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 newborn weighs 8 lb 6 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
8 lb 6 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 17:35 and finishes at 06:05 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.
17:3506:05
t = h
3.Dosage calculationsMedium
A patient weighs 60 kg and is prescribed 2 mg/kg as a single dose. Find the dose D in mg.
60 kg2 mg/kg
D = mg
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 1000 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/1000 mL2000 units/h
R = mL/h
5.IV infusion ratesMedium
An infusion is ordered at 60 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.
60 mL/h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 500 mg of a drug in 500 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
500 mg/500 mL10 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 100 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 infusion starts at 13:00 at 120 mL/h. After 3 hours the rate is changed to 200 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL120 mL/h · 3 h200 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 14 units/kg/h for a patient who weighs 102 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL14 units/kg/h102 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 29 mL/h. The patient weighs 104 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL29 mL/h104 kg
D = mcg/kg/min
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 8.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL750 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 100 mg. Draw up the dose: what volume V do you give?
2000 mg9.8 mL + 0.2 mL100 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 3.81 kg
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.
Ounces to pounds
6 oz/16 = 0.375 lb
8 + 0.375 = 8.375 lb
Pounds to kilograms
m = 8.375/2.2 = 3.807 ≈ 3.81 kg
Answer
m = 3.81 kg
2.Nursing math & unit conversions
Answer: t = 12.5 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
17:35 → 24:00 = 385 min
After midnight
00:00 → 06:05 = 365 min
Total
385 + 365 = 750 min
t = 750/60 = 12.5 h
Answer
t = 12.5 h
3.Dosage calculations
Answer: D = 120 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
2·60 = 120 mg
Answer
D = 120 mg
4.Dosage calculations
Answer: R = 100 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 = 2000/20 = 100 mL/h
Answer
R = 100 mL/h
5.IV infusion rates
Answer: R = 20 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
60/60 = 1 mL/min
Drip rate
R = 1·20 = 20 gtt/min
Answer
R = 20 gtt/min
6.IV infusion rates
Answer: D = 10 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
500/500 = 1 mg/mL
Dose rate
D = 1·10 = 10 mg/h
Answer
D = 10 mg/h
7.IV fluids & fluid balance
Answer: U = 1.08 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
250 + 475 + 200 + 375 = 1300 mL
Per kilogram per hour
U = 1300/(100·12) = 1.083 ≈ 1.08 mL/kg/h
Answer
U = 1.08 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 6.2 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.
First part
120·3 = 360 mL
1000 − 360 = 640 mL left
Second part
640/200 = 3.2 h
Total time
t = 3 + 3.2 = 6.2 h
Answer
t = 6.2 h
That is about 6 h 12 min, so the bag runs out at about 19:12.
9.Pediatric & critical-care dosing
Answer: R = 35.7 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
14·102 = 1 428 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1428/40 = 35.7 mL/h
Answer
R = 35.7 mL/h
10.Pediatric & critical-care dosing
Answer: D = 7.4 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
29·1600 = 46400 mcg/h
46400/60 = 773.3 mcg/min
Per kilogram
D = 773.3/104 = 7.436 ≈ 7.4 mcg/kg/min
Answer
D = 7.4 mcg/kg/min
11.Pharmacy calculations
Answer: V = 1.5 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
8.2 mL → 500 000 units/mL
Volume to give
V = 750 000/500 000 = 1.5 mL
Answer
V = 1.5 mL
12.Pharmacy calculations
Answer: V = 0.5 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.