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 2000 mg as a powder. The practice label says to add 19.2 mL of sterile water; the powder adds 0.8 mL to the volume. The prescribed dose is 1500 mg. What volume V do you draw up? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). You have 60 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1.5% ointment? Round to the nearest whole gram.
How many milligrams of drug m are in 2 mL of a 2% (w/v) solution?
An infusion contains 20000 units of a drug in 500 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
1000 mL was ordered over 10 hours. After 3 hours you find that 850 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 2 g of a drug in 500 mL. The order is 2 mg per minute. At what rate R do you set the pump, in mL/h?
Practice exercise (made-up values, not clinical guidance). An infusion of 50 units of regular insulin in 50 mL runs at 4 mL/h. How many units per hour D does the patient receive?
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 3 mcg/kg/min for a patient who weighs 51 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
Answer: V = 15 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: m = 60 g
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 g + 60 g = 120 g of 1.5% ointment.
Answer: m = 40 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: R = 25 mL/h
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: R = 121.4 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 = 30 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: D = 4 units/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 = 5.7 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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