS
Case in Point 12.1
(a) Molecular weight of CaCl H O Ca Cl
H
2 2
2 40 2 35 5 2
2 18
• = + × +
×
( + ) [ . ( )] –
[ ( 22 147
2
147
2
10
147
2
1
10
O
Valence
Conversion mg
mEq
mEq
mg
mEq
g
)] =
= =
× ×
000
100
10
7 35
mg
mL
g
× = . mL of injection
T hus, 7.35 mL of the injection contains 10 mEq of calcium and should be
added to the 500-mL bag of normal saline solution.
(b) Since 0.5 mEq of calcium is to be administered per hour and there are 10 mEq
of calcium in 507.35 mL of fluid (500 mL of N SS + 7.35 mL of calcium chloride
dihydrate injection), the volume of fluid to be administered per hour may be
calculated as:
0 5 507 35

10 mEq	h	×	=	mL h
Finally, the drops per minute may be calculated:
25 37 1 12 . 5 07 5 mL . /min /min h drops × × = drops drops ≈
60 min	h	mL

25 37
. .
mEq . /
mL
Case in Point 12.2
(a) Molecular weight of Fe (C H O ) Fe C H O 6 11 7 2 = + 56 ( 2 195 4 2+ ) [ ( )] 46 × 6 11 7 = –
2
446
2

0 12 mEq	1 kg	mg 446
2 2 lb	kg day	mEq 2
132 × llb ×	×	mg day = 1605 6 . /

Valence
Conversion mg
mEq
= =
.
/ .

mg day 1605 6 .

1 3

day
doses
tsp
mg
× ×
1
300
×× =
5 1
8 92
mL
tsp
. / mL dose
(b) 300 1
5
29 57
6
1
1000
10 65
mg
tsp
tsp
mL
mL
fl oz
fl oz g
mg
× × . × × = g ferr
. .
. . . ous gluconate
Case in Point 12.3

(a) 40 1000 mEq mL ×	12 60 15 28 8 mL drops min × × × = h mEq KCl .
drops	min	h

1
15

236 Pharma euti al c al ulations
(b) Molecular weight of KCl K Cl
Valence
Convers
= + =
=
39 35 5 74 5 + –
1
( ) . ( ) .
iion mg
mEq
mEq
mg
mEq
g
mg
g KCl
=
× × =
74 5
1
28 8
74 5
1
1
1000
2 15
.
.
.
.

(c) 28 8 74 5 . . mEq ×	28 8 . = mmol	×
1 mEq	mg
mg	mmol

1
74 5
.
(d) Dextrose:
Molecular weight = 180
Dextrose does not dissociate, therefore the
“number of species” = 1
Conversion mg
mOsmol
g
mL
mg

g	L
×	×	×

mL
mOsmol
m
=
180
1
5
100
1000 1000 1
180 g
= 277 78 . / mOsmol L
Sodium chloride:
Molecular weight of N aCl N a Cl
N umber of specie
= + = 23 ( ) . ( ) . 35 5 58 5 + –
ss N a and Cl
Conversion mg
mOsmol
g
mL

mg 1000 1 000 2 mL mOsmol	0 9 .
g	100	58 5 mg	L
×	×	307 69

= =
2 + –
58 5
2
( )
.
× = mOsmol L
.
. /
Potassium chloride:

