This document provides an overview of pharmaceutical calculations. It discusses various measurement systems used in pharmacy like metric, apothecary, and household systems. It focuses on metric system and covers measurement of weight and volume including common units and instruments. It also discusses density, specific gravity, specific volume and their calculations. Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance evaluated at the same temperature. Various examples are provided to demonstrate calculations of weight, volume, density, specific gravity and specific volume.

1. Pharmaceutical calculations
By: Abera J (B.Pharm., MSc in Clinical Pharmacy).
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2. Introduction
• Pharmaceutical calculation,
– is the area of study that applies the basic
principles of mathematics to the preparation and
safe and effective use of pharmaceuticals.
• Pharmaceutical calculation,
– Encompasses calculation of amounts of
components being added to a compounded total
parenteral nutrition to the drops per minute rate on
the label of an intravenous bag.
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3. Introduction…
• Pharmacy technician requires a variety of skills
and abilities,
– The most important is the ability to carry out
important mathematic calculations.
• The goal of this module is to provide a basic review
of the many types of pharmacy calculations that
pharmacy technicians are required to be equipped
with.
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4. Measurement of weight and volume
 Pharmaceutical measurement of weight and
volume is an important part of pharmacy practice.
 The knowledge and application of pharmaceutical
pharmaceutical and clinical applications are
essential for the practice of pharmacy.
 The measurement systems include:
i. Metric systems
ii. Apothecary systems
iii. Household Systems 4

5.  Many pharmaceutical calculations have been simplified
by the shift from apothecary to metric system of
measurements.
 In the house hold system of measurement, the
patients use household measuring devices such as;
teaspoon, tablespoon, tea cup, wine glass. etc.
though this system is inaccurate, due to increased
home care delivery system are widely used.
 Therefore, only metric system will be discussed
here.
Measurement of weight and volume…
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7. Volume measurement
 The liter is the metric unit of volume.
 The table of metric volume follows:
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8. Volume measurement….
 Common instruments for the pharmaceutical
measurement of volume;
Range from micropipets, and burettes used in
analytic procedures to large, industrial-size
calibrated vessels
 Examples of common containers for measuring volume
are:
 Graduated Measuring Cylinders- 5ml,10ml,50ml
 Conical measures-100ml,200ml,250ml,500ml
 Beakers-100ml,200ml,300ml
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9. Volume measurement…
 An important factor in the accuracy of an
instrument used for measuring volume is the
surface area of the liquid in it.
 Accuracy increase as the surface area
increases.
 However, a decrease in surface area decreases
the convenience of transferring a liquid to and
from the equipment.
Therefore, accuracy and convenience should
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10. Measure of Weight
• The unit of weight in the metric system is
the gram(g). The table of metric weights
follows:
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11. Measure of Weight…
 The selection of balance and scale for weight
measurements depends on the task at hand,
Ranges from highly sensitive electronic analytic
balances and prescription balances in
extemporaneous compounding procedures to large-
capacity scales in the industrial manufacturing
and production of pharmaceutical products.
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12. Measure of Weight…
 Weight is a measure of the gravitional
force acting on a body,
it is directly proportional to the body’s mass.
 Weight is measured by means of a balance.
 In dispensing (hospital and community
pharmacies), the type of balance used is
called Prescription balance.
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13. There are two main types of prescription
balances:
1) Class A Prescription Balance
 Has a sensitivity requirement of 6mg with
no load and with a load of 10g on each pan
 The maximum amount that can be weighed
on this balance is 120g. E.g. Torison
prescription balance
2) Class B Prescription Balance
 Has a sensitivity requirement of 30mg. 13

14. Prescription balances
 Their major purpose being the same (i.e.
weighing), balances are differentiated from each
other by the following parameters:
1.Sensitivity
2.Sensitivity Requirements
3.Capacity
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15. Prescription balances…
Sensitivity
 Is the smallest weight that makes a perceptible change in the
pointer of a balance which indicates the equilibrium position.
Sensitivity Requirements(SR)
 The minimum weight required to move the pointer by one
division on the scale.
 SR for class A prescription Balance is 6mg while that of
class B prescription balance is 30mg.
 N.B. The smaller the weight required to move the
indicator one division, the more sensitive is the balance.
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16. Prescription balances…
Capacity
 Is the maximum weight, which a balance can
weigh.
 The capacity of most class A and class B
prescription balance is 120g
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17. Prescription balances…
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18. Example
1. If a chlorpheniramine maleate tablet weighs
0.26gm, one-fourth of the same tablet weighs how
many milligrams? Since the answer is required in
milligrams, convert the weight ofthe tablet into
milligrams first.
0.26g=0.26x1000=260mg
1/4x260mg=65mg
Answer: 65mg
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19. Example…
2. Add 1.25g, 35mg and 80µg, and express the
results in milligrams.
Convert all the units into the same denomination
and then perform the computation.
1.25g=1250mg, and 80µg = 0.08mg
Therefore, 1250mg+0.08mg+35mg=1285.08mg
Answer=1285.08mg
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20. Example…
3. In calibrating a medicinal dropper, 2ml of a
pediatric solution resulted in 48 drops. If it is
desired to administer 0.08 mL of the medication to
a baby. approximately how many drops should be
given?
48 drops /2mL =Xdrops.0.08mL
X=1.922 or 2 drops
Answer =2 drops
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21. Example…
4. What is a minimum amount that can be weighed
on a class A prescription balance with a potential
error of not more than 10%
 %Error = 100*6mg/Q
 Q=100*6/10= 60mg
Answer = 60 mg
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22. Density, specific gravity and specific
volume
• Density (d) is mass per unit volume of a
substance.
• It is usually expressed as grams per cubic
centimeter (g/cc).
• Density may be calculated by dividing mass by
volume, that is:
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23. Example
•What is the density of hydrochloric acid
weighing 20mL and 40g?
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Density…

