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Pharmacy Calculations Practice for MPharm Students: 10 Worked Questions

Ten original pharmacy calculation questions for MPharm students, fully worked with the common mistakes: doses, unit conversions, concentrations, dilutions, infusions, displacement, paediatric and renal dosing.

By Umar Majid ·

You get good at pharmacy calculations by working through realistic questions step by step, writing units on every line and learning from your mistakes. Below are 10 original practice questions covering the main types you'll meet in MPharm exams, the Oriel numeracy test and, later, Part 1 of the GPhC registration assessment.

Cover the working and have a go at each one with a calculator and paper. If you get one wrong, write down why. Over time, the pattern of your mistakes tells you more than your score does.

1. Weight-based dose

A patient weighing 82 kg is prescribed enoxaparin 1.5 mg/kg once daily for treatment of a deep vein thrombosis. You have pre-filled syringes containing 150 mg/mL. What dose in mg is needed, and what volume is that?

Working:

  • Dose = 1.5 mg/kg × 82 kg = 123 mg
  • Volume = 123 mg ÷ 150 mg/mL = 0.82 mL

Where people go wrong: assuming every syringe is 100 mg/mL. The higher-strength enoxaparin syringes are 150 mg/mL.

2. Unit conversion

A patient is prescribed digoxin 0.0625 mg once daily. You have digoxin elixir 50 micrograms/mL. What volume is each dose, and how much should you supply for 28 days?

Working:

  • 0.0625 mg × 1,000 = 62.5 micrograms
  • Volume per dose = 62.5 ÷ 50 = 1.25 mL
  • 28 days = 1.25 mL × 28 = 35 mL

Where people go wrong: dividing 0.0625 by 50 without converting first. Get both figures into the same unit before you divide.

3. Percentage concentration

A doctor needs 150 mg of lidocaine. You have lidocaine 2% w/v injection. What volume contains 150 mg?

Working:

  • 2% w/v = 2 g in 100 mL = 2,000 mg in 100 mL = 20 mg/mL
  • Volume = 150 mg ÷ 20 mg/mL = 7.5 mL

Where people go wrong: reading 2% as 2 mg/mL. A quick rule for % w/v is to multiply by 10 to get mg/mL. So 1% is 10 mg/mL and 2% is 20 mg/mL.

4. Dilution

You need to make 500 mL of chlorhexidine gluconate 0.05% w/v from a 20% w/v concentrate. What volume of concentrate do you need?

Working: use C1 × V1 = C2 × V2.

  • 20% × V1 = 0.05% × 500 mL
  • V1 = 25 ÷ 20 = 1.25 mL of concentrate, made up to 500 mL

Where people go wrong: putting the numbers the wrong way round and getting 200,000 mL. A strong concentrate always needs a small volume.

5. Infusion rate in micrograms/kg/minute

A 70 kg patient is prescribed dobutamine at 5 micrograms/kg/minute. The infusion is 250 mg in 50 mL. What rate in mL/hour should the pump be set to?

Working:

  • Dose per minute = 5 × 70 = 350 micrograms/minute
  • Dose per hour = 350 × 60 = 21,000 micrograms = 21 mg/hour
  • Concentration = 250 mg ÷ 50 mL = 5 mg/mL
  • Rate = 21 ÷ 5 = 4.2 mL/hour

Where people go wrong: forgetting to convert minutes to hours, which gives an answer 60 times too small.

6. Quantity to supply

A patient is prescribed beclometasone 200 micrograms twice daily. You have an inhaler delivering 100 micrograms per actuation, with 200 actuations per inhaler. How many inhalers do you supply for 8 weeks?

Working:

  • Puffs per dose = 200 ÷ 100 = 2
  • Puffs per day = 2 × 2 = 4
  • Puffs in 8 weeks = 4 × 56 days = 224
  • Inhalers = 224 ÷ 200 = 1.12, so supply 2 inhalers

Where people go wrong: rounding 1.12 down to 1. You can't supply part of an inhaler, so round up to cover the full course.

7. Displacement volume

A benzylpenicillin 600 mg vial has a displacement volume of 0.4 mL. You reconstitute it with 5.6 mL water for injection. What is the concentration, and what volume gives a 300 mg dose?

