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 6 ft 1 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.
6 ft 1 in1 ft = 12 in1 in = 2.54 cm
h = cm
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A maintenance infusion runs at 40 mL/h without a break. How many litres V does it deliver in 24 hours?
40 mL/h24 h
V = L
3.Dosage calculationsMedium
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?
15 kg4 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 7700 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
7700 units10000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 5 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL5 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 500 mg of a drug in 250 mL and runs at 20 mL/h. How many milligrams per hour D does the patient receive?
500 mg/250 mL20 mL/h
D = mg/h
7.IV fluids & fluid balanceMedium
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 57 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 was started at 06:00 and runs by pump at 80 mL/h. How many mL V are left in the bag at 10:00?
1000 mL80 mL/h06:00 → 10:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 55 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
80 units/kg55 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 39 mL/h. The patient weighs 65 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL39 mL/h65 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. The prescribed dose is 150 mg. What volume V do you draw up? Round to one decimal place.
500 mg1.8 mL+0.2 mL150 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 13% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 23% solution do you need? Round to the nearest whole mL.
23%3%13%450 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 185 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
6·12 + 1 = 73 in
Inches to centimetres
h = 73·2.54 = 185.4 ≈ 185 cm
Answer
h = 185 cm
2.Nursing math & unit conversions
Answer: V = 0.96 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.
Volume in a day
40 mL/h × 24 h = 960 mL
In litres
V = 960/1000 = 0.96 L
Answer
V = 0.96 L
3.Dosage calculations
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.
Dose from body weight
D = 4·15 = 60 mg
Volume
V = 60/50 = 1.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 1.2 mL
4.Dosage calculations
Answer: V = 0.77 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.
Volume
V = 7700/10000 = 0.77 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.77 mL
5.IV infusion rates
Answer: R = 17 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
5·60 = 300 min
Drip rate
R = 500·10/300 = 16.67 ≈ 17 gtt/min
Answer
R = 17 gtt/min
At the bedside you round to the nearest whole drop: 17 gtt/min.
6.IV infusion rates
Answer: D = 40 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.
Concentration
500/250 = 2 mg/mL
Dose rate
D = 2·20 = 40 mg/h
Answer
D = 40 mg/h
7.IV fluids & fluid balance
Answer: U = 2.8 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.
Total urine
450 + 425 + 200 + 200 = 1275 mL
Per kilogram per hour
U = 1275/(57·8) = 2.796 ≈ 2.8 mL/kg/h
Answer
U = 2.8 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 680 mL
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.
Elapsed time
06:00 → 10:00 = 4 h
Volume infused
80·4 = 320 mL
Volume left
V = 1000 − 320 = 680 mL
Answer
V = 680 mL
9.Pediatric & critical-care dosing
Answer: V = 0.88 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
80·55 = 4 400 units
Volume
V = 4400/5000 = 0.88 mL
Answer
V = 0.88 mL
10.Pediatric & critical-care dosing
Answer: D = 20 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.
Concentration
500 000/250 = 2000 mcg/mL
Micrograms per minute
39·2000 = 78000 mcg/h
78000/60 = 1300 mcg/min
Per kilogram
D = 1300/65 = 20 mcg/kg/min
Answer
D = 20 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.6 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.
Final volume
1.8 + 0.2 = 2 mL
Concentration
500/2 = 250 mg/mL
Volume to give
V = 150/250 = 0.6 mL
Answer
V = 0.6 mL
12.Pharmacy calculations
Answer: V = 225 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.