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Test your drug calculation skills with the following drug calculation practice questions and explanations.
Each question is written to reflect a realistic clinical scenario with a clear, step-by-step worked solution to allow you to understand the reasoning behind the correct answer.
Case 1
Question
A 45-year-old man is admitted with cellulitis and sepsis. He is prescribed vancomycin 15 mg/kg IV, to be infused over 2 hours. He weighs 95 kg.
Vancomycin comes as 500 mg vials, each reconstituted with 10 mL of water for injection, before being further diluted into 250 mL of 0.9% sodium chloride.
What volume (mL) of reconstituted vancomycin is needed to prepare this infusion?
Answer
28.5 mL
Explanation
The patient needs vancomycin 15 mg/kg IV, and they weigh 95 kg.
The total dose required is 15 x 95 = 1425 mg
We know each vial is reconstituted with 10 mL of water and contains 500 mg of vancomycin.
The concentration of the reconstituted vancomycin solution can then be calculated:
- 500 mg / 10 mL = 50 mg/mL
Now, calculate how much of the reconstituted solution is needed for the full dose:
- 1425 mg (total dose) / 50 mg/mL (concentration of the solution) = 28.5 mL
You need to draw up 28.5 mL of the reconstituted vancomycin solution to prepare the infusion.
Case 2
Question
A 7-year-old girl with osteosarcoma is to be started on IV morphine infusion for severe bone pain. The recommended dose is 20 micrograms/kg/hour. She weighs 21 kg.
Morphine is available as 50 mg/50 mL solution for infusion.
What is the required infusion rate (mL/hr) of morphine?
Answer
0.42 mL/hr
Explanation
To determine the hourly dose required, multiply the recommended dose by the weight: 20 x 21 kg = 420 micrograms/hr
To convert micrograms to mg, divide by 1000: 420 / 1000 = 0.42 mg/hr
The concentration of morphine is 50 mg/50 mL, which can be simplified by dividing the dose by the volume: 50 mg / 50 mL = 1 mg/mL
As 1 mL of morphine solution contains 1 mg, 0.42 mL must contain 0.42 mg.
Therefore, the infusion rate in mL/hr is 0.42 mL/hr.
Tip: the infusion rate can also be calculated by multiplying the hourly dose by the concentration (0.42 x 1 = 0.42 mL/hr)
Case 3
Question
A patient is prescribed warfarin 8 mg once daily for atrial fibrillation.
Due to a raised INR, the dose is reduced by 25%.
What is the new dose (mg) of warfarin to be administered?
Answer
6 mg
Explanation
Firstly, to determine the amount to reduce by, calculate 25% of the current dose. This is done by multiplying the current dose by 0.25: 8 x 0.25 = 2 mg
Then, to calculate the new dose, subtract the dose reduction from the original dose: 8 – 2 = 6 mg
Tip: this can alternatively be calculated in one step by multiplying the original dose by 0.75 (as you will then be administering 75% of the total dose after the 25% reduction): 8 x 0.75 = 6 mg
Case 4
Question
A patient requires treatment with intravenous aciclovir for encephalitis at a recommended dose of 10 mg/kg three times a day.
The patient weighs 75 kg.
What is the total daily dose (g) of aciclovir required?
Answer
2.25 g
Explanation
The patient weighs 75 kg, and the recommended dose is 10 mg/kg three times a day.
To calculate the dose required, multiply the dose per kilogram by the patient’s weight: 10 x 75 = 750 mg
Next, to calculate the total daily dose, multiply the dose required by the number of doses per day: 750 x 3 = 2250 mg
Finally, to convert milligrams to grams, divide the answer by 1000: 2250 / 1000 = 2.25 g
Case 5
Question
A 47-year-old woman is being discharged from the acute medical unit following a provoked deep vein thrombosis. She is to be prescribed a direct oral anticoagulant for 12 weeks.
The recommended dose of apixaban is 5 mg twice daily. Apixaban is available as 2.5 mg tablets which cost £2.45 per box of 20 tablets.
The recommended dose of dabigatran 150 mg twice daily. Dabigatran is available as 150 mg capsules which cost £45.90 per box of 60 capsules.
What is the difference in cost (£) between a 12 week course of apixaban and dabigatran?
Answer
£96.05
Explanation
Apixaban
To determine the number of tablets required, multiply the number of tablets per day by the number of days each week and by the number of weeks required: 4 tablets x 7 days x 12 weeks = 336 tablets
To determine the number of boxes required, divide the number of tablets required by the number of tablets in each box: 336 / 20 = 16.8 boxes
As a partial box cannot be given, round up to the nearest whole number = 17 boxes
To determine the cost, multiply the number of boxes by the cost per box: 17 boxes x £2.45 = £41.65
Dabigatran
To determine the number of capsules required, multiply the number of capsules per day by the number of days each week and by the number of weeks required: 2 capsules x 7 days x 12 weeks = 168 tablets
To determine the number of boxes required, divide the number of capsules required by the number of capsules in each box: 168 / 60 = 2.8 boxes
As a partial box cannot be given, round up to the nearest whole number = 3 boxes
To determine the cost, multiply the number of boxes by the cost per box: 3 boxes x £45.90 = £137.70
Cost difference
Lastly, to determine the difference in cost, subtract the cost of apixaban from the cost of the dabigatran: £137.70 – £41.65 = £96.05
Looking for more drug calculation practice questions?
The Geeky Medics drug calculation case collection contains over 100 cases to help you improve your drug calculation and numeracy skills.
Our drug calculation cases are ideal for:
- Medical, nursing, pharmacy, paramedic and midwifery students preparing for numeracy or prescribing assessments
- Clinicians undertaking independent prescribing/non-medical prescribing (NMP) courses
- Experienced clinicians returning to practice who need a rapid refresher
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