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’s temperature is 98.4 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
98.4 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 2.5 mcg/kg/min for a patient who weighs 47 kg. Express the dose rate D in mg/h. Round to two decimal places.
2.5 mcg/kg/min47 kg
D = mg/h
3.Dosage calculationsMedium
A child weighing 8 kg is prescribed 15 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?
8 kg15 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
You must prepare 500 mL of a 2% (w/v) solution from a 10% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 10%C₂ = 2%V₂ = 500 mL
V₁ = mL
5.IV infusion ratesMedium
A drip runs at 40 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 6 hours?
40 gtt/min60 gtt/mL6 h
V = mL
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 500 mL and runs at 15 mL/h. How many milligrams per hour D does the patient receive?
200 mg/500 mL15 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 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 15:00 at 125 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 mL125 mL/h · 2 h100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 16 units/kg/h for a patient who weighs 79 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL16 units/kg/h79 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 79 kg has an order for norepinephrine at 10 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL10 mcg/min79 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.9 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.9 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 320 mg. Draw up the dose: what volume V do you give?
2000 mg4.5 mL + 0.5 mL320 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 36.9 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
98.4 − 32 = 66.4
Multiply by 5/9
T = 66.4·5/9 = 36.89 ≈ 36.9 °C
Answer
T = 36.9 °C
2.Nursing math & unit conversions
Answer: D = 7.05 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 = 2.5 mcg/kg/min × 47 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 2.5·47·60/1000 = 7.05 mg/h
Answer
D = 7.05 mg/h
3.Dosage calculations
Answer: V = 3 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 = 15·8 = 120 mg
Volume
V = 120/40 = 3 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3 mL
4.Dosage calculations
Answer: V₁ = 100 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 = 2·500/10 = 100 mL
Answer
V₁ = 100 mL
5.IV infusion rates
Answer: V = 240 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
40·60/60 = 40 mL/h
Volume
V = 40·6 = 240 mL
Answer
V = 240 mL
6.IV infusion rates
Answer: D = 6 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
200/500 = 0.4 mg/mL
Dose rate
D = 0.4·15 = 6 mg/h
Answer
D = 6 mg/h
7.IV fluids & fluid balance
Answer: B = 500 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.
Total intake
oral: 200 + 100 + 350 = 650 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1350 mL
Total output
200 + 225 + 325 + 100 = 850 mL
Balance
B = 1350 − 850 = 500 mL
Answer
B = 500 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 4.5 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
125·2 = 250 mL
500 − 250 = 250 mL left
Second part
250/100 = 2.5 h
Total time
t = 2 + 2.5 = 4.5 h
Answer
t = 4.5 h
That is about 4 h 30 min, so the bag runs out at about 19:30.
9.Pediatric & critical-care dosing
Answer: R = 25.3 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
16·79 = 1 264 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1264/50 = 25.28 ≈ 25.3 mL/h
Answer
R = 25.3 mL/h
10.Pediatric & critical-care dosing
Answer: R = 18.8 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/32 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 mL/h
11.Pharmacy calculations
Answer: V = 0.9 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/1000 mL = 1 mg/mL
Volume
V = 0.9/1 = 0.9 mL
Answer
V = 0.9 mL
12.Pharmacy calculations
Answer: V = 0.8 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.