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 weight conversion gives 131.4642 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
131.4642 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 21:15 and finishes at 07:10 the next morning (24-hour clock). How many minutes t did it run?
21:1507:10
t = min
3.Dosage calculationsMedium
A child weighing 16 kg is prescribed 2 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
16 kg2 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 112 cm tall and weighs 22 kg. The prescription is 60 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
112 cm22 kg60 mg/m²
D = mg
5.IV infusion ratesMedium
An infusion is ordered at 200 mL/h, but no pump is available. It runs by gravity through a giving set of 15 gtt/mL. Find the drip rate R in drops per minute.
200 mL/h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1000 mg of a drug is diluted in 500 mL and given by gravity through a set of 60 gtt/mL. The order is 80 mg per hour. Find the drip rate R in drops per minute.
1000 mg/500 mL80 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 8-hour shift. The patient weighs 108 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 was started at 12:00 and runs by pump at 60 mL/h. How many mL V are left in the bag at 13:00?
500 mL60 mL/h12:00 → 13:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 15 units/kg/h for a patient who weighs 60 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL15 units/kg/h60 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 29 mL/h. The patient weighs 107 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL29 mL/h107 kg
D = mcg/kg/min
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 8.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 120 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 10% ointment? Round to the nearest whole gram.
120 g · 20%0%10%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 131.5 kg
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
131.4642 → 4
Only the next digit decides
131.4642 → 6
6 is 5 or more, so round 4 up.
The digits after it (42) are ignored: round once, never step by step.
Round
x = 131.5 kg
Answer
x = 131.5 kg
2.Nursing math & unit conversions
Answer: t = 595 min
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.
Before midnight
21:15 → 24:00 = 165 min
After midnight
00:00 → 07:10 = 430 min
Total
t = 165 + 430 = 595 min
Answer
t = 595 min
3.Dosage calculations
Answer: V = 1.6 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 = 2·16 = 32 mg
Volume
V = 32/20 = 1.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 1.6 mL
4.Dosage calculations
Answer: D = 49.64 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).
Body surface area
BSA = √(112·22/3600) = √0.6844 = 0.8273 m²
Dose
D = 60·0.8273 = 49.64 mg
Answer
D = 49.64 mg
5.IV infusion rates
Answer: R = 50 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.
Millilitres per minute
200/60 = 3.333 mL/min
Drip rate
R = 3.333·15 = 50 gtt/min
Answer
R = 50 gtt/min
6.IV infusion rates
Answer: R = 40 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
1000/500 = 2 mg/mL
Volume per hour
80/2 = 40 mL/h
Drip rate
R = 40·60/60 = 40 gtt/min
Answer
R = 40 gtt/min
7.IV fluids & fluid balance
Answer: U = 0.98 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
150 + 375 + 325 = 850 mL
Per kilogram per hour
U = 850/(108·8) = 0.9838 ≈ 0.98 mL/kg/h
Answer
U = 0.98 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 440 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
12:00 → 13:00 = 1 h
Volume infused
60·1 = 60 mL
Volume left
V = 500 − 60 = 440 mL
Answer
V = 440 mL
9.Pediatric & critical-care dosing
Answer: R = 9 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.
Units per hour
15·60 = 900 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 900/100 = 9 mL/h
Answer
R = 9 mL/h
10.Pediatric & critical-care dosing
Answer: D = 7.2 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
29·1600 = 46400 mcg/h
46400/60 = 773.3 mcg/min
Per kilogram
D = 773.3/107 = 7.227 ≈ 7.2 mcg/kg/min
Answer
D = 7.2 mcg/kg/min
11.Pharmacy calculations
Answer: V = 4.8 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
8.2 mL → 500 000 units/mL
Volume to give
V = 2 400 000/500 000 = 4.8 mL
Answer
V = 4.8 mL
12.Pharmacy calculations
Answer: m = 120 g
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.