Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. What is the concentration C in mg/mL after reconstitution?
Practice exercise (made-up values, not clinical guidance). You must prepare 500 mL of 6% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
A patient weighing 31 kg has a body surface area of 1.08 m². The prescription is 20 mg/m². Find the dose D in mg.
The prescription is 690 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?
Infuse 250 mL over 4 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
A drip runs at 30 gtt/min through a set of 60 gtt/mL. There are 400 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 1.5 units/h. Find the pump rate R in mL/h. Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A patient who weighs 81 kg has an order for norepinephrine at 4 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
Answer: C = 100 mg/mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: V = 400 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Check: 100 mL of 30% contains 30 g of drug, which is 6% of 500 mL.
Answer: D = 21.6 mg
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).
Answer: V = 0.69 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 = 16 gtt/min
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.
At the bedside you round to the nearest whole drop: 16 gtt/min.
Answer: t = 13.3 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.
Answer: R = 1.5 mL/h
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 = 7.5 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.
The order is per minute for the whole patient, so the weight is not needed.
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