Introduction to Pharmaceutical Calculation

Units of measurement and metric conversion

Measurement• is the process of obtaining quantitative

information about the physical world.

Unit of measurement• any division of quantity accepted as a

standard of measurement or exchange.

Units of measurement used in Pharmacy

1. Avoirdupois System • mainly used in measuring bulk medication

encountered in manufacturing.• Commonly used to measure weight• Standard measure for weight is grain (gr)

Pound Ounces Grains

(lb) (oz) (gr)

1 = 16 = 7000

1 = 437.5

Units of measurement used in Pharmacy

2. Apothecary System• Commonly used for prescribing and

dispensing medication• Commonly used for measuring volume• Standard of measure for weight is grain

(gr)• Standard of measure for volume is minim

( )

Apothecary System

• WeightPound Ounces Drams Scruples Grain

(lb) ( ) (ʒ) ( ϶ ) (gr)

1 = 12 = 96 = 288 = 57601 = 8 = 24 =

480

1 = 3 = 60

1 = 20

Apothecary System

• VolumeGallons Pints Fluid Fluid Minims

Ounces Drams

(gal) (pt) (f ) (f ʒ)( )

1 = 8 = 128 = 1024 = 61,440

1 = 16 = 128 =7,680 1 = 8 =

480 1 = 60

Units of measurement used in Pharmacy

3. Metric System • is based on the decimal system in which

everything is measured in multiples or fractions of 10.

• major systems of weights and measurement used in medicine.

• Uses standard measures: Gram for weight (g) Liter for volume (l) Meter for length or distance (m)

Metric conversion

• process of restating a metric measurement in a larger or smaller metric unit of measurement.

Ex: converting from kilograms to grams

Metric units are denoted by prefixes• Greek prefixes- multiplier• Latin prefixes - fractions of the base unit

Metric conversion

Tips:1. Understand the different units of

measurement and what they measure (example: gram for weight).

2. Memorize the relationship between the units of measurements 1 kg = 1000 g.

3. Know where to move the decimal point to convert accurately.

Unit Abbrevia-tion

Fraction Exponent Decimal Word

Micro mc 1/1,000,000 10-6 0.000001 Millionth

Milli m 1/1,000 10-3 0.001 Thousandth

Centi c 1/100 10-2 0.01 Hundredth

Deci d 1/10 10-1 0.1 Tenth

Base unit g,m,l 1 100 1 One

Deka da 10 101 10 Ten

Hecto h 100 102 100 Hundred

Kilo k 1000 103 1000 Thousand

Prefixes with Standard Measures

Length: standard measure is meter

1 kilometer (km) = 1000 meters (m)

1 meter (m) = 100 centimeters (cm)

1 centimeter (cm) = 1 millimeter(mm)

1 meter (m) = 1000 millimeter (mm)

Prefixes with Standard Measures

Volume: the standard measure is liter (L)

1 Liter (L) = 1000 milliliter (ml)

1 Deciliter = 100 milliliter (ml)

1 Centiliter = 10 milliliter (ml)

1 Liter = 1, 000, 000 microliter (mcl)

10 Deciliter = 1 liter (L)

100 Centiliter = 1 liter (L)

Prefixes with Standard Measures

Weight: Standard measure is gram (g)

1 Kilogram (kg) = 1000 grams (g)

1 Gram (g) = 1000 milligrams (mg)

1 Centigram (cg) = 10 milligrams (mg)

1 Decigram (dg) = 100 milligrams (mg)

1 milligram (mg) = 1,000 micrograms (mcg)

1 gram (g) = 1,000,000 micrograms (mcg)

Prefixes with Standard Measures

Length : Standard measure is meter (m)

1 Kilometer = 1000 meters (m)

1 Meter (m) = 100 centimeter (cm)

1 Meter (m) = 10 decimeter (dm)

1 Meter (m) = 1000 millimeter (mm)

Conversion

Example 1:

How many minims are there in 25 fluid ounces?

25 fl x 8 fl ʒ x 60 = 12,000

1 fl 1 fl ʒ

Example 2:

How many ounces are 465 scruples?

465 ϶ x 1ʒ x 1 = 19.375

3϶ 8ʒ

Convert the following

1. 30 ml = _________ fluid ounces

2. 855 ml = ________ pints

3. 92 gr = _________ ounces (apothecary)

4. 2.8 kg = ________ mg

5. 75 cm = ________ dm

6. 6 km = _________ cm

7. 453 mm = _______ m

Convert the following

8. 0.00085 dg = _________ mcg

9. 100 mm = ___________ cm

10. 15 km = ___________m

11. 2,846,230 mcl = ______L

12. 2 kg = _____________cg

13. 56,000 mm = ________km

14. 5 kg = ______________dg

Sample Problems

1. The prescription order calls for preparation of 1.5g of menthol and salicylic acid (equal quantity) in an ointment base. Express the quantity of each ingredients in mg.

Sample Problems

2. Abdul Azziz needs to take Amoxicillin 500mg 1 capsule 3 times per day for 7 days to treat his chest infection. How much amoxicillin will he consume during the course of antibiotic treatment? Express the answer in grams (g).

Temperature

Scales of Temperature Measurement

1. Celsius – °C- also known as Centigrade

- scale was devised by dividing the range of temperature between the freezing and boiling temperatures of pure water at standard atmospheric conditions (sea level pressure) into 100 equal parts

2. Fahrenheit – °F

-non-metric temperature scale was devised and evolved over time so that the freezing and boiling temperatures of water are whole numbers, but not round numbers as in the Celsius temperature scale.

3. Kelvin – K

- temperature scale is an extension of the degree Celsius scale down to absolute zero, a hypothetical temperature characterized by a complete absence of heat energy.

Mathematical Formula for Conversion

Celsius to Fahrenheit: F = C x (9/5) + 32

Fahrenheit to Celsius: C = (F - 32) x (5/9)

Celsius to Kelvin: K = degree Celsius + 273.15

Kelvin to Celsius: Celsius = K - 273.15

Sample Problems

1. Convert 35°C to °FFormula : F = C x (9/5) + 32

° F = 35 x (9/5) + 32

= 35 x 1.8 + 32

= 95 °F

2. Convert 112 °F to °C° C = (F - 32) x (5/9)

= (112 F – 32) x 0.55

= 44 ° C

Common Pharmaceutical Equivalents

 Solids• 1 ounce (oz) = 28.35 g• 1 pound (lb) = 454 g• 1 kilogram = 2.2 lbs

Liquids• 1 gallon = 3785 ml • 1 quart = 946 ml• 1 pint = 473 ml• 1 fluid ounce (fl) = 29.57 ml, rounded to 30 ml• 1 teaspoonful (tsp ) = 5 ml• 1 tablespoonful (tbsp )= 15 ml• 1 milliliter (ml) = 20 drops (gtts)