Drug calculations — formulas
Drug calculation formulas:
worked examples for drug calculations
Here are the drug calculation formulas for dosage, dilution, infusion rate, unit conversion, percentages, mmol and IU, with an explanation and a worked example for each. Bookmark the page and look things up when you need to.
Dosage
The basic formula for working out how much of a drug to give, whether it is tablets, injections or an oral liquid.
Amount = (500 ÷ 250) × 1 = 2 tablets
Dilution
The dilution formula is used to work out how to dilute a solution of one concentration to another concentration.
Here C1 and V1 are the concentration and volume before dilution, and C2 and V2 are the concentration and volume after dilution.
100 × V1 = 20 × 50 → V1 = 1000 ÷ 100 = 10 ml stock solution, with diluent added to make up to 50 ml.
Infusion rate
Infusion rate in ml/h is used to set infusion pumps, and is worked out from volume and time.
Infusion rate = 1000 ÷ 8 = 125 ml/h
Drip rate (ml and drops)
Used when the infusion rate has to be worked out in drops per minute instead of ml/h, for example when no infusion pump is used.
Drops/min = (500 × 20) ÷ 240 = about 41.7 drops/min
Unit conversion
Common unit conversions that are often needed as an intermediate step in a drug calculation.
Volume: 1 litre = 1000 ml
Time: 1 hour = 60 minutes
The method is always the same: multiply by 1000 to go to a smaller unit, and divide by 1000 to go to a larger unit.
Percentage solutions
Drugs are sometimes labelled as a percentage, for example a glucose solution. The percentage is the number of grams in 100 ml of solution.
Amount = (5 × 500) ÷ 100 = 25 g of glucose
Mmol and IU
Some drugs are dosed not by weight but in millimoles (mmol), for example electrolytes such as potassium, or in international units (IU), for example insulin and heparin. The conversion factor between mmol and mg differs between substances because it depends on the molecular weight, so there is no general formula. The conversion is always based on the properties of the drug in question, which are given in the question or on the product information.
Frequently asked questions about drug calculation formulas
What is the most important formula in drug calculations?+
There is no single most important formula, but the basic dosage formula (prescribed dose ÷ available strength × amount per unit) comes up in the most situations, from tablets to injections and infusions.
How do you calculate a dilution in drug calculations?+
A dilution is calculated with the formula C1 × V1 = C2 × V2, where C is concentration and V is volume before and after dilution. You rearrange to find the unknown, usually the volume of stock solution to draw up.
How do you convert between mg and micrograms?+
1 mg is 1000 micrograms. To convert mg to micrograms, multiply by 1000, and to convert micrograms to mg, divide by 1000.
How do you calculate an infusion rate in ml/h?+
Infusion rate in ml/h is the total volume in ml divided by the time in hours: Infusion rate = Volume in ml ÷ Time in hours.
What do mmol and international units (IU) mean in drug calculations?+
Mmol (millimoles) is a measure of amount of substance, used for example for electrolytes such as potassium and sodium. International units (IU) measure biological activity and are used for drugs such as insulin and heparin, where the amount cannot always be expressed by weight.
The formulas on this page are a study tool for practising drug calculations. They do not replace your course materials or your university's, employer's or NHS trust's own guidance, which may differ slightly. Always follow your course and local policy.
Go deeper, topic by topic
Theory, examples and calculators for each topic.
Unit conversion: mg, micrograms, g and ml →
Infusion rate: work out ml per hour →
Body surface area and dose per kg and per m² →
mmol, units and ratios in drug calculations →
Timing and daily dose calculations →
Tablets and oral liquids →
Body surface area calculator (Mosteller) for dose per m² →
Percent to mg/ml: converter and explanation →
Infusion time calculator: how long does an infusion take? →
Daily dose calculator: dose per kg and per administration →
How do you calculate mg per ml? Formula and calculator →
How many drops are in a ml? Drop factor explained →
Put the formulas to work on practice questions
The formulas only stick when you use them. Dos is a practice app for drug calculations, with practice tests of ten questions across every topic, a built-in calculator next to each question and statistics per topic.