24. Specific Gravity
• Specific gravity (sp gr) is a ratio, expressed decimally,
of the weight of a substance to the weight of an equal
volume of a substance chosen as a standard, both
substances at the same temperature or the
temperature of each being known.
• Specific gravity may be calculated by dividing the
weight of a given substance by the weight of an equal
volume of water
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25. Specific Gravity…
 Because substances expand or contract at different
rates when their temperatures change, accurate work
necessitates allowing carefully for variations in the specific
gravity of a substance.
 In the USP, the standard temperature for specific
gravities is 25°C, except for that of alcohol, which is
15.56°C by government regulation.
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26. Specific Gravity…
 The density of a substance:
is a concrete number (1.8 g/mL in the example),
varies with the units of measure used
 Specific gravity:
A ratio between like quantities is an abstract
number (1.8 in the example).
Has no dimension and is therefore a constant
value for each substance (when measured under
controlled conditions).
The specific gravity of water is always 1.
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27. Specific Gravity…
• Substances that have a specific gravity of
less than 1 are lighter than water
• Substances that have a specific gravity
greater than 1 are heavier than water
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28. Specific Gravity…
Example 2
 If 52.5 mL of oil weighs 48.8g, what is the
specific gravity of the oil?
Answer
 52.5 mL of water weighs 52.5gm.
 Therefore, specific gravity of the oil =
48.8/52.5 = 0.929
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29. Specific Gravity…
Example-3: If 54.96mL of an oil weighs 52.78g,
what is the specific gravity of the oil?
 54.96 mL of water weighs 54.96 g
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30. Specific Gravity…
Example-4: If a liter of a cough syrup weighs
1285g, what is its specific gravity?
• 1000ml of water weighs 1000g
Specific gravity of cough syrup = 1285g/1000g
=
=1.285
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31. Calculating the specific gravity of liquids
• A pycnometer is a special glass bottle used to
determine specific gravity.
• To calculate the specific gravity of a liquid by means
of a specific gravity bottle, the container is filled and
weighed first with water and then with the liquid.
• By subtracting the weight of the empty container
from the two weights, we have the weights of equal
volumes, even though we may not know the volumes
exactly.
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32. Calculating the specific gravity of
liquids…
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33. Calculating the specific gravity of
liquids…
Exampe-2: A 50mL pycnometer is found to weigh 120g
when empty, 171g when filled with water, and 160g
when filled with an unknown liquid. Calculate the
specific gravity of the unknown liquid.
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34. Calculating the specific gravity of solids using
displacement methods
 To calculate the specific gravity of a solid heavier than
and insoluble in water, simply divide the weight of the
solid in air by the weight of water that it displaces
when immersed in it.
 The weight of water displaced (apparent loss of weight in
water) is equal to the weight of an equal volume of water.
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35. Calculating the specific gravity of solids
using displacement methods…
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36. Calculating the specific gravity of solids using
displacement methods….
Example-2: A glass weighs 12.64 g in air, 8.57 g when
immersed in water, and 9.12 g when immersed in an oil.
 Calculate the specific gravity of the oil
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37. Specific Volume
 Specific volume, in pharmaceutical practice, is
usually defined as an abstract number
representing the ratio, expressed decimally, of the
volume of an equal weight of another substance
taken as a standard, both having the same
temperature.
 Water is the standard for liquids and solids.
 It may be calculated by dividing the volume of a
given mass by the volume of an equal weight of
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38. Specific Volume…
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39. Specific Volume…
 Because specific gravity and specific volume are
reciprocals,
 a substance that is heavier than water will have a higher
specific gravity and a lower specific volume,
 whereas a substance that is lighter than water will have a
lower specific gravity and a higher specific volume.
 It follows, therefore, that we may determine the specific
volume of a substance by dividing 1 by its specific
gravity, and we may determine the specific gravity of
a substance by dividing 1 by its specific volume.
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40. Specific Volume…
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41. Use of Specific Gravity in Calculations of Weight and
Volume
 The weights of equal volumes and the volumes of equal
weights of liquids are proportional to their specific
gravities.
 To calculate, therefore, the weight of a given volume or
the volume of a given weight of a liquid, its specific
gravity must be known.
 When specific gravity is used as a factor in a calculation,
the result should contain no more significant figures than
the number in the factor.
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43. THANK YOU.
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