OUR LADY OF FATIMA UNIVERSITY
College of Pharmacy
PHARMACEUTICAL
CALCULATIONS AND
TECHNIQUES
PHCL111
TOPIC 1
FUNDAMENTALS OF PHARMACEUTICAL
CALCULATIONS
UNIT
OUTCOMES
1.
2.
3.
4.
5.
UNIT OUTLINE
1.
2.
3.
PHARMACEUTICAL CALCULATIONS
•
Basic math operations
Arabic
Numerals
One
Two
Three
Four
Five
Six
Seven
Eight
=1
=2
=3
=4
=5
=6
=7
=8
Roman Numerals
ss
I or i
V or v
X or x
L or l
C or c
D or d
M or m
=½
=1
=5
= 10
= 50
= 100
= 500
= 1000
Basic math operations
Arabic
Numerals
One
Two
Three
Four
Five
Six
Seven
Eight
=1
=2
=3
=4
=5
=6
=7
=8
Roman Numerals
ss
I or i
V or v
X or x
L or l
C or c
D or d
M or m
=½
=1
=5
= 10
= 50
= 100
= 500
= 1000
Basic math operations
Arabic
Numerals
One
Two
Three
Four
Five
Six
Seven
Eight
=1
=2
=3
=4
=5
=6
=7
=8
Roman Numerals
ss
I or i
V or v
X or x
L or l
C or c
D or d
M or m
=½
=1
=5
= 10
= 50
= 100
= 500
= 1000
EXAMPLE:
1.
EXAMPLE
FRACTION
1
 Numerator
------7  Denominator
RATIO
Represents the relationship of two numbers.
1:7
Example
Two parts to nine parts
Three parts to twelve
parts
Fraction
Ratio
2_
9
2:9
_3_
12
3 : 12
PROPORTION
An expression of two equal ratios.
3
8
3:8 = 9:24  3:8 :: 9:24 
::
9
24

3
8
=
9
24
MEANS AND EXTREMES
means
Proportion Rule:
A:B = C:D
BxC=AxD
3:8
=
9:24
extremes
extremes
3
8
=
9
24
means
Example:
1. If an insulin injection contains 100 units of insulin in each milliliter,
how many milliliters should be injected to receive 40 units of insulin?
100 𝑢𝑛𝑖𝑡𝑠
=
1 𝑚𝐿
100 𝑢𝑛𝑖𝑡𝑠)(𝑋
100 𝑢𝑛𝑖𝑡𝑠
=
40 𝑢𝑛𝑖𝑡𝑠
𝑋
40 𝑢𝑛𝑖𝑡𝑠)(1𝑚𝐿
100 𝑢𝑛𝑖𝑡𝑠
(40)(1 𝑚𝐿)
𝑥 =
100
𝑥 = 0.40 mL
Example:
2. A formula for 1250 tablets contains 6.25 grams of diazepam. How
many grams of diazepam should be used in preparing 550 tablets?
1250 𝑡𝑎𝑏𝑙𝑒𝑡𝑠
=
6.25 𝑔𝑟𝑎𝑚𝑠
1250 𝑡𝑎𝑏𝑙𝑒𝑡𝑠)(𝑋
1250 𝑡𝑎𝑏𝑙𝑒𝑡𝑠
=
550 𝑡𝑎𝑏𝑙𝑒𝑡𝑠
𝑋
550 𝑡𝑎𝑏𝑙𝑒𝑡𝑠)(6.25 𝑔𝑟𝑎𝑚𝑠
1250 𝑡𝑎𝑏𝑙𝑒𝑡𝑠
(550)(6.25 𝑔𝑟𝑎𝑚𝑠)
𝑥 =
1250
𝑥 = 2.75 grams
DIMENSIONAL ANALYSIS
Involves the logical sequencing and placement of a series of ratios into an equation.
Calculate the number of seconds in a day.
Wanted Quantity & Unit
Conversion Factor
Given Quantity
Conversion Computation
Example:
1. A cough syrup contains 10 mg of dextromethorphan
hydrobromide per 5 mL. How many milligrams of the drug are
contained in a 120-mL container of the syrup?
10 𝑚𝑔
5 𝑚𝐿
× 120 𝑚𝐿
= 240 𝑚𝐿
Percent


Example
1. In a clinical study of niacin as a lipid-altering agent, 60% of the
90 patients in the study group developed flushing. Calculate the
number of patients having this reaction.
60%
60
× 90
100
=
60 𝑥 90
100
=
54
SIGNIFICANT FIGURES
•
•
•
•
•
•
•
•
PRACTICE PROBLEMS:
1. A cough syrup contains 10 mg of dextromethorphan hydrobromide per 5
mL. How many milligrams of the drug are contained in a 120-mL container of
the syrup?
2. A 15-mL package of nasal spray delivers 20 sprays per milliliter of solution,
with each spray containing 1.5 mg of drug.
(a) How many total sprays will the package deliver?
(b) How many milligrams of drug are contained in the 15-mL package
of the spray?
Answer:
1. A cough syrup contains 10 mg of dextromethorphan hydrobromide
per 5 mL. How many milligrams of the drug are contained in a 120-mL
ontainer of the syrup?
10 𝑚𝑔
=
5 𝑚𝐿
10 𝑚𝑔)(120 𝑚𝐿
5 𝑚𝐿
=
𝑋
120 𝑚𝐿
𝑋)(5 𝑚𝐿
5 𝑚𝐿
(10𝑚𝑔)(120)
𝑥 =
5
𝑥 = 240 mg
Answer:
2. A 15-mL package of nasal spray delivers 20 sprays per milliliter of solution, with each spray
containing 1.5 mg of drug.
(a) How many total sprays will the package deliver?
(b) How many milligrams of drug are contained in the 15-mL package of the spray?
15𝑚𝐿
=
𝑋
15 𝑚𝐿)(20 𝑠𝑝𝑟𝑎𝑦𝑠
1 𝑚𝐿
=
1𝑚𝐿
20 𝑠𝑝𝑟𝑎𝑦𝑠
(1𝑚𝐿) 𝑋)
1 𝑚𝐿
(15𝑚𝐿)(20)
𝑥 =
1
𝑥 = 300 sprays/ 15 mL package
Answer:
2. A 15-mL package of nasal spray delivers 20 sprays per milliliter of solution, with each spray
containing 1.5 mg of drug.
(a) How many total sprays will the package deliver?
(b) How many milligrams of drug are contained in the 15-mL package of the spray?
1.5𝑚𝑔
=
1 𝑠𝑝𝑟𝑎𝑦
1.5 𝑚𝑔)(300 𝑠𝑝𝑟𝑎𝑦𝑠
=
1 𝑠𝑝𝑟𝑎𝑦
𝑋
300 𝑠𝑝𝑟𝑎𝑦𝑠
(𝑋) 1 𝑠𝑝𝑟𝑎𝑦)
1 𝑠𝑝𝑟𝑎𝑦
(1.5𝑚𝑔)(300)
𝑥 =
1
𝑥 = 450 mg
VIDEO LINKS
https://www.youtube.com/watch?v=TD7YN13sABk
https://www.youtube.com/watch?v=XyhX5z1UKUA
REFERENCES:
Ansel, Howard C., Pharmaceutical calculations, 15th ed., Philadelphia :
Wolters Kluwer Health, 2017