Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
A child weighing 29 kg is prescribed 5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
A patient weighs 156.2 lb. The prescription is 15 mg/kg as a single dose, and the stock contains 50 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?
A drip runs at 35 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 4 hours?
A bag contains 500 mg of a drug in 250 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 6 units/h. Find the pump rate R in mL/h. Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 6 mL/h. The patient weighs 107 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 8-hour shift. The patient weighs 80 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 75 mL/h. At 12:00, 100 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 35.4 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A blood glucose result is 74 mg/dL. Using 1 mmol/L = 18 mg/dL for glucose, find c in mmol/L. Round to one decimal place.
Answer: V = 5.8 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: V = 21.3 mL
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 = 560 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: D = 20 mg/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 = 6 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: D = 1.5 mcg/kg/min
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.
Answer: U = 1.21 mL/kg/h
Intake and output: intake counts everything that goes in (oral fluids, IV infusions, IV medications and flushes, tube feeds); ice chips count as half their volume. Output counts urine, drains, vomit and other losses. Balance = total intake − total output; a negative balance is a net loss. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: t = 12 h
Infusion time: time (h) = volume to infuse (mL)/rate (mL/h); use the volume still left in the bag, not the bag size. Volume infused = rate × time. Convert decimal hours to hours and minutes with the fraction × 60 (0.5 h = 30 min, not 50 min). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
That is about 12 h 00 min, so the bag runs out at about 00:00.
Answer: T = 95.7 °F
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Answer: c = 4.1 mmol/L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
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