Write the given quantity with its unit and the unit you want.
Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
Dosage calculations
Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg
Method
Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
Estimate first and check that the answer is reasonable.
IV infusion rates
Pump rate
mL/h = volume (mL)/time (h)
Drip rate
drops/min = volume (mL) × drop factor / time (min)
Infusion time
time (h) = volume (mL)/rate (mL/h)
Method
Pump rate in mL/h: volume divided by time in hours.
Drip rate in drops/min: volume × drop factor divided by time in minutes.
For time remaining: volume left divided by the rate.
Round as the question or the equipment requires.
IV fluids & fluid balance
Holliday–Segar per hour
4 mL/kg (first 10 kg) + 2 mL/kg (next 10 kg) + 1 mL/kg (each kg above 20)
Holliday–Segar per day
100 / 50 / 20 mL/kg for the same bands
Fluid balance
intake − output
Ice chips
count as half their volume
Urine output
mL/kg/h = mL / (kg × h)
Infusion time
time (h) = volume left (mL) / rate (mL/h)
Volume infused
mL = rate × time
Pediatric & critical-care dosing
Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
2Practice problems
1.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A patient is 4 ft 5 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.
4 ft 5 in1 ft = 12 in1 in = 2.54 cm
h = cm
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 3 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.
3 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min
3.Dosage calculationsMedium
A patient weighs 80 kg and is prescribed 5 mg/kg as a single dose. Find the dose D in mg.
80 kg5 mg/kg
D = mg
4.Dosage calculationsHard
You must prepare 200 mL of a 2% (w/v) solution from a 20% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 20%C₂ = 2%V₂ = 200 mL
V₁ = mL
5.IV infusion ratesMedium
Infuse 500 mL over 12 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL12 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
500 mg of a drug is diluted in 500 mL and given by gravity through a set of 60 gtt/mL. The order is 100 mg per hour. Find the drip rate R in drops per minute.
500 mg/500 mL100 mg/h60 gtt/mL
R = gtt/min
7.IV fluids & fluid balanceMedium
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 20:00 at 150 mL/h. After 2 hours the rate is changed to 100 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL150 mL/h · 2 h100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 57 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg57 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 73 kg has an order for nitroglycerin at 50 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL50 mcg/min73 kg
R = mL/h
11.Pharmacy calculationsMedium
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.
3.2 mL → 1 000 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 500 mL of 4% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
20%0%4%500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 135 cm
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.
Height in inches
4·12 + 5 = 53 in
Inches to centimetres
h = 53·2.54 = 134.6 ≈ 135 cm
Answer
h = 135 cm
2.Nursing math & unit conversions
Answer: D = 50 mcg/min
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.
Set up the chain
D = 3 mg/h × (1000 mcg/1 mg) × (1 h/60 min)
Calculate
D = 3000/60 = 50 mcg/min
Answer
D = 50 mcg/min
3.Dosage calculations
Answer: D = 400 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.
Dose
5·80 = 400 mg
Answer
D = 400 mg
4.Dosage calculations
Answer: V₁ = 20 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.
Volume of stock
V₁ = 2·200/20 = 20 mL
Answer
V₁ = 20 mL
5.IV infusion rates
Answer: R = 14 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.
Time in minutes
12·60 = 720 min
Drip rate
R = 500·20/720 = 13.89 ≈ 14 gtt/min
Answer
R = 14 gtt/min
At the bedside you round to the nearest whole drop: 14 gtt/min.
6.IV infusion rates
Answer: R = 100 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).
Concentration
500/500 = 1 mg/mL
Volume per hour
100/1 = 100 mL/h
Drip rate
R = 100·60/60 = 100 gtt/min
Answer
R = 100 gtt/min
7.IV fluids & fluid balance
Answer: I = 2210 mL
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.
Add the intake
oral: 150 + 150 + 300 = 600 mL
ice chips: 120/2 = 60 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 1·50 = 50 mL
I = 2210 mL
Answer
I = 2210 mL
8.IV fluids & fluid balance
Answer: t = 4 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.
First part
150·2 = 300 mL
500 − 300 = 200 mL left
Second part
200/100 = 2 h
Total time
t = 2 + 2 = 4 h
Answer
t = 4 h
That is about 4 h 00 min, so the bag runs out at about 00:00.
9.Pediatric & critical-care dosing
Answer: V = 3.4 mL
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.
Units needed
60·57 = 3 420 units
Volume
V = 3420/1000 = 3.42 ≈ 3.4 mL
Answer
V = 3.4 mL
10.Pediatric & critical-care dosing
Answer: R = 15 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.
Concentration
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
50·60 = 3000 mcg/h
Pump rate
R = 3000/200 = 15 mL/h
Answer
R = 15 mL/h
11.Pharmacy calculations
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.
Concentration from the label
3.2 mL → 1 000 000 units/mL
Volume to give
V = 2 400 000/1 000 000 = 2.4 mL
Answer
V = 2.4 mL
12.Pharmacy calculations
Answer: V = 400 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.
Alligation parts
20%: 4 − 0 = 4 parts
0%: 20 − 4 = 16 parts
total: 20 parts
Water
V = 500·16/20 = 400 mL
Answer
V = 400 mL
Check: 100 mL of 20% contains 20 g of drug, which is 4% of 500 mL.