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 5 ft 6 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.
5 ft 6 in1 ft = 12 in1 in = 2.54 cm
h = cm
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:35 and finishes at 00:10 the next morning (24-hour clock). How many minutes t did it run?
18:3500:10
t = min
3.Dosage calculationsMedium
A patient weighs 15 kg and is prescribed 2 mg/kg as a single dose. Find the dose D in mg.
15 kg2 mg/kg
D = mg
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
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 drip runs at 42 gtt/min through a set of 15 gtt/mL. There are 750 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min15 gtt/mL750 mL
t = 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.
juice: 200 mLtea: 150 mLIV infusion: 100 mL/h × 12 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 07:30 and runs by pump at 80 mL/h. How many mL V are left in the bag at 08:30?
1000 mL80 mL/h07:30 → 08:30
V = mL
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 12 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 mL12 units/kg/h87 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 4 mcg/kg/min for a patient who weighs 57 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL4 mcg/kg/min57 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 3.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
3.2 mL → 1 000 000 units/mL2 400 000 units
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 600 mg. Draw up the dose: what volume V do you give?
2000 mg3.4 mL + 0.6 mL600 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 168 cm
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.
Height in inches
5·12 + 6 = 66 in
Inches to centimetres
h = 66·2.54 = 167.6 ≈ 168 cm
Answer
h = 168 cm
2.Nursing math & unit conversions
Answer: t = 335 min
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
18:35 → 24:00 = 325 min
After midnight
00:00 → 00:10 = 10 min
Total
t = 325 + 10 = 335 min
Answer
t = 335 min
3.Dosage calculations
Answer: D = 30 mg
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
2·15 = 30 mg
Answer
D = 30 mg
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 = 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: t = 4.5 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.
Rate in mL/h
42·60/15 = 168 mL/h
Time left
t = 750/168 = 4.464 ≈ 4.5 h
Answer
t = 4.5 h
7.IV fluids & fluid balance
Answer: I = 1750 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 + 150 = 350 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 2·100 = 200 mL
I = 1750 mL
Answer
I = 1750 mL
8.IV fluids & fluid balance
Answer: V = 920 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
07:30 → 08:30 = 1 h
Volume infused
80·1 = 80 mL
Volume left
V = 1000 − 80 = 920 mL
Answer
V = 920 mL
9.Pediatric & critical-care dosing
Answer: R = 10.4 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
12·87 = 1 044 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1044/100 = 10.44 ≈ 10.4 mL/h
Answer
R = 10.4 mL/h
10.Pediatric & critical-care dosing
Answer: R = 8.6 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
4·57 = 228 mcg/min
228·60 = 13680 mcg/h
Pump rate
R = 13680/1600 = 8.55 ≈ 8.6 mL/h
Answer
R = 8.6 mL/h
11.Pharmacy calculations
Answer: V = 2.4 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration from the label
3.2 mL → 1 000 000 units/mL
Volume to give
V = 2 400 000/1 000 000 = 2.4 mL
Answer
V = 2.4 mL
12.Pharmacy calculations
Answer: V = 1.2 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.