Molecular weight of KCl N umber of species = =

K + +

39 ( ) . ( ) . 35 5 74 5 + –
22
74 5
2
40
1000
1000 74
( )
.
K and Cl
Conversion mg
mOsmol
mEq
mL
mL
L
–
=
× ×
..
.
5 /
1
2
74 5
80
mg
mEq
mOsmol
mg
× = mOsmol L
Total osmolarity:
277.78 mOsmol/L (Dextrose) + 307.69 mOsmol/L (N aCl) + 80 mOsmol/L
(KCl) = 665.47 mOsmol/L
N OT E: T he osmolarity of serum is about 300 mOsmol/L, so this solution is
hyperosmotic.
12 • e l ctrolyt s olution : Milli quival nt , Millimol , and Millio mol 237
Practice Problems
1. 0.699 to 1.59 mcg/mL copper
2. 3.001 mmol/mL phosphate
4.36 mEq/mL potassium
3. 4 mEq/mL potassium chloride
4. 9.42 mL ammonium chloride
injection
5. 0.298% potassium chloride
6. 6.762 g calcium chloride
7. 100 mEq ammonium chloride
8. 14.73 mEq potassium
9. 180.18 g sodium chloride
10. 7.45 g potassium chloride
11. 20 mL potassium chloride
solution
12. 1.37 mEq sodium
13. 2.49 mEq/mL sodium chloride
14. 74.93 g sodium bicarbonate
15. 131 mmol/L N a+
111 mmol/L Cl–
29 mmol/L C 3H 5O 3-
5 mmol/L K+
2 mmol/L Ca2+
16. 166.67 mEq sodium lactate
17. 153.85 mEq/L sodium chloride
18. 20.13 mEq potassium chloride
19. 9.34 mEq potassium
20. 4.36 mEq/L potassium
21. 162 g potassium citrate
22. 25 mEq potassium
23. 147.01 mEq sodium
4.03 mEq potassium
4.49 mEq calcium
155.53 mEq chloride
24. 2.7 mEq sodium
25. (a) 100 mEq ammonium
(b) 0.54% ammonium chloride
26. 0.2% sodium chloride
27. 5.42 mEq potassium
28. 25 mL sodium bicarbonate
injection
29. 4.65 mEq calcium
30. 20.13 mEq potassium chloride
31. 32.43 mEq lithium
32. 19.996% w/v magnesium chloride hexahydrate
33. (a) 28.08 g potassium gluconate
(b) 60 mL syrup
34. 11.61 mEq potassium
35. 296 mg lithium carbonate per 5 mL
36. 300 mg/L magnesium sulfate
37. 30.2 mEq potassium chloride per day
38. 27.07 mEq/L sodium
3.16 mEq/L magnesium
39. 62.4 mEq Ca2+/day
57.14 mEq Mg2+/day
40. 1092 mL isotonic sodium chloride
solution
41. 713 mL water
42. 120 mEq sodium
38.27 mEq potassium
8.87 mEq magnesium
43. 0.79 mEq/mL magnesium
44. 7.78 to 15.56 mL calcium gluceptate
injection
45. 1035 mg/L sodium
1242.5 mg/L chloride
780 mg/L potassium
1890 mg/L citrate
46. 108.2 mEq/L chloride
47. 138.89 mL/h potassium acetate
infusion
48. 473.06 mEq sodium
132.38 mEq chloride
49. 12.94 mEq/tab sodium
1.14 mEq/tab potassium
8.08 mmol/tab phosphate
50. (a) 8.75 mEq sodium
(b) 0.27 mmol/mL magnesium
chloride
51. (a) 24.9 mEq potassium chloride
(b) 12.45 mL potassium chloride
injection
(c) 645.47 mOsmol/L
52. 14 mOsmol/L
53. 154 mOsmol/L
54. 4000 mOsmol/L
55. (a) 0.595 mEq/mL sodium
bicarbonate
(b) 297.62 mEq sodium bicarbonate
(c) 1190.48 mOsmol/L
56. 2000 mOsmol/L
57. (a) 27.78 mL/h mannitol injection
(b) 549.45 mOsmol mannitol
58. 500.34 mOsmol/L
59. 655.69 mOsmol/L
60. 654.98 mOsmol/L
238 Pharma euti al c al ulations
References
1. Prince SJ. Calculations. International Journal of Pharmaceutical Compounding 2001;5:485.
2. O smolality and O smolarity. U S Pharmacopeial Convention, Inc. United States Pharmacopeia 37 N ational
Formulary 32 [book online]. Rockville, MD: US Pharmacopeial Convention, Inc.; 2014.
3. VAPRO Vapor Pressure Osmometer [product literature]. Logan, UT: Wescor, Inc.; 1997.
4. Plasma-Lyte 56 in Plastic Container [product label information]. U.S. Food and Drug Administration. Department
of H ealth and H uman Services. [U.S. Food and Drug Administration Website.] Available at: http://www.accessdata.fda.gov/scripts/cder/drugsatfda/index.cfm?fuseaction=Search.Label_ApprovalH istory#labelinfo. Accessed
January 30, 2015.
5. Lewis JL. Water and sodium balance. In: Porter RS, ed. The Merck Manual Professional Edition [book online].
W hitehouse Station, N J: Merck & Co., Inc.; 2014.
6. Prince SJ. Calculations. International Journal of Pharmaceutical Compounding 1998;2:378.
7. Prince SJ. Calculations. International Journal of Pharmaceutical Compounding 1999;3:311.
8. Cardioplegic solution. Available at: http://www.drugs.com/pro/cardioplegic.html. Accessed February 6, 2015.
61. (a) 3.49 mmol calcium gluconate
(b) 6.98 mEq calcium gluconate
(c) 10.47 mOsmol calcium
gluconate
62. Yes, all labeled concentrations are
correct
63. (a) 3990.93 mOsmol/L
(b) 75.18 mEq sodium
64. 292.84 mOsmol/kg
65. 307.66 mOsmol/kg
239
Injections
Injections are sterile pharmaceutical solutions or suspensions o a drug substance in an aqueous or nonaqueous vehicle. T hey are administered by needle into almost any part o the
body, including the joints (intra-articular), joint f uid (intrasynovial), spinal column (intraspinal), spinal f uid (intrathecal), arteries (intra-arterial), and in an emergency, even the heart
(intracardiac). H owever, most injections are administered into a vein (intravenous, I.V., IV),
muscle (intramuscular, I.M., IM), skin (intradermal, I.D., ID, intracutaneous), or under the skin
(subcutaneous, sub-Q, SQ, hypodermic).
Depending upon their use, injections are packaged in small volumes in ampulsa or in
pre illed disposable syringes or single-dose use, in vials and pen injectors or single- or
multiple-dose use, or in large-volume plastic bags or glass containers or administration by
slow intravenous infusion.
Some injections are available as prepared solutions or suspensions with their drug content labeled as, or example, “10 mg/mL.” Others contain dry powder or reconstitution
to form a solution or suspension by adding a speci ied volume o diluent prior to use and are
labeled as, or example, “10 mg/vial.” In the latter case, the calculations required to determine the correct volume o diluent needed to prepare an injection o a certain concentration
are provided in Chapter 17.
Small-volume injections may be administered as such or they may be used as additives to large-volume parenteral luids or intravenous in usion. T he term parenteral is
de ined as any medication route other than the alimentary canal and thus includes all routes
o injection.
aAn ampul (also ampule or ampoule) is a small hermetically sealed glass container.
Ob j e c t ive s
Upon successful completion of this chapter, the student will be able to:

P rform al ula on for andard adul and p d a r	n ra nou nfu on .
P rform al ula on for r P rform al ula on for add	al ar n ra nou nfu on . o n ra nou nfu on .

P rform ra -of-flow al ula on for n ra nou nfu on u l z ng m d a on ord r ,
andard a l , and nomogram .
13
Intravenous Infusions, Parenteral
Admixtures, Rate-of-Flow
Calculations
240 Pharma euti al c al ulations
Intravenous Infusions
Intravenous (IV) infusions are sterile, aqueous preparations administered intravenously
in relatively large volumes. T hey are used to extend blood volume and/or provide electrolytes, nutrients, or medications. Most intravenous in usions are administered to critical
care, inf rm, dehydrated, or malnourished patients or to patients prior to, during, and/or
ollowing surgery. Intravenous in usions are widely employed in emergency care units, in
hospitals and other patient care institutions, and in home care. Pharmacists participate in
the preparation and administration o institutional as well as home intravenous in usion
therapy. T he United States Pharmacopeia has established requirements or the compounding
o sterile preparations.1
Most intravenous in usions are solutions; however, some are very ine dispersions o
nutrients or therapeutic agents or blood and blood products. Although some intravenous
solutions are isotonic or nearly isotonic with blood, isotonicity is not absolutely necessary
because the volumes o luid usually administered are rapidly diluted by the circulating
blood.2
Commercially prepared in usions are available in glass or plastic bottles or collapsible
plastic “bags” in volumes o 50 mL (a minibag), 100 mL, 250 mL, 500 mL, and 1000 mL.
T he smaller volumes ind particular application in treating pediatric patients and adults
who require relatively small volumes o in usate. W hen a smaller IV bag is attached to the
tubing o a larger IV being administered, it is re erred to as an IV piggyback (IVPB). T he
abbreviation LVP is commonly used to indicate a large-volume parenteral, and SVP indicates
a small-volume parenteral.
Some common solutions or intravenous in usion are listed in Table 13.1. Additional
components or additives requently are added to these basic solutions.
An administration set is attached to an intravenous bottle or bag to deliver the luid into
a patient’s vein. T he sets may be standard (macrodrip) or pediatric (microdrip). Depending
on the particular set used, the drip rate can vary rom 10 to 15 drops/mL or standard sets
to 60 drops/mL or microdrip sets. It should be noted that in some literature, particularly
that o nursing, the abbreviations gtt or drop and mcgtt or microdrop are used.
T he passage o an in usion solution into a patient’s vein o entry may be assisted by
gravity (the solution is hung on a stand well above the portal o entry) or by electronic
Tab 13.1 •  So me Co mmo n In TRAve n o u S In Fu SIo n So l u TIo n S

