Pharmaceutical
`Calculations
`
`13th Edition
`
`Howard C. Ansel, PhD
`Professor and Dean Emeritus
`College of Pharmacy
`University of Georgia
`Athens, Georgia
`
`
`IPR2018-01020 and IPR2018-01021, Exhibit 1019, Page 1
`
`

`

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`13th Edition
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`This textbook is intended to provide the underpinnings of the methods used in pharmaceutical calculations. The
`drugs, drug products, formulas, equations, uses, and doses are included in this textbook for the sole purpose of
`providing examples in the types of calculations described. The information is not intended for use in any practice
`or clinical application, nor should it be considered or construed as specific for any individual patient nor as a
`substitute for current drug package inserts. The author, editors, and publisher make no warranty, express or
`implied, with regard to the contents and use of this publication and are not responsible, as a matter of product
`liability, negligence, or otherwise, for any injury resulting from any material contained herein.
`9 8 7 6 5 4 3 2 1
`Printed in China
`First Edition, 1945
`Library of Congress Cataloging-in-Publication Data
`Ansel, Howard C., 1933-
`Pharmaceutical calculations / Howard C. Ansel.—13th ed.
`p. ; cm.
`Includes bibliographical references and index.
`ISBN 978-1-58255-837-0
`1. Pharmaceutical arithmetic. I. Title.
`[DNLM: 1. Drug Dosage Calculations. 2. Dosage Forms. 3. Drug Compounding—methods. 4.
`Prescriptions, Drug. 5. Weights and Measures. QV 748 A618p 2010]
`RS57.S86 2010
`615′.1401513—dc22
`
`2008045672
`Care has been taken to confirm the accuracy of the information presented and to describe generally
`accepted practices. However, the authors, editors, and publisher are not responsible for errors or omissions or
`for any consequences from application of the information in this book and make no warranty, expressed or
`implied, with respect to the currency, completeness, or accuracy of the contents of the publication.
`Application of this information in a particular situation remains the professional responsibility of the
`practitioner; the clinical treatments described and recommended may not be considered absolute and
`universal recommendations.
`The authors, editors, and publisher have exerted every effort to ensure that drug selection and dosage set
`forth in this text are in accordance with the current recommendations and practice at the time of publication.
`However, in view of ongoing research, changes in government regulations, and the constant flow of
`information relating to drug therapy and drug reactions, the reader is urged to check the package insert for
`each drug for any change in indications and dosage and for added warnings and precautions. This is
`particularly important when the recommended agent is a new or frequently employed drug.
`Some drugs and medical devices presented in this publication have Food and Drug Administration (FDA)
`clearance for limited use in restricted research settings. It is the responsibility of the health care provider to
`ascertain the FDA status of each drug or device planned for use in his or her clinical practice.
`LWW.COM
`
`
`IPR2018-01020 and IPR2018-01021, Exhibit 1019, Page 2
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`

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`82
`
`PHARMACEUTICAL CALCULATIONS
`
`Percent weight-in-volume (w/v) expresses the number of grams of a constituent in 100 mL
`of solution or liquid preparation and is used regardless of whether water or another liquid is
`the solvent or vehicle. Expressed as:
`% w/v.
`Percent volume-in-volume (v/v) expresses the number of milliliters of a constituent in 100
`mL of solution or liquid preparation. Expressed as:
`% v/v.
`Percent weight-in-weight (w/w) expresses the number of grams of a constituent in 100 g of
`solution or preparation. Expressed as:
`% w/w.
`
`The 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; and
`for solutions of gases in liquids, percent weight-in-volume.
`
`Special Considerations in Percentage Calculations
`In general, the nature of the ingredients in a pharmaceutical preparation determines the basis
`of the calculation. That is, a powdered substance dissolved or suspended in a liquid vehicle
`would generally be calculated on a weight-in-volume basis; and 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. Based on these considerations, 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. Table 6.1
`presents examples of the usual basis for calculations of concentration for some dosage forms.
`In most instances, use of percentage concentrations in the manufacture and labeling of phar-
`maceutical preparations is restricted to instances in which the dose of the active therapeutic
`ingredient (ATI) is not specific. For example, the ATIs in ointments, lotions, external solutions,
`and similar products may commonly be expressed in percent strength (e.g., a 1% hydrocortisone
`ointment). However, in most dosage forms, such as tablets, capsules, injections, oral solutions,
`and syrups, among others, the amounts of ATIs are expressed in definitive units of measure,
`such as milligrams per capsule, milligrams per milliliter, or other terms. On the other hand, in
`many pharmaceutical formulations, pharmaceutical components such as flavoring agents, solvents,
`excipients, preservatives, and so on, may be expressed in terms of their percentage concentration.
`Specific gravity may be a factor in a number of calculations involving percentage concentration.
`Many formulations are presented on the basis of weight, even though some of the ingredients
`are liquids. Depending on the desired method of measurement, it may be necessary to convert
`
`TABLE 6.1 EXAMPLES OF PHARMACEUTICAL
`DOSAGE FORMS IN WHICH THE ACTIVE
`INGREDIENT IS OFTEN CALCULATED AND
`EXPRESSED ON A PERCENTAGE BASIS
`
`PERCENTAGE BASIS
`Weight-in-volume
`
`Volume-in-volume
`
`Weight-in-weight
`
`EXAMPLES OF APPLICABLE DOSAGE FORMS
`Solutions (e.g., ophthalmic, nasal, otic,
`topical, large-volume parenterals),
`and lotions
`Aromatic waters, topical solutions, and
`emulsions
`Ointments, creams, and gels
`
`
`IPR2018-01020 and IPR2018-01021, Exhibit 1019, Page 3
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`

