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 185 cm tall. Using 1 in = 2.54 cm, find the height h in inches. Round to one decimal place.
185 cm1 in = 2.54 cm
h = in
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 2 mcg/kg/min for a patient who weighs 86 kg. Express the dose rate D in mg/h. Round to two decimal places.
2 mcg/kg/min86 kg
D = mg/h
3.Dosage calculationsMedium
A dose of 50 mg is needed from a 10% (w/v) solution. What volume V contains this dose?
50 mg10% w/v
V = mL
4.Dosage calculationsHard
A child weighing 14 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give? Round to one decimal place.
14 kg10 mg/kg120 mg/5 mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 10 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 mL10 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 400 mg in 500 mL runs at 18 mL/h. How many micrograms per minute D does the patient receive?
400 mg/500 mL18 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 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
jelly: 120 mLwater: 300 mLIV infusion: 50 mL/h × 8 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 100 mL/h. At 12:30, 150 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL150 mL infused100 mL/h
t = h
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 16 units/kg/h for a patient who weighs 87 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL16 units/kg/h87 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 5 mcg/kg/min for a patient who weighs 87 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min87 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.3 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.3 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 1950 mg. Draw up the dose: what volume V do you give?
2000 mg3.4 mL + 0.6 mL1950 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 72.8 in
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.
Centimetres to inches
h = 185/2.54 = 72.83 ≈ 72.8 in
Answer
h = 72.8 in
2.Nursing math & unit conversions
Answer: D = 10.32 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 mcg/kg/min × 86 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 2·86·60/1000 = 10.32 mg/h
Answer
D = 10.32 mg/h
3.Dosage calculations
Answer: V = 0.5 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.
Concentration
10% = 100 mg/mL
Volume
V = 50/100 = 0.5 mL
Answer
V = 0.5 mL
4.Dosage calculations
Answer: V = 5.8 mL
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Dose from weight
10·14 = 140 mg
Volume
V = (140/120)·5 = 5.833 ≈ 5.8 mL
Answer
V = 5.8 mL
5.IV infusion rates
Answer: R = 8 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
10·60 = 600 min
Drip rate
R = 500·10/600 = 8.333 ≈ 8 gtt/min
Answer
R = 8 gtt/min
At the bedside you round to the nearest whole drop: 8 gtt/min.
6.IV infusion rates
Answer: D = 240 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
400000 mcg/500 mL = 800 mcg/mL
Dose per hour
18·800 = 14400 mcg/h
Dose per minute
D = 14400/60 = 240 mcg/min
Answer
D = 240 mcg/min
7.IV fluids & fluid balance
Answer: I = 1020 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.
Add the intake
oral: 120 + 300 = 420 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 2·100 = 200 mL
I = 1020 mL
Answer
I = 1020 mL
8.IV fluids & fluid balance
Answer: t = 3.5 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.
Volume left
500 − 150 = 350 mL
Time
t = 350/100 = 3.5 h
Answer
t = 3.5 h
That is about 3 h 30 min, so the bag runs out at about 16:00.
9.Pediatric & critical-care dosing
Answer: R = 13.9 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
16·87 = 1 392 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1392/100 = 13.92 ≈ 13.9 mL/h
Answer
R = 13.9 mL/h
10.Pediatric & critical-care dosing
Answer: R = 26.1 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
5·87 = 435 mcg/min
435·60 = 26100 mcg/h
Pump rate
R = 26100/1000 = 26.1 mL/h
Answer
R = 26.1 mL/h
11.Pharmacy calculations
Answer: V = 0.3 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/1000 mL = 1 mg/mL
Volume
V = 0.3/1 = 0.3 mL
Answer
V = 0.3 mL
12.Pharmacy calculations
Answer: V = 3.9 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.