14th February 2024
Drug calculations are a common feature of Med School interviews. Calculation stations appear in MMIs, while some schools, like Keele University, require candidates to complete a maths test as part of the admissions process. This blog will take you through some of the more clinically useful calculations that could come up.

How Are Drug Calculations Used?

Many medical schools consider simple math calculations essential to your future studies and the profession as a whole, highlighting the potential dangers of incorrect math applications.

Keele Medical School

Keele University‘s rationale for assessing calculation skills is as follows:

“It is very important that doctors are able to use simple maths to solve problems during their
work. Incorrect calculations can have very serious consequences for patient safety. Therefore we have introduced a maths test to ensure that students accepted to study medicine are able to undertake the type of calculation needed.”

Keele also gives more information about what you can expect during the admissions maths test:

Questions “will all be related to clinical scenarios, although no clinical knowledge is required to answer the questions.”

“The clinical maths test consists of 20 maths questions to be completed in 30 minutes. Those who qualify for the UKCAT special educational needs [UKCATSEN] test will be given extra time on the day. There are no trick questions and the answers are all realistic. All of the questions are based on the sort of calculations doctors do every day using basic maths skills.”

Keele University has also released a document with some practice questions and complete worked answers. These will give you an idea of the difficulty level of you can expect. You should practise these in timed conditions as part of your interview prep.

Birmingham Medical School

Birmingham says this about their calculation station, which is completed on a separate day from the rest of your online interview:

“You will be asked to undertake simple mathematical calculations involving data that has clinical relevance. The mathematical skills that are being tested are at GCSE level and below.

“The sophistication of each task is to recognise which piece or pieces of data need to be manipulated at a particular stage and to determine the precise mathematical approach that needs to be applied. There will be a number of stages in the calculations and to establish the order in which these are performed is important too.”

The tasks can include dosage calculation, concentration/volume calculation, unit conversion and percentage concentration calculation, among others.

Note: Whether you are allowed to use a calculator or not depends on the medical school.

Sunderland Medical School

Sunderland runs a Numeracy Test as part of its interview selection process. It consists of a 40-minute online test that contains approximately 20 questions with some having multiple sections.

According to the university, the level of numeracy required for the test is that for GCSE maths. It can include drug dosage calculations and concentration calculations.

You can practice some of their questions here.


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How Do You Convert Between Units?

In clinical practice, one of the most useful types of calculations to know is converting between units.


You prescribe a patient 1 g of paracetamol. How many milligrams is this?

A: 1 g = 1000 mg  

Drug Calculations Summary Table

Unit Gram Equivalents Exponential Form
Kilogram (kg) 1000.0 g 103 g
Gram (g) 1.0 g 1 g
Milligram (mg) 0.001 g 10-3 g
Microgram (μg) 0.000,001 g 10-6 g
Nanogram (ng) 0.000,000,001 g 10-9 g

You may find it helpful to write out the number with a decimal point after it. The decimal point moves three places to the left for every unit you move up (e.g. from grams to kilograms) and three places to the right every time you move down a unit (e.g from grams to milligrams). You need to move the decimal point six places if you move through two units (e.g from milligrams to nanograms).

How Do You Work Out Concentrations?

Some drug calculations might involve working out the volume of solution needed to give the required dose of a drug. One way to tackle these types of questions is to set up a simple equation where X is the variable you are trying to find. For example:

You are asked to give a patient weighing 50 kg a 1 mg/kg IV injection. The syringe contains 100 mg in 2 ml. What volume of the solution in the syringe do you need to give?

So the patient weighs 50 kg and you need to give 1 mg per kg. 1 x 50 mg = 50 mg. Therefore you need to give a total dose of 50 mg.

The question states there is 100 mg in 2 ml. You need to give 50 mg and therefore need to find out what volume contains 50 mg.

You can set up an equation where X is the volume of the solution you are trying to find:

100 mg = 50 mg
  2mls       X mls

Rearrange the equation to find X:

X = 50 mg x 2 mls
              100 mg

(X= 1ml)

Percentage Concentrations

Some questions might give you a concentration in the form of a percentage – for example, a patient is given a 5% solution of a drug. By convention, this means there are 5 g of the drug in every 100 ml. You can then use this information to work out what volume of a solution you need to give for the correct dose.

An example could be:

You are asked to give a patient 10 g of the drug WondaDrug. This comes as a 5% solution in bags containing 1 L. What volume of the 1 L bag do you need to give?

5% means there are 5 g of WondaDrug in every 100 ml.

100ml  X   
5g          10 g

Rearrange the equation to find X:

X = 100 x 10

(X= 200 ml)

Here is another example:

You are asked to give a patient 1ml of 1% lidocaine. How many mg are you giving the patient?

1% means there is 1 g in 100 mL. Therefore there is 1000 mg in 100 mL, and there is 10 mg in every 1 mL.

Resultantly, you are administering 10mg of lidocaine to the patient.


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