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 1:10 000. You need 0.1 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
Practice exercise (made-up values, not clinical guidance). You must prepare 400 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
A child weighing 15 kg is prescribed 4 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
An infusion contains 50000 units of a drug in 1000 mL. The prescription is 1200 units per hour. At what rate R do you set the pump, in mL/h?
A drip runs at 100 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 2 hours?
A bag contains 1 g of a drug in 500 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). An infusion of 100 units of regular insulin in 250 mL runs at 10 mL/h. How many units per hour D does the patient receive?
Practice exercise (made-up values, not clinical guidance). A patient who weighs 70 kg has an order for norepinephrine at 6 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
Answer: V = 1 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 = 360 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: 40 mL of 23% + 360 mL of 3% = 400 mL.
Answer: V = 1.2 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 10 mL syringe every small line is 0.2 mL.
Answer: R = 24 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: V = 200 mL
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 = 45 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 = 11.3 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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