This document discusses various calculations used in sterile compounding. It covers learning objectives, types of calculations including basic formula, ratio and proportion, dimensional analysis, IV flow rates, IV drip rates, and alligations. It provides examples of how to perform each type of calculation and notes the specific scenarios where each method is best used. The goal is for readers to understand the principles and practice calculations to determine the correct method based on the medication and sterile compounding procedure.

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Chapter 5
Calculations for Sterile
Compounding
2012 Paradigm Publishing

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Learning Objectives
 Explore the evolution of mathematical formulas used in sterile
compounding.
 Understand the principles of pharmacy dosage calculations.
 Practice several types of pharmaceutical calculations using a
basic formula, ratio and proportion, dimensional analysis,
intravenous flow rates, intravenous drip rates, and alligations.
 Determine the best method of solving pharmaceutical dosage
questions based on the medication labeling and sterile
compounding procedure required.
2012 Paradigm Publishing

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Topics
 Learning Objectives
 Introduction
 Calculations as Part of the Anteroom Protocol
 Dosage Calculations
 Special Considerations
 Common Pharmacy Equivalents and Conversions
 Basic Formula Calculations
 Ratio and Proportion Calculations
 Dimensional Analysis Calculations
 IV Flow Rate Calculations
 IV Drip Rate Calculations
 Alligation Calculations
 Calculation Skills in the Sterile Compounding Environment
 Chapter Summary
2012 Paradigm Publishing
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Introduction
 The majority of the CSPs assembled will require the
application of one or more pharmacy calculation
methods to determine the volume of the medication,
additive, or solution component needed to prepare a
CSP or to resolve the number of CSPs necessary for a
24-hour supply
numerous other calculation methods are used by
pharmacy personnel to determine information such as
day’s supply, quantity to be dispensed, and average
wholesale price (AWP)
2012 Paradigm Publishing

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Calculations as Part of the
Anteroom Protocol
 The prescriber includes the names of the desired
medications, the desired doses, and the dosing
intervals as part of the CSP order
the prescriber also determines the desired base solution
and infusion rate for large-volume parenterals (LVPs)
most small-volume parenterals (SVPs), however, are
prepared using standard base solutions and volumes and
are administered using standard administration times
2012 Paradigm Publishing

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Calculations as Part of the
Anteroom Protocol…/2
 Once the medication order is
received, personnel then
enter the information into the
computer system and
generate a label for each CSP
the pharmacist and IV
technician must verify that the
CSP label matches the
medication order and is 100%
accurate
2012 Paradigm Publishing

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Calculations as Part of the
Anteroom Protocol…/3
 Looking for words or abbreviations that identify a
number, dose, volume, amount, or route can help in
identifying the medications needed for sterile
compounding
2012 Paradigm Publishing

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Calculations as Part of the
Anteroom Protocol…/4
2012 Paradigm Publishing

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Dosage Calculations
 The calculations are based
on information on the CSP
label and the label on the
stock medication container
begin the calculation process
by determining the
concentration; this
information can be found on
the medication label
these calculations determine
the drug volume
2012 Paradigm Publishing

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Dosage Calculations…/2
 Locating and understanding label information is an
important initial step in ensuring accuracy in
pharmacy calculations and in sterile compounding
2012 Paradigm Publishing

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Special Considerations
 One consideration is that the volume (in milliliters [mL]
or liters [L]) and strength (in percent [%]) of the base
solution are not to be included in any equation in which
personnel are asked to determine the amount or volume
of drug that is to be drawn up for a desired dose
 Another consideration when performing pharmacy
calculations is that an IV technician chooses a method or
formula based on the type of CSP being prepared as well
as a personal calculation preference
2012 Paradigm Publishing

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 In addition to understanding basic math principles,
the IV technician must memorize the most
commonly used equivalents and metric conversions
2012 Paradigm Publishing
Common Pharmacy Equivalents and
Conversions

