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 40.8 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
40.8 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 8 mcg/kg/min for a patient who weighs 53 kg. Express the dose rate D in mg/h. Round to two decimal places.
8 mcg/kg/min53 kg
D = mg/h
3.Dosage calculationsMedium
How many milligrams of drug m are in 10 mL of a 1% (w/v) solution?
1% w/v10 mL
m = mg
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 1000 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/1000 mL1000 units/h
R = mL/h
5.IV infusion ratesMedium
A drip runs at 25 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 3 hours?
25 gtt/min15 gtt/mL3 h
V = mL
6.IV infusion ratesHard
A bag contains 100 mg of a drug in 50 mL and runs at 8 mL/h. How many milligrams per hour D does the patient receive?
100 mg/50 mL8 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 patient weighs 103 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 bag runs by pump at 150 mL/h. At 10:00, 500 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL500 mL infused150 mL/h
t = h
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 20 units/kg/h for a patient who weighs 55 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL20 units/kg/h55 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 37 mL/h. The patient weighs 78 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL37 mL/h78 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.46 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.46 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 3.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 975 mg. Draw up the dose: what volume V do you give?
1000 mg3.6 mL + 0.4 mL975 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 105.4 °F
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.
Multiply by 9/5
40.8·9/5 = 73.44
Add 32
T = 73.44 + 32 = 105.4 °F
Answer
T = 105.4 °F
2.Nursing math & unit conversions
Answer: D = 25.44 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 = 8 mcg/kg/min × 53 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 8·53·60/1000 = 25.44 mg/h
Answer
D = 25.44 mg/h
3.Dosage calculations
Answer: m = 100 mg
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
1% = 1 g/100 mL = 10 mg/mL
Mass of drug
m = 10·10 = 100 mg
Answer
m = 100 mg
4.Dosage calculations
Answer: R = 50 mL/h
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.
Concentration
20000/1000 = 20 units/mL
Pump rate
R = 1000/20 = 50 mL/h
Answer
R = 50 mL/h
5.IV infusion rates
Answer: V = 300 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
25·60/15 = 100 mL/h
Volume
V = 100·3 = 300 mL
Answer
V = 300 mL
6.IV infusion rates
Answer: D = 16 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
100/50 = 2 mg/mL
Dose rate
D = 2·8 = 16 mg/h
Answer
D = 16 mg/h
7.IV fluids & fluid balance
Answer: U = 0.69 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
200 + 500 + 150 = 850 mL
Per kilogram per hour
U = 850/(103·12) = 0.6877 ≈ 0.69 mL/kg/h
Answer
U = 0.69 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 3.3 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
1000 − 500 = 500 mL
Time
t = 500/150 = 3.333 ≈ 3.3 h
Answer
t = 3.3 h
That is about 3 h 20 min, so the bag runs out at about 13:20.
9.Pediatric & critical-care dosing
Answer: R = 27.5 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
20·55 = 1 100 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1100/40 = 27.5 mL/h
Answer
R = 27.5 mL/h
10.Pediatric & critical-care dosing
Answer: D = 12.6 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
37·1600 = 59200 mcg/h
59200/60 = 986.7 mcg/min
Per kilogram
D = 986.7/78 = 12.65 ≈ 12.6 mcg/kg/min
Answer
D = 12.6 mcg/kg/min
11.Pharmacy calculations
Answer: V = 4.6 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 = 0.46/0.1 = 4.6 mL
Answer
V = 4.6 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.