S	ti a	Abbr iati
0.9% sodium chloride 0.45% sodium chloride 5% dextrose in water 10% dextrose in water 5% dextrose in 0.9% sodium chloride 5% dextrose in 0.45% sodium chloride	NS (normal saline) ½NS D5W or D5W D10W or D10W D5NS or D5NS D5½NS or D51/2NS

Ringer’s injection (0.86% sodium chloride, 0.03%
potassium chloride, 0.033% calcium chloride)
RI

Lactated Ringer’s injection 5% dextrose in lactated Ringer’s

LR or LRI D5LR or D5LR

aAll solutions are prepared in sterile water for injection (SWI), USP. In addition to the solutions
listed, other concentrations of dextrose and sodium chloride are commercially available. These
solutions may be administered as such or used as vehicles for therapeutic agents, nutrients,
or other additives.
13 • intravenous infus ons, Parenteral Adm xtures, Rate-of-Flow c al ulat ons 241
1 2 3 4 5 6 7 8 9
Medication
port
Back
check valve
Solution
port and cover
Airway valve
Piercing device
Drip chamber
Injection or y site
Injection or y site
Threaded lock
Cap
Slide clamp
Roller clamp
FIGu Re 13.1 •  A depiction of an intravenous fluid with
an administration set.
242 Pharma euti al c al ulations
volumetric in usion pumps. Some in usion pumps can be calibrated to deliver microin usion
volumes, such as 0.1 mL/h, to as much as 2000 mL/h, depending on the drug being administered and the requirements o the patient. Electronic controllers can be used to maintain
the desired low rate. T he use o latest technology “smart” pumps can reduce intravenous
administration errors by virtue o so tware that requires ewer human programming entries
at the patient’s bedside. Errors may also be reduced through the use o bar codes to ensure
correct medication delivery and through wireless technology that allows a nurse to monitor
the rate o low and the remaining volume o an in usion when not physically present in a
patient’s room.
In the administration o in usions, special needles or catheters provide intravenous
entry or the intravenous luid. Large-, intermediate-, and small-gauge (bore) needles or
catheters are used, with the portal o entry selected based on the patient’s age (i.e., adult,
child, in ant, or neonate) and the clinical circumstances. T he narrower the gauge, the
slower the low rate and thus the longer period required to in use a speci ied volume.
Veins o the back o the hand, orearm, subclavian, jugular, and scalp (e.g., in premature
neonates) may be used. Figure 13.1 depicts an intravenous luid and attached administration set (see also Fig. 14.1). Figure 13.2 shows a typical intravenous setup with a piggyback
attachment.
Intravenous in usions may be continuous or intermittent. In continuous infusions,
large volumes o luid (i.e., 250 to 1000 mL), with or without added drug, are run into a vein
uninterrupted, whereas intermittent infusions are administered during scheduled periods.2
T he rapid in usion o a medication into a vein is termed IV push and is usually conducted
in 1 to 5 minutes depending upon the medication.
Critical Care
By def nition, critical care (or intensive care) is the specialized care o patients whose
conditions are li e-threatening and who require comprehensive care and constant monitoring. In the hospital, such care is provided in an intensive care unit (ICU), a critical
care unit (CCU), or an intensive treatment (or therapy) unit (IT U ). T hese units,
sta ed by specially trained critical care physicians and nurses, utilize equipment and
medications expressly intended to treat critically ill pediatric and adult patients. Clinical
pharmacy services in the critical care setting have expanded dramatically over the years
