2. Chapter 5
Calculations for Sterile Compounding

3. 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.

4. 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
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5. 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)

6. 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

7. 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

8. 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

9. Calculations as Part of the Anteroom Protocol…/4

10. 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

11. Dosage Calculations…/2
Locating and understanding label information is an important initial step in ensuring accuracy in pharmacy calculations and in sterile compounding

12. 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

13. Common Pharmacy Equivalents and Conversions
In addition to understanding basic math principles, the IV technician must memorize the most commonly used equivalents and metric conversions

14. Common Pharmacy Equivalents and Conversions…/2

15. Common Pharmacy Equivalents and Conversions…/3

16. Common Pharmacy Equivalents and Conversions…/4
Sterile compounding personnel must also memorize the conversions from standard time (clock time) to military time

17. Your Turn
For dosage calculations, begin the calculation process by determining this.
weight
volume
concentration
thickness
In Slide Show view, click here to see the answer to Question 1. Then click again to advance to Question 2.
Standard time is called this.
regular time
clock time
average time
military time
In Slide Show view, click here to see the answer to Question 2.

18. 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

19. 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

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

21. 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

22. 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

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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. Alligation Calculations…/3
Performing an Alligation Calculation
Identify the variables by determining the component concentrations
Fill in the concentration strengths
Find the values
Set up a ratio
Use a formula

36. 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

37. Your Turn This is the basic formula. H/D = x mL X/D = h mL D/H = x mL
X/H = d mL
In Slide Show view, click here to see the answer to Question 3. Then click again to advance to Question 4.
An equation using drop factor is sometimes called this.
ratio and proportion calculation
IV flow rate calculation
alligation calculation
IV drip rate calculation
In Slide Show view, click here to see the answer to Question 4.