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Common Pharmacy Equivalents and
Conversions…/2
2012 Paradigm Publishing

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Common Pharmacy Equivalents and
Conversions…/3
2012 Paradigm Publishing

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Common Pharmacy Equivalents and
Conversions…/4
 Sterile compounding personnel must also memorize
the conversions from standard time (clock time) to
military time
2012 Paradigm Publishing

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Your Turn
2012 Paradigm Publishing
1) For dosage calculations, begin the calculation process by determining
this.
a. weight
b. volume
c. concentration
d. thickness
2) Standard time is called this.
a. regular time
b. clock time
c. average time
d. military time
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Basic Formula Calculations
 The basic formula method is a simple process to
calculate most parenteral medication dosages and
may be used when the concentration on the drug
label is provided in units per one milliliter
 D/H = x mL
D = desired dose
H = concentration on hand
x = unknown volume of drug needed to be drawn up
2012 Paradigm Publishing

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Basic Formula Calculations…/2
 The basic formula method is best used in sterile
compounding scenarios that meet the following
criteria:
the prescriber has ordered a CSP with a single medication
additive
the drug is in an injectable form
the medication label provides you with the concentration
of the drug in the form of number of units per one milliliter
2012 Paradigm Publishing

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Basic Formula Calculations…/3
Performing a Basic Formula
Calculation
1. Find the desired dose (D)
2. Determine the
concentration on hand (H)
3. Divide D by H
The resulting answer equals
x mL
2012 Paradigm Publishing

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Ratio and Proportion Calculations
 The ratio and proportion method may be used
whenever three of the four values in a proportion are
known, thus allowing the IV technician to solve for
the fourth, unknown value of the proportion
 H mg = D mg
Y mL x mL
H mg = number of milligrams on hand
Y mL = number of milliliters in the concentration on hand
D mg = desired dose
x mL = unknown volume of drug needed to be drawn up
2012 Paradigm Publishing

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Ratio and Proportion
Calculations…/2
 The ratio and proportion method is best used in
sterile compounding scenarios that meet the
following criteria:
the stock drug is already in a liquid, injectable form (does
not need to be reconstituted; the medication label
identifies the concentration of the drug in a form other
than the form milligrams per one milliliter
the stock drug is in a powdered form and requires
reconstitution prior to drawing it up for injection
either a liquid or powdered drug requires the completion
of several additional steps to solve the problem
2012 Paradigm Publishing

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Ratio and Proportion
Calculations…/3
Performing a Ratio and
Proportion Calculation
1. Set up the ratio
2. Cross-multiply Y × D
3. Divide the answer
from step 2 by H
 The resulting answer
equals x mL
2012 Paradigm Publishing

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Dimensional Analysis Calculations
 The dimensional analysis method, also known as
“calculation by cancellation,” is another approach
that some IV technicians prefer to use when a
dosage calculation involves multiple steps
based on the principle that any number can be multiplied
by one without changing its value
first determine the answer that is needed, and then use
the values provided to perform a series of calculations
2012 Paradigm Publishing

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Dimensional Analysis
Calculations…/2
 The dimensional analysis method for solving
pharmacy dosage calculations is best used in sterile
compounding scenarios that meet either of the
following criteria:
to determine the volume of drug needed to prepare the
CSP, the IV technician must answer several questions by
performing multiple calculations
the IV technician must make one or more conversions
between various units of measure
2012 Paradigm Publishing

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Dimensional Analysis
Calculations…/3
 Performing a Dimensional Analysis Calculation
put the unknown quantity (the x you want to define) on its
own on the left side of the equation, followed by an equal
sign
on the right side, record a series of ratios, using both
standard equivalents and information provided by the
medication label and the CSP label
then multiply the ratios together to provide the answer to
the problem
2012 Paradigm Publishing

