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 101.8153 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
101.8153 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 40 mcg/min. Express this dose rate D in mg/h.
40 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
A child weighing 12 kg is prescribed 15 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
12 kg15 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
You must prepare 100 mL of a 2.5% (w/v) solution from a 50% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 50%C₂ = 2.5%V₂ = 100 mL
W = mL
5.IV infusion ratesMedium
Infuse 250 mL over 2 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL2 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 4 g of a drug in 1000 mL. The order is 1 mg per minute. At what rate R do you set the pump, in mL/h?
4 g/1000 mL1 mg/min
R = mL/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 12-hour shift. The patient weighs 70 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 infusion starts at 18:00 at 120 mL/h. After 4 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.
1000 mL120 mL/h · 4 h100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 50 mL runs at 4 mL/h. How many units per hour D does the patient receive?
100 units/50 mL4 mL/h
D = units/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 10 mcg/kg/min for a patient who weighs 69 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL10 mcg/kg/min69 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.3 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.3 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 100 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1% ointment? Round to the nearest whole gram.
100 g · 2.5%0.5%1%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 101.8 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
101.8153 → 8
Only the next digit decides
101.8153 → 1
1 is 4 or less, so 8 stays.
The digits after it (53) are ignored: round once, never step by step.
Round
x = 101.8 kg
Answer
x = 101.8 kg
2.Nursing math & unit conversions
Answer: D = 2.4 mg/h
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 = 40 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 40·60/1000 = 2.4 mg/h
Answer
D = 2.4 mg/h
3.Dosage calculations
Answer: V = 9 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 = 15·12 = 180 mg
Volume
V = 180/20 = 9 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 9 mL
4.Dosage calculations
Answer: W = 95 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 = 2.5·100/50 = 5 mL
Water to add
W = 100 − 5 = 95 mL
Answer
W = 95 mL
5.IV infusion rates
Answer: R = 21 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
2·60 = 120 min
Drip rate
R = 250·10/120 = 20.83 ≈ 21 gtt/min
Answer
R = 21 gtt/min
At the bedside you round to the nearest whole drop: 21 gtt/min.
6.IV infusion rates
Answer: R = 15 mL/h
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
4000 mg/1000 mL = 4 mg/mL
Dose per hour
1·60 = 60 mg/h
Pump rate
R = 60/4 = 15 mL/h
Answer
R = 15 mL/h
7.IV fluids & fluid balance
Answer: U = 2.14 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
400 + 475 + 500 + 425 = 1800 mL
Per kilogram per hour
U = 1800/(70·12) = 2.143 ≈ 2.14 mL/kg/h
Answer
U = 2.14 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 9.2 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
120·4 = 480 mL
1000 − 480 = 520 mL left
Second part
520/100 = 5.2 h
Total time
t = 4 + 5.2 = 9.2 h
Answer
t = 9.2 h
That is about 9 h 12 min, so the bag runs out at about 03:12.
9.Pediatric & critical-care dosing
Answer: D = 8 units/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.
Concentration
100/50 = 2 units/mL
Units per hour
D = 4·2 = 8 units/h
Answer
D = 8 units/h
10.Pediatric & critical-care dosing
Answer: R = 41.4 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
10·69 = 690 mcg/min
690·60 = 41400 mcg/h
Pump rate
R = 41400/1000 = 41.4 mL/h
Answer
R = 41.4 mL/h
11.Pharmacy calculations
Answer: V = 3 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.3/0.1 = 3 mL
Answer
V = 3 mL
12.Pharmacy calculations
Answer: m = 300 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.