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 of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 3.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 2% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
A patient weighs 90 kg and is prescribed 2 mg/kg as a single dose. Find the dose D in mg.
A patient is 160 cm tall and weighs 72 kg. The prescription is 250 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
1500 mL was ordered over 6 hours. After 3 hours you find that 860 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 drip runs at 28 gtt/min through a set of 15 gtt/mL. There are 600 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). A bag contains 20 000 units of heparin in 500 mL. The order is 15 units/kg/h for a patient who weighs 72 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A patient who weighs 71 kg has an order for nitroglycerin at 5 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
Answer: V = 2.4 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 = 540 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: 60 mL of 20% contains 12 g of drug, which is 2% of 600 mL.
Answer: D = 180 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Answer: D = 447.2 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: R = 286.7 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: t = 5.4 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 = 27 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 = 3 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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