Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
A solution has a ratio strength of 1:1000. You need 0.2 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
A vial holds 250 mg of powder. You add 3.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 187.5 mg. Draw up the dose: what volume V do you give?
How many milligrams of drug m are in 100 mL of a 2% (w/v) solution?
The prescription is 940 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1000 mL was ordered over 8 hours. After 5 hours you find that 420 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
A bag contains 4 g of a drug in 1000 mL. The order is 1.5 mg per minute. At what rate R do you set the pump, in mL/h?
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 107 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 87 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
Answer: V = 0.2 mL
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.
Answer: V = 3 mL
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.
Answer: m = 2000 mg
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Answer: V = 0.94 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
On this 1 mL syringe every small line is 0.01 mL.
Answer: R = 140 mL/h
Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
Answer: R = 22.5 mL/h
Dose-based infusions: concentration = amount of drug in the bag/bag volume. Pump rate (mL/h) = dose per hour/concentration, and dose per hour = mL/h × concentration. Convert per-minute doses to per-hour (× 60) and keep the mass units the same (1 g = 1000 mg, 1 mg = 1000 mcg).
Answer: V = 1.3 mL
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: R = 26.1 mL/h
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
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