to provide pharmacokinetic services and patient monitoring or drug e f cacy and adverse
drug reactions.3 Lists o drugs used in providing critical care may be ound in the re erences cited.4–6
Common Intravenous Infusion Solutions
Aqueous solutions o dextrose, sodium chloride, and lactated Ringer’s injection are the most
commonly used intravenous uids. Table 13.1 describes the content o these solutions,
which may be administered as such or with additional drug or nutritional components.
Example Calculations of Basic Intravenous Infusions
(1) How many grams each of dextrose and sodium chloride are used to prepare a 250-mL bag
of D5½N S for intravenous infusion?
250 mL × 0.05 (5% w/v) = 12.5 g dextrose
250 mL × 0.0045 (0.45% w/v) = 1.125 g sodium chloride
13 • intravenous infus ons, Parenteral Adm xtures, Rate-of-Flow c al ulat ons 243
(2) Calculate the milliequivalents of sodium and millimoles of dextrose in the above solution.
Molecular weight of N aCl = 58.5 g
Equivalent weight of N aCl = 58.5 g
1 mEq N aCl = 58.5 mg
mEq in 1.125 g N aCl = 1125 mg/58.5 mg per 1 mEq = 19.2 mEq N a+
Molecular weight of dextrose (C 6H 12O 6) = 180.16 g
1 mmol dextrose = 180.16 mg
mmol in 12.5 g dextrose = 12,500 mg/180.16 mg per 1 mmol
= 69.38 or 69.4 mmol dextrose
(3) A pharmacist prepared a liter of a 15% dextrose solution in sterile water for injection using a dextrose injection, 700 mg/mL. How many milliliters of the injection were
required?
Dextrose needed: 1000 mL × 15% – 150 g
700 mg/mL = 0.7 g/mL
150
1
0 7
g 214 28
mL
g
× = or
.
. . 214 mL 3
Small-volume
piggyba ck
antibiotic
Large-volume IV
solution, usually 1000 mL
(D5W or NS)
The small-volume product is
plugged into a Y-site inje ction
IV tubing to patient
FIGu Re 13.2 •  A typical intravenous infusion setup with a piggybacked antibiotic. (Courtesy of Lacher B.
Pharmaceutical Calculations for the Pharmacy Technician. Baltimore, MD: Lippincott Williams & Wilkins, 2008.)
244 Pharma euti al c al ulations
Example Calculations of Infusion Administration Sets
(1) Calculate the total drops in the delivery o 250 mL o an in usion when using the ollowing
administration sets: (a) 15 drops/mL, (b) 20 drops/mL, and (c) 60 mcgtts/mL.
(a) 15 drops/mL × 250 mL = 3750 drops
(b) 20 drops/mL × 250 mL = 5000 drops
(c) 60 microdrops/mL × 250 mL = 15,000 microdrops
(2) For each o the above, calculate the number o drops delivered each minute i the in usion
is to last 2 hours.
2 hours = 120 minutes
250 mL/120 min = 2.08 mL/min
(a) 15 drops/mL × 2.08 mL (per minute) = 31.2 or 31 drops/minute
(b) 20 drops/mL × 2.08 mL = 41.6 or 42 drops/minute
(c) 60 microdrops/mL × 2.08 mL = 124.8 or 125 microdrops/minute
Or
mL
h
h mcgtt
mL
mcgtt
,
min
,
min
250
2
1
60
60
1
15 000
120
× × = = 125 crodr mi ops minute /
Alternatively, the answers may be derived by dividing the total drops delivered
by each administration set by the delivery time of 120 minutes:
(a) 3750 drops/120 minute = 31.2 or 31 drops/minute
(b) 5000 drops/120 minute = 41.6 or 42 drops/minute
(c) 15,000 microdrops/120 minute = 125 microdrops/minute
(3) A rural patient is being transported by ambulance to a hospital 3 hours away. During
transport, the patient is to be in used with 750 mL o normal saline injection. For each
delivery set, calculate the rate o f ow in drops/minute: (a) 15 gtts/mL, (b) 20 gtts/mL, and
(c) 60 mcgtts/mL.
3 hours = 180 minutes
750 mL/180 min = 4.17 mL/min
(a) 15 drops/mL × 4.17 mL/min = 62.55 or 63 drops/minute
(b) 20 drops/mL × 4.17 mL/min = 83.4 or 83 drops/minute
(c) 60 microdrops/mL × 4.17 mL/min = 250.2 or 250 microdrops/minute
Or
mL
h