`

`CHAPTER 6 • PERCENTAGE, RATIO STRENGTH, AND OTHER EXPRESSIONS OF CONCENTRATION
`
`83
`
`weight to liquid or, in some instances, vice versa. Thus, the student should recall the equations
`from the previous chapter, namely:
`
`g ⳱ mL ⳯ sp gr
`mL ⳱ g
`sp gr
`
`Percentage Weight-in-Volume
`In a true expression of percentage (i.e., parts per 100 parts), the percentage of a liquid preparation
`(e.g., solution, suspension,
`lotion) would represent the grams of solute or constituent in
`100 g of the liquid preparation. However, in practice, the pharmacist most frequently uses a
`different definition of percentage for solutions and for other liquid preparations, one in which
`the parts of the percentage represent grams of a solute or constituent in 100 mL of solution or
`liquid preparation.
`Indeed, in weight-in-volume expressions, the ‘‘correct’’ strength of a 1% (w/v) solution or
`other liquid preparation is defined as containing 1 g of constituent in 100 mL of product. This
`variance to the definition of true percentage is based on an assumption that the solution/liquid
`preparation has a specific gravity of 1, as if it were water. It is on this assumption that each 100
`mL of solution/liquid preparation is presumed to weigh 100 g and thus is used as the basis for
`calculating percentage weight-in-volume (e.g., 1% w/v ⳱ 1% of [100 mL taken to be] 100 g
`⳱ 1 g in 100 mL).
`Taking water to represent any solvent or vehicle, we may prepare weight-in-volume percentage
`solutions or liquid preparations by the SI metric system if we use the following rule.
`Multiply the required number of milliliters by the percentage strength, expressed as a decimal,
`to obtain the number of grams of solute or constituent in the solution or liquid preparation.
`The volume, in milliliters, represents the weight in grams of the solution or liquid preparation as if it
`were pure water.
`Volume (mL, representing grams) ⳯ % (expressed as a decimal) ⴔ grams (g) of solute
`or constituent
`
`Examples of Weight-in-Volume Calculations
`
`How many grams of dextrose are required to prepare 4000 mL of a 5% solution?
`
`4000 mL represents 4000 g of solution
`5% ⳱ 0.05
`4000 g ⳯ 0.05 ⳱ 200 g, answer.
`
`Or, solving by dimensional analysis:
`
`5 g
`100 mL
`
`⳯ 4000 mL ⳱ 200 g, answer.
`
`How many grams of potassium permanganate should be used in compounding the following prescrip-
`tion?
`嗱 Potassium Permanganate
`Purified Water ad
`Sig. as directed.
`250 mL represents 250 g of solution
`0.02% ⳱ 0.0002
`250 g ⳯ 0.0002 ⳱ 0.05 g, answer.
`
`0.02%
`250 mL
`
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`IPR2018-01020 and IPR2018-01021, Exhibit 1019, Page 4
`
`