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 122.2266 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
122.2266 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 0.5 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.
0.5 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min
3.Dosage calculationsMedium
A child weighing 16 kg is prescribed 10 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
16 kg10 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 140 cm tall and weighs 34 kg. The prescription is 175 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
140 cm34 kg175 mg/m²
D = mg
5.IV infusion ratesMedium
A drip runs at 50 gtt/min through a set of 20 gtt/mL. How many millilitres V does the patient receive in 4 hours?
50 gtt/min20 gtt/mL4 h
V = mL
6.IV infusion ratesHard
An infusion of 200 mg in 250 mL runs at 10 mL/h. How many micrograms per minute D does the patient receive?
200 mg/250 mL10 mL/h
D = mcg/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 patient weighs 73 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 13:30 and runs by pump at 80 mL/h. How many mL V are left in the bag at 18:30?
500 mL80 mL/h13:30 → 18:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 14 units/kg/h for a patient who weighs 67 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL14 units/kg/h67 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 2.5 mcg/kg/min for a patient who weighs 57 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL2.5 mcg/kg/min57 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg9.6 mL+0.4 mL
C = mg/mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 20 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 6% ointment? Round to the nearest whole gram.
20 g · 10%2%6%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 122.2 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
122.2266 → 2
Only the next digit decides
122.2266 → 2
2 is 4 or less, so 2 stays.
The digits after it (66) are ignored: round once, never step by step.
Round
x = 122.2 kg
Answer
x = 122.2 kg
2.Nursing math & unit conversions
Answer: D = 8.3 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 = 0.5 mg/h × (1000 mcg/1 mg) × (1 h/60 min)
Calculate
D = 500/60 = 8.333 ≈ 8.3 mcg/min
Answer
D = 8.3 mcg/min
3.Dosage calculations
Answer: V = 6.4 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 = 10·16 = 160 mg
Volume
V = 160/25 = 6.4 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 6.4 mL
4.Dosage calculations
Answer: D = 201.2 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 = √(140·34/3600) = √1.322 = 1.15 m²
Dose
D = 175·1.15 = 201.2 mg
Answer
D = 201.2 mg
5.IV infusion rates
Answer: V = 600 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.
Rate in mL/h
50·60/20 = 150 mL/h
Volume
V = 150·4 = 600 mL
Answer
V = 600 mL
6.IV infusion rates
Answer: D = 133.3 mcg/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
200000 mcg/250 mL = 800 mcg/mL
Dose per hour
10·800 = 8000 mcg/h
Dose per minute
D = 8000/60 = 133.3 mcg/min
Answer
D = 133.3 mcg/min
7.IV fluids & fluid balance
Answer: U = 1.94 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
475 + 250 + 500 + 475 = 1700 mL
Per kilogram per hour
U = 1700/(73·12) = 1.941 ≈ 1.94 mL/kg/h
Answer
U = 1.94 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 100 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
13:30 → 18:30 = 5 h
Volume infused
80·5 = 400 mL
Volume left
V = 500 − 400 = 100 mL
Answer
V = 100 mL
9.Pediatric & critical-care dosing
Answer: R = 23.5 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
14·67 = 938 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 938/40 = 23.45 ≈ 23.5 mL/h
Answer
R = 23.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 8.6 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
2.5·57 = 142.5 mcg/min
142.5·60 = 8550 mcg/h
Pump rate
R = 8550/1000 = 8.55 ≈ 8.6 mL/h
Answer
R = 8.6 mL/h
11.Pharmacy calculations
Answer: C = 100 mg/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
9.6 + 0.4 = 10 mL
Concentration
C = 1000/10 = 100 mg/mL
Answer
C = 100 mg/mL
12.Pharmacy calculations
Answer: m = 20 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.