h min

mcgtt mL 60 1

mcgtt
,
,
min
750
3
1
60
45 000
180
× × = = 250 microdrops minute /
Or,
(a) 750 mL × 15 gtts/mL = 11,250 drops
11,250/180 min = 62.5 or 63 drops/minute
(b) 750 mL × 20 gtts/mL = 15,000 drops
15,000 drops/180 minute = 83.3 or 83 drops/minute
(c) 750 mL × 60 mcgtts/mL = 45,000 microdrops
45,000 mcgtts/180 min = 250 microdrops/minute
(4) Compare (a) the number o drops and (b) the length o time, in minutes, required to deliver
50-mL o intravenous solutions when using a microdrip set, at 60 drops/mL, and a standard
administration set, at 15 drops/mL, i in each case one drop is to be administered per second.
Microdrip set:
(a) 60 drops/mL × 50 mL = 3000 drops
(b) 3000 drops ÷ 60 drops/minute = 50 minutes
13 • intravenous infus ons, Parenteral Adm xtures, Rate-of-Flow c al ulat ons 245
Standard set:
(a) 15 drops/mL × 50 mL = 750 drops
(b) 750 drops ÷ 60 drops/minute = 12.5 minutes
Or, by dimensional analysis:
50
60

1 mL	drops
×	×

1
60
50
15
1
1
6
mL
drops
mL
drops
mL
× × =
min
min
50 minutes
00 drops
= 12 5 minutes .
Intravenous Push (IVP) Drug Administration
T he rapid injection of intravenous medications, as in emergency or critical care situations, is
termed IV push, IVP, IV, or sometimes a bolus dose. For the most part, drugs administered by
IV push are intended to quickly control heart rate, blood pressure, cardiac output, respiration,
or other life-threatening conditions. Intravenous push medications frequently are administered
in a short time frame (from <1 to 5 minutes), but slowly enough so as to not cause a too rapid
effect. T he safe administration of a drug by IV push depends on precise calculations of dose
and rate of administration. W hen feasible, a diluted injection rather than a highly concentrated
one (e.g., 1 mg/mL versus 5 mg/mL) may be administered as an added safety precaution.7
T he IV push may be injected directly into a vein or into a portal of an intravenous set.
If the medication is administered via an administration set, a second injection of saline may
be used to “flush” or help to push the medication into the bloodstream. A flush also may be
used to clean an infusion line before and/or after use. An example of an intravenous flush
syringe is shown in Figure 13.3.
FIGu Re 13.3 •  An intravenous flush syringe. (Courtesy of Becton Dickinson.)
246 Pharma euti al c al ulations
Example Calculations of IV Push Drug Administration
(1) A physician orders enalaprilat (VASOTEC IV) 2 mg IVP for a hypertensive patient.
A pharmacist delivers several 1-mL injections, each containing 1.25 mg of enalaprilat.
How many milliliters of the injection should be administered?
1 25
1
2
1 0 6
.
mg ; . ( .
mL
mg
x mL
= = x mL from one syringe and mL from anot 1 6 mL hher)
Or, by dimensional analysis:
2
1
1 25
mg
mL
mg
× =
.
1 6 mL .
(2) A physician orders midazolam hydrochloride (VERSED) 2 mg IV Stat. A pharmacist
delivers a vial containing midazolam hydrochloride 5 mg/mL. How many milliliters should
be administered?
5 1
mg 2
mL
mg
x mL
= = ; . x 0 4 mL
Or, by dimensional analysis:
2
1 5
mg
mL
mg
× = 0 4 mL .
(3) General guidelines in the treatment of severe diabetic ketoacidosis include an initial bolus
dose of 0.1 to 0.4 unit of insulin/kg IVP, followed by an insulin drip. Calculate the bolus
dosage range for a 200-lb patient.
200 lb ÷ 2.2 lb/kg = 90.9 kg
90.9 kg × 0.1 unit/kg = 9.09 units
90.9 kg × 0.4 unit/kg = 36.36 units
Special Considerations in Pediatric IV Infusion Deliveryb
Medication error in pediatric patients is a special concern in institutional practice.8 T here
is the ever-present need or weight-based dosing and highly individualized dose calculations that must be diligently per ormed. A reduction in errors has been achieved by the
use o web-based calculators to per orm in usion calculations, use o a limited number o
standardized drug concentrations to prepare in usions (as noted below), and the utilization
o smart-pump technology that reduces the number o human calculations required in dose
and rate-o -f ow determinations.
Depending on the institutional protocol, a medication order or an intravenous in usion or a 10-kg child may be stated as, or example, “dopamine 60 mg/100 mL, IV to run
at 5 mL/h to give 5 mcg/kg/min.” At some institutions in which standardized drug products
bAlthough all calculations pertaining to drug dosage and administration must be per ormed with 100% accuracy,
it must be emphasized that pediatric patients are most vulnerable to mediation errors with o ten dire consequences. T he report cited here underscores this point: Levine SR, et al. Guidelines or preventing medication
errors in pediatrics. Journal of Pediatric Pharmacology and Therapeutics 2001;6:426–442. Available at: http://www.
ismp.org/N ewsletters/acutecare/articles/20020601.asp. Accessed May 12, 2014.
13 • intravenous infus ons, Parenteral Adm xtures, Rate-of-Flow c al ulat ons 247
and established protocols have been developed, the same medication order may be written
simply as “dopamine 5 mcg/kg/min IV” to provide equivalently accurate drug dosing of the
patient.9 T his is because the standard solution of dopamine used in the institution, containing 60 mg of dopamine in each 100 mL and run at 5 mL/h, would deliver the same dose o
5 mcg/kg/min to the 10-kg patient. Calculate it:
60
100 5
3
mg
mL
x mg
mL
x mg or
= =
;
3000 mcg dopamine administered per hour
33000 60 50 mcg h mcg dopamine administered per minute ÷ = min/
Since the 50 mcg/min are administered to a 10-kg child, the dose, per kg per minute, is:
50
10 1
mcg

