Lecture Math for the pharmacy technician Concepts and calculations Chapter 6 – Lynn M. Egler, Kathryn A. Booth

Chapter 6, Dosage calculations, teaches the techniques for calculating doses. Building on information from earlier chapters, students are taught how to calculate the amount to dispense, using all four methods of dosage calculations: ratio proportion, fraction proportion, dimensional analysis, and formula. Students will also learn to calculate estimated days supply.

Concepts and Calculations

Chapter 6: Dosage Calculations

Egler • Booth

Learning Objectives

 Identify the information on a

medication order and drug label needed to calculate the desired dose.

 Convert the dosage ordered to the desired dose.

When you have successfully completed Chapter 6, you will

have mastered skills to be able to:

 Calculate the amount to dispense of

a drug.

 Recognize common errors that

occur during dose calculations.

 Calculate estimated days supply.

 This chapter will bring all of the previous information

together to calculate the amount of medication to

To calculate medication dosages you must know:

Desired Dose:

 The amount of the drug to be dispensed at a single time.

 Its unit of measurement must be the same as the dosage

unit.

Dosages and Doses (con’t)

Dosage ordered:

 The total amount of drug the physician has ordered,

along with the frequency.

 Its unit of measurement may not be the same as that of

the dosage unit.

 The amount of drug contained within a dosage unit

of medication.

Dose on hand:

tablet, the dose on hand is 250 mg.

Dosages and Doses (con’t)

 The unit of measurement for the desired dose

must be the same as the unit of measurement

of the dose on hand before the amount to

dispensed can be calculated

 This is calculated by converting the dose

ordered into the same unit of measurement as

the dose on hand; once converted it becomes

the desired dose.

 Before calculating the amount to be

dispensed, you must first determine the

desired dose.

 The dosage ordered is not always written in

the same units that are found on the drug

label.

 You must convert the dosage ordered into a

desired dose having the same units as the

Calculating the Desired Dose

 Each gives the same result

 Use the method that you like

 Once you identify your favorite method,

follow the color coding of that method in the

book

Fraction Proportion Method

Procedure Checklist 6-1

1. Write the conversion factor with the units

that you are converting to in the numerator

and the units you are converting from in the

denominator.

2. Write a fraction with the unknown,”?,” in the

numerator and the number that you need to

convert in the denominator.

Fraction Proportion Method

The dosage ordered is 0.2 mg once a day.

The dosage strength is 100 mcg/tablet.

Find the desired dose.

Desired Dose = 200 mcg

 In a fraction proportion, units from the

fraction can be canceled only when they

are the same portion of the fraction

Units in the denominator of one fraction

cannot be canceled with units found in

the numerator of the other

Always include the units when performing

calculations.

Ratio Proportion Method

Procedure Checklist 6-2

1. Write the conversion factor as a ratio A : B

so that A has the units of the value that you

are converting (the dosage ordered) and B

has the unit of value of the dose on hand.

2. Write a second C : D so that C is the

missing value (desired dose) and D is the

number that is being converted (the dosage

ordered).

3 Write the proportion in the form A : B :: C : D.

Note: When using the ratio proportion method

to calculate the desired dose, C indicates the unknown value (desired dose).

4 Cancel units

5 Solve the proportion by multiplying means

and extremes.

Ratio Proportion Method (con’t)

Example

Practice by determining the desired dose.

The desired dose is 325 mg

The order reads: ASA gr v PO daily.

The drug label indicates 325 mg tablets.

Find the desired dose.

 In a ratio proportion, units can be

canceled only when they are found

in the same part of each of the

ratios.

Always include the units when

performing calculations.

Dimensional Analysis

Procedure Checklist 6-3

1. Determine the units of measure for the

answer and place it as the unknown on one side of the equation.

2. On the other side of the equation, write a

conversion factor with the units of measure for the answer on top and the units you are converting from on the bottom.

3 Multiply the conversion factor by the number

that is being converted over one.

4 Cancel units on the right side of the equation

The remaining unit of measure on the right side of the equation should match the

unknown unit of measure on the left side of the equation.

Dimensional Analysis (con’t)

Example

Find the desired dose for the following:

Ordered: Levsinex timecaps ER 1500 mcg once

daily

On hand: Levsinex timecaps 0.375 mg

Desired dose = 1.5 mg

 In dimensional analysis, units can be

canceled only when they are found in

both the numerator and the

denominator of the fraction.

Always include the units when

performing calculations.

