Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
A dose of 100 mg is needed from a 5% (w/v) solution. What volume V contains this dose?
A patient is 138 cm tall and weighs 43 kg. The prescription is 75 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
Infuse 250 mL over 8 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
200 mg of a drug is diluted in 100 mL and given by gravity through a set of 15 gtt/mL. The order is 120 mg per hour. Find the drip rate R in drops per minute.
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 20 units/kg/h for a patient who weighs 100 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 87 kg has an order for nitroglycerin at 30 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. 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 79 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 500 mL bag runs by pump at 60 mL/h. At 11:00, 300 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 dose is charted at 23:40 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 fl oz of juice, 3 tsp of cough syrup, ¼ cup of tea. Using the equivalents given, find the total oral intake V in mL.
Answer: V = 2 mL
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: D = 96.29 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 = 31 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: 31 gtt/min.
Answer: R = 15 gtt/min
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: R = 40 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 = 9 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.
Answer: U = 1.78 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 = 3.3 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 3 h 20 min, so the bag runs out at about 14:20.
Answer: 11:40 PM
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Answer: V = 135 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
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