kg Or, by dimensional analysis:

kg

x mcg
= = ; x 5 mcg dopamine kg / /min
60
100
1000
1
5
1
1
60
50 10

mg	mL	h
mL	h	min
× × × =

mcg
mg
mcg dose for kg c
/min ( – hild) = 5 mcg/kg/min
All medication doses for pediatric patients, including those administered intravenously,
must be carefully determined from available literature and reference sources.
In addition to medications administered by intravenous infusion to pediatric patients,
fluid and electrolyte therapy is especially important in the clinical management of preterm
and term neonates, particularly those with extremely low birth weights who tend to have
greater loss of water through the skin, especially when they are maintained in a warm
incubator.10
Example Calculations of Pediatric Infusions
(1) Calculate the daily in usion volume o D10W to be administered to a neonate weighing
3 lb. 8 oz. on the basis o 60 mL/kg/day.
3 lb 8 oz. = 3.5 lb ÷ 2.2 lb/kg = 1.59 kg or 1.6 kg
1.6 kg × 60 mL = 96 mL
(2) Using an administration set that delivers 60 drops/mL at 20 drops/minute, calculate the
total time or the above in usion.
96
60
1
1
20

mL × × = 288 minutes, or 4 hours 48 minutes
drops	minute
mL	drops

(3) Gentamicin sul ate, 2.5 mg/kg, is prescribed or a 1.5-kg neonate. Calculate (a) the dose o
the drug and, (b) when the drug is placed in a 50-mL IV bag, the f ow rate, in mL/min, i
the in usion is to run or 30 minutes.
(a) 2.5 mg/kg × 1.5 kg = 3.75 mg gentamicin sulfate
(b) 50 mL ÷ 30 minutes = 1.67 mL/minute
(4) A neonate born at 32 weeks’ gestation weighs 2005 g and is trans erred to the hospital’s neonate intensive care unit with a diagnosis o sepsis. Among the physician’s
orders are aminophylline 5 mg/kg IV q6h, ce otaxime 50 mg/kg q12h, and vancomycin
10 mg/kg q12h.11
248 Pharma euti al c al ulations
(a) Calculate the initial dose of each drug, in milligrams.
N eonate s weight g kg
g
’ . = 2005 × 1 = kg
1000
2 005
Aminophylline initial dose mg kg kg or
Cefota
= 5 2 005 10 025 / . . × = 10 mg
xime in