Review and Practice

Desired dose: 250 mg

Determine the desired dose

Ordered: Penicillin VK 0.25 g

On hand: Penicillin VK 500 mg

Once you have determined the

desired dose, you still must

calculate the amount to

dispense.

Calculating the Amount to

Dispense (con’t)

To calculate the amount of medication to dispense (A), the

following information must be known:

The desired dose (D) or the amount of drug to

be given at a single time

This is the dosage ordered converted to the

same units as the dose on hand, if

necessary.

The dosage strength or the dose on hand (H)

per the dosage unit (Q).

The dose on hand (H) is the amount of drug

contained in a dosage unit.

The dosage unit (Q) is the unit by which you will

measure the medication-tablets, capsules,

milliliters, teaspoons, etc (Find this on the

medication label).

to Dispense (con’t)

Procedure 6-4 Calculating the Amount to

Dispense by Fraction Proportion:

1 Set up the proportion as follows:

dosage unit amount to dispense dose on hand desired dose

D

A H

to Dispense (con’t)

Example:

 Ordered: 250 mg IM

 Dosage strength available: 0.5 g/mL

 Find the amount to dispense

Procedure 6-5 Calculating the Amount to

Dispense by Ratio Proportion:

1 The proportion will be set up as follows:

dosage unit : dose on hand :: amount to

dispense : desired dose

Or

Q : H :: A : D

2 Cancel units

3 Multiply the means and extremes then solve for

the missing value

Calculating the Amount

to Dispense (con’t)

 Ordered is Famvir 500 mg PO q 8h

 On hand: Famvir 250 mg tabs

 Find the amount to dispense

Amount to dispense = 2 tablets

Calculating the Amount

to Dispense (con’t)

Procedure 6-6 Calculating the Amount to

Dispense by Dimensional Analysis:

With dimensional analysis you will not need to

calculate the desired dose and amount to dispense separately

You will place your unknown (amount to dispense)

on one side of the equation then multiply a series of factors on the right side of the

equation.

Canceling units will help you determine the equation

has been set up correctly.

Procedure 6-6 Calculating the Amount to

Dispense by Dimensional Analysis (con’t):

1 Determine the units of measure for the answer

and place it as the unknown on one side of the

equation.

2 On the right side of the equation, write a

conversion factor with the units of measurement

for the desired dose on top and the unit of

measurement for the dose on hand.

to Dispense (con’t)

Procedure 6-6 Calculating the Amount to

Dispense by Dimensional Analysis (con’t):

3 Multiply the conversion factor by a second

factor: the dosage unit over the dose on hand.

4 Multiply by a third factor: dose ordered over the

number one.

5 Cancel units on the right side of the equation

The remaining unit of measure on the right side

of the equation should match the unknown unit

of measure on the left side of the equation.

6 Solve the equation.

to Dispense (con’t)

Procedure 6-7 Calculating Amount to Dispense Using the

Formula Method:

1 Determine the desired dose Determine the dose on hand (H)

and dosage unit (Q).

2 Fill in the formula

•D for the desired dose

•H for the dose on hand

•Q for the dosage unit in the formula

•A for the unknown or the amount to dispense

A

xQ =

H D

Procedure 6-7 Calculating Amount to Dispense Using the

Formula Method (cont.):

3 Cancel the units.

4 Solve for the unknown.

to Dispense (con’t)

Example:

 The dosage ordered is 500 mg PO q 8 h

 On hand: Famvir 250 mg/tabs

 Find the amount to dispense

Amount to dispense = 2 tablets

 As a pharmacy technician you may need

to determine the estimated days

supply of a prescription, which is how

long the medication will last the patient

if taken correctly

Estimated Days Supply (con’t)

 To determine estimated days supply you

will multiply amount of medication to dispense by days needed over the

number of dosage units per day

Amount to dispense × ? days = estimated days supply

dosage units per day

The amount of the drug to be dispensed at a single time is

Review and Practice

True or False

If a medication has 300 mg of drug per tablet, the dose on

hand is 300 mg.

Answer: True

The MAR reads Glucotrol 10 mg PO qd The desired dose is mg.

Answer: 10 mg

Review and Practice

Calculate the amount to dispense.

 Ordered: Prednisone 10 mg PO qid

 On hand: Prednisone 5 mg tablets

Answer (Using ratio proportion)

5 mg : 1 tablet : : 10 mg : ? tablet

1 x 10 = 5 x ?

? = 2 Amount to dispense: 2 tablets

Performing dosage calculations is

a large part of the pharmacy

technician’s daily responsibilities

It is important to always use any

resources available to you when

performing dosage calculations