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 98.2 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
98.2 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 21:25 and finishes at 05:35 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
21:2505:35
t = h
3.Dosage calculationsMedium
A child weighing 16 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
16 kg7.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 250 mL. The prescription is 500 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/250 mL500 units/h
R = mL/h
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 15 gtt/mL. Find the drip rate R in drops per minute.
120 mL/h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1000 mg of a drug is diluted in 500 mL and given by gravity through a set of 20 gtt/mL. The order is 150 mg per hour. Find the drip rate R in drops per minute.
1000 mg/500 mL150 mg/h20 gtt/mL
R = gtt/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: 150 mLmilk: 240 mLIV infusion: 75 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 was started at 08:00 and runs by pump at 80 mL/h. How many mL V are left in the bag at 09:30?
500 mL80 mL/h08:00 → 09:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 100 mL. The order is 2 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL2 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 84 kg has an order for nitroglycerin at 30 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 mL30 mcg/min84 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.74 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.74 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 2.3 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 600 mg. Draw up the dose: what volume V do you give?
1000 mg2.3 mL + 0.2 mL600 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 36.8 °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
98.2 − 32 = 66.2
Multiply by 5/9
T = 66.2·5/9 = 36.78 ≈ 36.8 °C
Answer
T = 36.8 °C
2.Nursing math & unit conversions
Answer: t = 8.17 h
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.
Before midnight
21:25 → 24:00 = 155 min
After midnight
00:00 → 05:35 = 335 min
Total
155 + 335 = 490 min
t = 490/60 = 8.167 ≈ 8.17 h
Answer
t = 8.17 h
3.Dosage calculations
Answer: V = 4.8 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 = 7.5·16 = 120 mg
Volume
V = 120/25 = 4.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 4.8 mL
4.Dosage calculations
Answer: R = 6.25 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
20000/250 = 80 units/mL
Pump rate
R = 500/80 = 6.25 mL/h
Answer
R = 6.25 mL/h
5.IV infusion rates
Answer: R = 30 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 = 2·15 = 30 gtt/min
Answer
R = 30 gtt/min
6.IV infusion rates
Answer: R = 25 gtt/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
1000/500 = 2 mg/mL
Volume per hour
150/2 = 75 mL/h
Drip rate
R = 75·20/60 = 25 gtt/min
Answer
R = 25 gtt/min
7.IV fluids & fluid balance
Answer: I = 1310 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 + 150 + 240 = 510 mL
IV infusion: 75·8 = 600 mL
IV antibiotic: 2·100 = 200 mL
I = 1310 mL
Answer
I = 1310 mL
8.IV fluids & fluid balance
Answer: V = 380 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
08:00 → 09:30 = 1.5 h
Volume infused
80·1.5 = 120 mL
Volume left
V = 500 − 120 = 380 mL
Answer
V = 380 mL
9.Pediatric & critical-care dosing
Answer: R = 2 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.
Concentration
100/100 = 1 units/mL
Pump rate
R = 2/1 = 2 mL/h
Answer
R = 2 mL/h
10.Pediatric & critical-care dosing
Answer: R = 18 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.
30·60 = 1800 mcg/h
Pump rate
R = 1800/100 = 18 mL/h
Answer
R = 18 mL/h
11.Pharmacy calculations
Answer: V = 7.4 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 = 0.74/0.1 = 7.4 mL
Answer
V = 7.4 mL
12.Pharmacy calculations
Answer: V = 1.5 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.