Working:

  • Final volume = 5.6 mL + 0.4 mL = 6 mL
  • Concentration = 600 mg ÷ 6 mL = 100 mg/mL
  • Volume for 300 mg = 300 ÷ 100 = 3 mL

Where people go wrong: ignoring displacement. If you added 6 mL of water instead, the final volume would be 6.4 mL (93.75 mg/mL), and 3 mL would only give about 281 mg. In practice, check the product information or your local guide.

8. Paediatric dose

A child weighing 13 kg with croup is prescribed a single dose of oral dexamethasone 0.15 mg/kg. You have dexamethasone oral solution 2 mg/5 mL. What volume should be given, to one decimal place?

Working:

  • Dose = 0.15 mg/kg × 13 kg = 1.95 mg
  • Concentration = 2 mg ÷ 5 mL = 0.4 mg/mL
  • Volume = 1.95 ÷ 0.4 = 4.875 mL, so 4.9 mL to one decimal place

Where people go wrong: rounding too early. Round the dose to 2 mg first and you get 5 mL. Unless the question says otherwise, round once, at the end.

9. Renal function and dose selection

A 70-year-old man weighs 72 kg and has a serum creatinine of 130 micromol/L. Use the Cockcroft-Gault equation to estimate his creatinine clearance, then choose the dose of Drug X from this table (a made-up table for practice).

Creatinine clearance Dose of Drug X
More than 50 mL/min 500 mg twice daily
30 to 50 mL/min 250 mg twice daily
Less than 30 mL/min 250 mg once daily

CrCl (mL/min) = (140 − age) × weight (kg) × 1.23 (male) ÷ serum creatinine (micromol/L)

Working:

  • (140 − 70) = 70
  • 70 × 72 × 1.23 = 6,199.2
  • 6,199.2 ÷ 130 = 47.7, so 48 mL/min
  • Dose = 250 mg twice daily

Where people go wrong: entering serum creatinine as 0.13 mmol/L instead of 130 micromol/L. That gives about 47,700 mL/min, which is impossible, and would push you into the highest dose band. Check which units the equation expects, and use the right constant: 1.23 for men, 1.04 for women. Our Cockcroft-Gault and renal dosing guide goes into more detail.

10. Ratio strength

Adrenaline 1 in 1,000 is used for intramuscular injection in anaphylaxis. (a) What is its concentration in mg/mL? (b) What volume gives an adult dose of 500 micrograms? (c) What is the concentration of adrenaline 1 in 10,000 in micrograms/mL?

Working:

  • (a) 1 in 1,000 = 1 g in 1,000 mL = 1,000 mg in 1,000 mL = 1 mg/mL
  • (b) 500 micrograms = 0.5 mg, so 0.5 mg ÷ 1 mg/mL = 0.5 mL
  • (c) 1 in 10,000 = 1 g in 10,000 mL = 0.1 mg/mL = 100 micrograms/mL

Where people go wrong: mixing up 1 in 1,000 and 1 in 10,000. The second is ten times weaker.

All 10 answers

Question Type Answer
1 Weight-based dose 123 mg, 0.82 mL
2 Unit conversion 1.25 mL per dose, 35 mL
3 % w/v concentration 7.5 mL
4 Dilution 1.25 mL
5 Infusion rate 4.2 mL/hour
6 Quantity to supply 2 inhalers
7 Displacement 100 mg/mL, 3 mL
8 Paediatric dose 4.9 mL
9 Renal dosing 48 mL/min, 250 mg twice daily
10 Ratio strength 1 mg/mL, 0.5 mL, 100 micrograms/mL

For more examples grouped by type, see our guide to the 9 GPhC calculation types.

Common questions

How often should I practise calculations as an MPharm student? Little and often. Ten to fifteen minutes a day is enough to keep the methods fresh.

Do I need to learn the Cockcroft-Gault equation? You should be able to use it confidently. Exam questions often give you the equation, but you still need to apply it quickly and correctly.

When should I round? At the end, unless the question tells you to round a dose first or the answer has to be something you can actually supply, like a whole inhaler.

Will these help with the Oriel numeracy test? Yes, for method, units and speed. The Oriel numeracy test is 10 questions in 20 minutes with no clinical context, so practise working quickly.

Want more practice?

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