Pharmacy Calculations: practice problems and exam questions

Percentage and ratio strength, reconstitution with powder volume, multi-strength labels and alligation, as practice exercises for pharmacy and nursing students.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Pharmacy calculationspercentage strength and ratio strength · reconstitution and concentrations · alligationcalculations
  2. Dosage calculationstablets and liquids · weight-based doses · doses and concentrationscalculations
  3. Clinical pharmacokineticshalf-life, levels and loading doses · clearance, Vd, S and F · regimen design and renal adjustmentcalculations

Exam tips for Pharmacy Calculations

  • 1% w/v is 1 g per 100 mL, which is 10 mg per mL.
  • After reconstitution, divide by the final volume, not by the diluent alone.
  • In alligation the parts cross: the higher strength gets T − L parts.

Worked examples

Pharmacy calculationsEasy
0123455 mL

A solution is 0.5% w/v. You need 9 mg of the drug. Draw up the volume in the syringe: what volume V is that?

0.5% w/v9 mg

Find V (mL)

Show hints
  1. x% w/v means x g in 100 mL.
  2. 0.5% w/v = 5 mg/mL.
  3. On this 5 mL syringe every small line is 0.1 mL.
Show the answer and the step-by-step solution

Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.

Strength in mg/mL

0.5 g/100 mL = 5 mg/mL

Volume

V = 9/5 = 1.8 mL

Answer

V = 1.8 mL
Dosage calculationsMedium
17 kgBSA = 0.86 m²250 mg/m²D = ? mg

A patient weighing 17 kg has a body surface area of 0.86 m². The prescription is 250 mg/m². Find the dose D in mg.

17 kgBSA = 0.86 m²250 mg/m²

Find D (mg)

Show hints
  1. The order is per m² of body surface area.
  2. D = dose per m² × BSA. The weight is not needed.
  3. 250·0.86.
Show the answer and the step-by-step solution

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 250·0.86 = 215 mg

Answer

D = 215 mg

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Dosage calculator (desired over have)Weight-based dose calculator (mg/kg)Body surface area calculator (BSA)Reconstitution calculator (powder volume and concentration)Loading dose and maintenance dose calculator (pharmacokinetics)Alligation calculator

Related courses

Nursing MathClinical PharmacokineticsPharmacy technician math practicePharmacologyLab Values for NursesMaternity NursingPediatric and Critical-Care DosingNCLEX-style dosage calculations
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