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 3:55 PM. Which entry is the same time on the 24-hour clock? Click it.
3:55 PM
114:55
215:55
316:55
403:55
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 2 tsp of an oral suspension every 8 hours for 7 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
2 tspevery 8 hours7 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A child weighing 9 kg is prescribed 10 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
9 kg10 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 14 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give? Round to one decimal place.
14 kg15 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 120 mL/h, but no pump is available. It runs by gravity through a giving set of 20 gtt/mL. Find the drip rate R in drops per minute.
120 mL/h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 100 mg of a drug in 50 mL and runs at 25 mL/h. How many milligrams per hour D does the patient receive?
100 mg/50 mL25 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 total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 12:00 and runs by pump at 100 mL/h. How many mL V are left in the bag at 16:00?
1000 mL100 mL/h12:00 → 16:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 10 000 units of heparin in 250 mL. The order is 15 units/kg/h for a patient who weighs 103 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
10 000 units/250 mL15 units/kg/h103 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 95 kg has an order for nitroglycerin at 5 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL5 mcg/min95 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.37 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.37 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 13% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%13%600 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 15:55
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
15:55
Answer
15:55
2.Nursing math & unit conversions
Answer: V = 210 mL
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.
Volume per dose
2 tsp = 2·5 = 10 mL
Whole course
V = 10 mL × 3/day × 7 = 210 mL
Answer
V = 210 mL
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 = 10·9 = 90 mg
Volume
V = 90/10 = 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: V = 5.3 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
15·14 = 210 mg
Volume
V = (210/40)·1 = 5.25 ≈ 5.3 mL
Answer
V = 5.3 mL
5.IV infusion rates
Answer: R = 40 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.
Millilitres per minute
120/60 = 2 mL/min
Drip rate
R = 2·20 = 40 gtt/min
Answer
R = 40 gtt/min
6.IV infusion rates
Answer: D = 50 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 = 2·25 = 50 mg/h
Answer
D = 50 mg/h
7.IV fluids & fluid balance
Answer: I = 1870 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: 200 + 180 + 120 = 500 mL
ice chips: 240/2 = 120 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 1·50 = 50 mL
I = 1870 mL
Answer
I = 1870 mL
8.IV fluids & fluid balance
Answer: V = 600 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
12:00 → 16:00 = 4 h
Volume infused
100·4 = 400 mL
Volume left
V = 1000 − 400 = 600 mL
Answer
V = 600 mL
9.Pediatric & critical-care dosing
Answer: R = 38.6 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
15·103 = 1 545 units/h
Concentration
10 000/250 = 40 units/mL
Pump rate
R = 1545/40 = 38.63 ≈ 38.6 mL/h
Answer
R = 38.6 mL/h
10.Pediatric & critical-care dosing
Answer: R = 3 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
5·60 = 300 mcg/h
Pump rate
R = 300/100 = 3 mL/h
Answer
R = 3 mL/h
11.Pharmacy calculations
Answer: V = 0.37 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 = 0.37/1 = 0.37 mL
Answer
V = 0.37 mL
12.Pharmacy calculations
Answer: V = 300 mL
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.