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Dimensional Analysis
Calculations…/4
 The unit of measure in the numerator of the first
ratio must be the same as the unit of measure you
are solving, and the unit of measure in each
successive numerator must match the unit of
measure in the preceding denominator
as a result of this setup, the units of measure in each
alternate numerator–denominator will cancel out, such
that the only unit of measure remaining is the one you
must solve
2012 Paradigm Publishing

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IV Flow Rate Calculations
 A daily IV run, or the batch typically requires a 24-hour
supply of CSPs
 Several types of IV flow rate calculations will determine the
answer to one or more of the following:
How long will this bag last?
What time will the next bag be needed?
How many bags will be needed for the patient for a 24-hour
period?
 These may all be solved using IV flow rate calculations that
employ simple addition, division, and/or multiplication
2012 Paradigm Publishing

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IV Flow Rate Calculations…/2
 The three methods for solving IV flow rate questions
are best used in sterile compounding scenarios that
meet the following criteria:
the infusion rate in mL/hour is provided on the medication
order or CSP label
the total volume is provided on the medication order or
CSP label
the current time is known or may be easily determined
2012 Paradigm Publishing

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IV Flow Rate Calculations…/3
Performing an IV Flow Rate Calculation
 The answers to the three questions can be
determined by setting up a division or multiplication
problem
when calculating IV flow rates, you must know the total
volume of the LVP and either 1) the infusion rate in
milliliters per hour (mL/hr) or 2) the number of hours over
which the LVP is to be infused
this information can be found on the medication order or
the CSP label
2012 Paradigm Publishing

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IV Drip Rate Calculations
 The drop factor method relies on the specific drop
factor (gtts/mL), or the number of drops per
milliliter, that a certain type of IV tubing delivers
 Each of the different types of IV tubing delivers a
different drop factor
macrodrip IV tubing may deliver either 10 gtts/mL or 20
gtts/mL
microdrip IV tubing delivers 60 gtts/mL
 An equation using drop factor is sometimes called an
IV drip rate calculation
2012 Paradigm Publishing

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IV Drip Rate Calculations…/2
 The drop factor method is best used in situations
that meet the following criteria:
the total volume to be infused is known
the total infusion time is known
the drop factor of the IV tubing is known
the desired answer is to be provided in drops per minute
(gtts/min)
total volume in mL × drop factor = drops
infusion time in minutes minute
2012 Paradigm Publishing

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Alligation Calculations
 The pharmacy may be required to mix two different
strengths of the same active ingredient of a drug or
solution to make the desired strength
a higher-percent strength of a drug or solution is mixed
with a lower-percent strength of a drug or solution in
order to make the desired strength
 This scenario requires you to employ a calculation
called the alligation method, or simply alligation
rarely performed by IV technicians
2012 Paradigm Publishing

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Alligation Calculations…/2
 The alligation method of solving pharmacy dosage
calculations is best used in compounding situations
that meet any of the following criteria:
two or more strengths of the same active ingredient or
solution must be used to prepare the desired strength of a
drug or solution
the desired strength of the drug or solution is known
the total volume of the CSP is known
2012 Paradigm Publishing

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Alligation Calculations…/3
Performing an Alligation Calculation
1. Identify the variables by determining the component
concentrations
2. Fill in the concentration strengths
3. Find the values
4. Set up a ratio
5. Use a formula
2012 Paradigm Publishing

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Calculation Skills in the
Sterile Compounding Environment
 Accurate calculation and measurement of the
components or ingredients of the formulation are
critical
the pharmacy technician must have an understanding of
historical practices and a working knowledge of current
systems of measurement and pharmacy calculations
in order to perform accurate calculations, you must write
down the equation and verify that you have the correct
information in the correct place within the formula
2012 Paradigm Publishing

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Your Turn
2012 Paradigm Publishing
3) This is the basic formula.
a. H/D = x mL
b. X/D = h mL
c. D/H = x mL
d. X/H = d mL
4) An equation using drop factor is sometimes called this.
a. ratio and proportion calculation
b. IV flow rate calculation
c. alligation calculation
d. IV drip rate calculation
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