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 dose is charted at 3:40 PM. Which entry is the same time on the 24-hour clock? Click it.
3:40 PM
103:40
215:40
316:40
414:40
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 12 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.
12 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min
3.Dosage calculationsMedium
A prefilled syringe of epinephrine (adrenaline) is labelled 1:10 000 (0.1 mg/mL). The prescription is 1 mg IV in cardiac arrest. What volume V do you give?
1:10 0001 mg
V = mL
4.Dosage calculationsHard
The prescription is 1 mg. The ampoule contains 4000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1 mg4000 mcg/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 5 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
500 mL5 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 2 g of a drug in 250 mL. The order is 4 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/250 mL4 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 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 13:30 and runs by pump at 100 mL/h. How many mL V are left in the bag at 16:30?
500 mL100 mL/h13:30 → 16:30
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 15 units/kg/h for a patient who weighs 50 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL15 units/kg/h50 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 31 mL/h. The patient weighs 94 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL31 mL/h94 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.84 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.84 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 102.5 mg. Draw up the dose: what volume V do you give?
250 mg9.8 mL + 0.2 mL102.5 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 15:40
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Convert the hour
3 PM → 3 + 12 = 15
Answer
15:40
Answer
15:40
2.Nursing math & unit conversions
Answer: D = 200 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 = 12 mg/h × (1000 mcg/1 mg) × (1 h/60 min)
Calculate
D = 12000/60 = 200 mcg/min
Answer
D = 200 mcg/min
3.Dosage calculations
Answer: V = 10 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
1:10 000 = 1 g/10000 mL = 0.1 mg/mL
Volume
V = 1/0.1 = 10 mL
Answer
V = 10 mL
US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.
4.Dosage calculations
Answer: V = 0.25 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.
Same units
1 mg = 1000 mcg
Volume
V = 1000/4000 = 0.25 mL
Answer
V = 0.25 mL
5.IV infusion rates
Answer: R = 100 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
5·60 = 300 min
Drip rate
R = 500·60/300 = 100 gtt/min
Answer
R = 100 gtt/min
6.IV infusion rates
Answer: R = 30 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
2000 mg/250 mL = 8 mg/mL
Dose per hour
4·60 = 240 mg/h
Pump rate
R = 240/8 = 30 mL/h
Answer
R = 30 mL/h
7.IV fluids & fluid balance
Answer: B = 1365 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: 300 + 100 + 240 = 640 mL
ice chips: 100/2 = 50 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 2·50 = 100 mL
total intake = 2290 mL
Total output
175 + 425 + 325 = 925 mL
Balance
B = 2290 − 925 = 1365 mL
Answer
B = 1365 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 200 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 → 16:30 = 3 h
Volume infused
100·3 = 300 mL
Volume left
V = 500 − 300 = 200 mL
Answer
V = 200 mL
9.Pediatric & critical-care dosing
Answer: R = 18.8 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
15·50 = 750 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 750/40 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 mL/h
10.Pediatric & critical-care dosing
Answer: D = 5.5 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
31·1000 = 31000 mcg/h
31000/60 = 516.7 mcg/min
Per kilogram
D = 516.7/94 = 5.496 ≈ 5.5 mcg/kg/min
Answer
D = 5.5 mcg/kg/min
11.Pharmacy calculations
Answer: V = 8.4 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 = 0.84/0.1 = 8.4 mL
Answer
V = 8.4 mL
12.Pharmacy calculations
Answer: V = 4.1 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.