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Booth • Whaley
Chapter 7
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CHAPTER 7
METHODS of DOSAGE
CALCULATIONS
Learning Objectives
When you have completed Chapter 7, you will be able to:
• Describe how the information on a
physician’s order, Medication
Administration Record (MAR), or
prescription, along with the drug label and
package insert, are used to calculate the
desired dose.
Chapter 7
3
Learning Objectives (con’t)
• Convert the dosage ordered to the desired
dose, using both fraction proportion, ratio
proportion, or dimensional analysis.
• Calculate the amount to administer of a
drug, using any of the methods of dosage
calculation, fraction proportion, ratio
proportion, dimensional analysis, or formula.
• Recognize common errors that occur during
dose calculations.
Chapter 7
4
Introduction
• This chapter will bring all of the previous
information together to calculate the
amount of medication to administer to a
patient.
• You will use:
– Basic math
– Information from the physician’s order
– Drug labels
– Method of converting quantities from one
unit of measurement to another
Chapter 7
5
Dosages and Doses
To calculate medication
dosages you must know:
Desired Dose:
• The amount of the drug to be
administered at a single time.
• Its unit of measurement must be the
same as the dosage unit.
Chapter 7
6
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.
Chapter 7
7
Dosages and Doses (con’t)
Dose on hand:
• The amount of drug
contained within a
dosage unit of
medication.
• If a medication has 250 mg of drug per
tablet, the dose on hand is 250 mg.
Chapter 7
8
Dosages and Doses
Rule 7 - 1
• 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
administer 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.
Chapter 7
9
Calculating the Desired
Dose
• Before calculating the amount to be
administered, 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
dose on hand.
Chapter 7
10
Calculating the Desired
Dose (con’t)
• Three methods to calculate desired dose:
– Fraction proportion
– Ratio proportion
– Dimensional analysis
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
Chapter 7
11
Fraction Proportion
Method
Procedure Checklist 3-1
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.
Chapter 7
12
Fraction Proportion
Method (con’t)
3. Set the two fractions up as a proportion.
4. Cancel units.
5. Cross multiply, then solve for the unknown
value.
Work out this Example:
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
Chapter 7
13
Error Alert!
• 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.
Chapter 7
14
Ratio Proportion Method
Procedure Checklist 3-2
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).
Chapter 7
15
Ratio Proportion Method
(con’t)
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.
Chapter 7
16
Ratio Proportion Method
(con’t)
Example
Practice by determining the desired dose.
The order reads: ASA gr v PO daily.
The drug label indicates 325 mg tablets.
Find the desired dose.
The desired dose is 325 mg.
Chapter 7
17
Error Alert!
• 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.
Chapter 7
18
Dimensional Analysis
Procedure Checklist 3-3
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.
Chapter 7
19
Dimensional Analysis
(con’t)
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.
5. Solve the equation.
Chapter 7
20
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
Chapter 7
21
Error Alert!
• 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.
Chapter 7
22
Review and Practice
Determine the desired dose.
Ordered: Penicillin VK 0.25 g
On hand: Penicillin VK 500 mg
Desired dose: 250 mg
Wonderful !
Chapter 7
23
Calculating the Amount to
Administer
Once you have
determined the
desired dose,
you still must
calculate the
amount to
administer.
Chapter 7
24
Calculating the Amount
to Administer (con’t)
Rule 7 - 2
To calculate the amount of medication
to administer (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.
Chapter 7
25
Calculating the Amount
to Administer (con’t)
Rule 7 - 2 (con’t)
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)
Chapter 7
26
Calculating the Amount
to Administer (con’t)
Procedure 7-1 Calculating the Amount to
Administer by Fraction Proportion:
1. Set up the proportion as follows:
dosage unit
amount to administer
dose on hand
desired dose
2. Cancel units
QA
H D
3. Cross multiply, then solve for the unknown value
Chapter 7
27
Calculating the Amount
to Administer (con’t)
Example:
• Ordered: 250 mg IM
• Dosage strength available: 0.5 g/mL
• Find the amount to administer
Amount to administer = 0.5 mL
Chapter 7
28
Calculating the Amount
to Administer (con’t)
Procedure 7-2 Calculating the Amount to Administer
by Ratio Proportion:
1. The proportion will be set up as follows:
dosage unit : dose on hand :: amount to
administer : desired dose
Or
Q : H :: A : D
2. Cancel units
3. Multiply the means and extremes then solve for
the missing value
Chapter 7
29
Calculating the Amount
to Administer (con’t)
Example:
The dosage ordered is Famvir 500 mg PO q 8h
On hand: Famvir 250 mg tabs
Find the amount to administer
Amount to administer = 2 tablets
Chapter 7
30
Calculating the Amount
to Administer (con’t)
Procedure 7-3 Calculating the Amount to
Administer by Dimensional Analysis:
With dimensional analysis you will not need to
calculate the desired dose and amount to
administer separately.
You will place your unknown (amount to administer)
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.
Chapter 7
31
Calculating the Amount
to Administer (con’t)
Procedure 7-3 Calculating the Amount to
Administer 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.
Chapter 7
32
Calculating the Amount
to Administer (con’t)
Procedure 7-3 Calculating the Amount to
Administer 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.
Chapter 7
33
Calculating the Amount
to Administer (con’t)
Example:
The order reads: Prozac Liquid 40 mg daily
On hand: Prozac 20 mg/5 mL
Find the amount to administer
Amount to administer = 10 mL
Chapter 7
34
Calculating the Amount
to Administer (con’t)
Procedure 7-4 Calculating Amount to Administer Using
the Formula Method:
1. Determine the desired dose. Determine the dose on hand
(H) and dosage unit (Q)
D xQ A
H
2. Fill 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 administer
Chapter 7
35
Calculating the Amount
to Administer (con’t)
Procedure 7-4 Calculating Amount to Administer
Using the Formula Method (con’t):
3. Cancel the units
4. Solve for the unknown
Chapter 7
36
Calculating the Amount
to Administer (con’t)
Example:
The dosage ordered is 500 mg PO q 8 h
On hand: Famvir 250 mg/tabs
Find the amount to administer
Amount to administer = 2 tablets
Chapter 7
37
Apply Your Knowledge
The amount of the drug to be administered at
a single time is called the:
a. dosage ordered
b. dosage unit
c. desired dose
d. dosage strength
Answer: c. desired dose
Chapter 7
38
Apply Your Knowledge
True or False
If a medication has 300 mg of drug per
tablet, the dose on hand is 300 mg.
Answer: True
Chapter 7
39
Apply Your Knowledge
The MAR reads Glucotrol 10 mg PO qd.
The desired dose is ____ mg.
Answer: 10 mg
Chapter 7
40
Apply Your Knowledge
Calculate the amount to administer.
• 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 administer: 2 tablets
Chapter 7
41
Methods of Dosage Calculations
Each problem
that I solved
became a rule,
which served
afterwards to
solve other
problems.
-- Rene
Descartes
Chapter 7
THE END
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