Pharmaceutical Calculations and Dosage Forms: Weights & Measures, Percentage Solutions, Powders, Liquid Formulations and Solubility Enhancement

Pharmaceutical Calculations and Dosage Forms: Weights & Measures, Percentage Solutions, Powders, Liquid Formulations and Solubility Enhancement

PHARMACEUTICAL CALCULATIONS

Metrology

During the dispensing of drugs, it is essential for a pharmacist to possess a sound and thorough knowledge of weights and measures, as accurate calculations are critical for ensuring correct dosing, patient safety, and therapeutic effectiveness. Metrology, the science of measurement, plays a vital role in pharmaceutical calculations, particularly in compounding and dispensing practices.

Systems of weights and measures used in pharmacy are broadly classified into two main types:

1. Imperial system
2. Metric system

1. Imperial System

The imperial system is an older system of weights and measures that was traditionally used in pharmacy. In this system, weight is defined as the gravitational force acting on a body and is directly proportional to its mass. For pharmaceutical purposes, the imperial system is divided into two subsystems for measuring weight and volume.

These are:
(a) Avoirdupois system
(b) Apothecaries’ system

(a) Avoirdupois System
In the avoirdupois system, the primary unit of weight is the pound (lb), and all other units of mass are derived from it. This system is mainly used where only weight measurements are required, especially in compounding.

Standard conversions are as follows:

• 1 pound (lb) = 16 ounces (oz)
• 1 pound = 7000 grains
• 1 ounce (oz) = 7000 ÷ 16 = 437.5 grains

Approximate metric equivalents:

• 437.5 grains = 1 ounce ≈ 28.35 g
• 7000 grains = 1 pound = 16 ounces ≈ 454 g
• 1 kilogram (kg) ≈ 2.2 pounds
• 1 grain ≈ 64.8 mg

(b) Apothecaries’ System
The apothecaries’ system includes both weight and volume measurements and was traditionally used in pharmaceutical compounding and in preparing concentrations for dilution. In this system, weight is measured in grains, while volume is measured in minims.

(i) Volume measurements:

• 1 teaspoonful (tsp) = 5 mL = 1 dram = 5 cubic centimeters (cc)
• 1 tablespoonful (tbsp) = 15 mL
• 29.57 mL = 1 fluid ounce (fl oz)
• 473 mL = 1 pint (pt) = 16 fluid ounces
• 946 mL = 1 quart = 2 pints
• 3784 mL = 1 gallon = 8 pints = 128 fluid ounces

(ii) Weight measurements:

• 1 grain = 64.8 mg
• 1 ounce = 480 grains ≈ 31.1 g

2. Metric System

The metric system is the most widely accepted system of measurement for weight and capacity in pharmacy. In India, the metric system was officially adopted in pharmaceutical practice from 1st April 1964 and is used in the Indian Pharmacopoeia. It is also employed in most countries worldwide, including the United States.

The metric system is based on decimal units, formed by combining standard prefixes such as kilo-, hecto-, deka-, deci-, centi-, and milli- with base units like gram, liter, and meter, making calculations simple and uniform.

Measurement of weight in the metric system:
The kilogram (kg) is the standard unit of weight, and all other units are derived from it.

• 1 kilogram (kg) = 1000 grams (g)
• 1 gram (g) = 1000 milligrams (mg)
• 1 milligram (mg) = 0.001 gram
• 1 microgram (µg or mcg) = 0.000001 gram
• 1 hectogram (hg) = 100 grams
• 1 decagram (dag) = 10 grams
• 1 decigram (dg) = 0.1 gram
• 1 centigram (cg) = 0.01 gram

Measurement of Volume or Capacity

For the measurement of volume or capacity in pharmaceutical calculations, the litre (L) is taken as the standard unit. All other units of volume are derived from it, making calculations simple and systematic.

• 1 litre (L) = 1000 millilitres (mL)

The following are apothecary and metric system conversion problems, solved using the ratio and proportion method. These conversions are commonly used in pharmaceutical practice to ensure accuracy in compounding and dispensing.

• 2000 grains = 4.167 oz (AP)
• 500 g = 16.077 oz (AP)
• 500 mg = 7.716 grains
• 100 fluid ounces = 6.25 pints
• 500 fluid ounces = 3.906 gallons
• 4.5 oz (AP) = 139.95 g
• 3 grains = 194.4 mg
• 20,000 mL = 5.284 gallons
• 3 pints = 1419 mL
• 119 mL = 4.024 fluid ounces
• 2.5 gallons = 320 fluid ounces
• 5000 grains = 10.417 oz (AP)
• 25 pints = 3.125 gallons
• 1500 mL = 3.171 pints
• 6 fluid ounces = 177.42 mL
• 0.75 gallon = 2838.75 mL
• 1000 grains = 2.083 oz (AP)
• 3.25 gallons = 26 pints
• 350 grains = 22,680 mg
• 2.5 oz (AP) = 1200 grains
• 1.5 teaspoonful = 7.5 mL
• 12.5 mL = 2.5 teaspoonful
• 1.5 fluid ounces = 44.355 mL
• 500 mg = 7.716 grains
• 500 fluid ounces = 3.906 gallons
• 375 mL = 12.682 fluid ounces
• 24 fluid ounces = 1.5 pints
• 275 g = 8.842 oz (AP)
• 500 mL = 33.333 tablespoonfuls
• 1 drop = 0.05 mL
• 1 teaspoonful = 5 mL
• 1 tablespoonful = 15 mL
• 1 wineglassful = 60 mL
• 1 tumblerful = 240 mL
• 1 inch = 2.54 cm
• 1 pint = 473 mL
• 1 gallon = 3785 mL
• 1 quart = 946 mL