Nursing Math: practice problems and exam questions

The math course of a nursing programme: metric, household and weight conversions, temperature and the 24-hour clock, rounding rules and dimensional analysis, followed by the dose, IV-rate and fluid calculations they are used for. All values are practice numbers, never clinical guidance.

Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.

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

Topics in this course

  1. Nursing math & unit conversionsmetric, weight and household units · temperature, 24-hour clock and rounding · dimensional analysis chainscalculations
  2. Dosage calculationstablets and liquids · weight-based doses · doses and concentrationscalculations
  3. IV infusion ratespump rate · drip rate · time and dose ratecalculations
  4. IV fluids & fluid balancemaintenance fluids (Holliday–Segar 4-2-1) · intake and output balance · infusion completion timecalculations
  5. Pediatric & critical-care dosingpediatric weight-based doses (mg/kg/day divided) · heparin and insulin infusions (units/h, mL/h) · titrated drips (mcg/kg/min to mL/h)calculations
  6. Pharmacy calculationspercentage strength and ratio strength · reconstitution and concentrations · alligationcalculations

Exam tips for Nursing Math

  • Put every quantity in the same unit before you calculate; a smaller unit gives a bigger number.
  • Write conversions as fractions so the unwanted units cancel, and round only the final answer.
  • Estimate first: a dose of 30 tablets or 0.003 mL means a conversion went wrong.

Worked examples

Nursing math & unit conversionsEasy
180 mL? cups1 cup = 8 fl oz = 240 mL

Practice exercise (made-up values, not clinical guidance). A dose of 180 mL is to be measured with a household measure. Using 1 cup = 8 fl oz = 240 mL, how many cups n is that?

180 mL1 cup = 8 fl oz = 240 mL

Find n (cup)

Show hints
  1. Find how many mL one cup holds.
  2. 1 cup = 8 fl oz = 240 mL.
  3. 180/240.
Show the answer and the step-by-step solution

Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.

Equivalent

1 cup = 8 fl oz = 240 mL

Divide

n = 180/240 = 0.75

Answer

n = 0.75 cup
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)IV flow rate and drip rate calculatorWeight-based dose calculator (mg/kg)Body surface area calculator (BSA)mcg/kg/min to mL/h calculator (weight-based infusion)Reconstitution calculator (powder volume and concentration)Pediatric safe dose range calculator (mg/kg/day)IV infusion time calculator (when will the infusion finish?)Nursing unit converter (mg, mcg, kg, lb, mL, tsp, °F, °C)Intake and output calculator (fluid balance)Parkland formula calculator (burn fluid resuscitation)Alligation calculatorHeparin infusion rate calculatorMaintenance fluids calculator (Holliday–Segar)

Related courses

NCLEX-style dosage calculationsNCLEX-style practice questions (RN)NCLEX-PN-style practice questions (LPN/LVN)Pharmacy technician math practicePediatric and Critical-Care DosingMaternity NursingPediatric NursingPharmacy Calculations
Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.