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 5 lb 15 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
5 lb 15 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ cup of tea, 8 fl oz of juice, 1 tsp of cough syrup, ½ tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 fl oz = 30 mL1 tsp = 5 mL1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A dose of 1000 mg is needed from a 20% (w/v) solution. What volume V contains this dose?
1000 mg20% w/v
V = mL
4.Dosage calculationsHard
An infusion contains 50000 units of a drug in 500 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
50000 units/500 mL2000 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 250 mL over 5 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL5 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 4 g of a drug in 1000 mL. The order is 1.5 mg per minute. At what rate R do you set the pump, in mL/h?
4 g/1000 mL1.5 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 8-hour shift. The patient weighs 101 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 11:00 at 80 mL/h. After 4 hours the rate is changed to 100 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 mL80 mL/h · 4 h100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 70 units/kg for a patient who weighs 79 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg79 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 29 mL/h. The patient weighs 87 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL29 mL/h87 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.34 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.34 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 40 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 10% ointment? Round to the nearest whole gram.
40 g · 20%0%10%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.7 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
15 oz/16 = 0.9375 lb
5 + 0.9375 = 5.938 lb
Pounds to kilograms
m = 5.938/2.2 = 2.699 ≈ 2.7 kg
Answer
m = 2.7 kg
2.Nursing math & unit conversions
Answer: V = 372.5 mL
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.
Each item in mL
½ cup = 0.5·240 = 120 mL
8 fl oz = 8·30 = 240 mL
1 tsp = 1·5 = 5 mL
½ tbsp = 0.5·15 = 7.5 mL
Add
V = 120 + 240 + 5 + 7.5 = 372.5 mL
Answer
V = 372.5 mL
3.Dosage calculations
Answer: V = 5 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
20% = 200 mg/mL
Volume
V = 1000/200 = 5 mL
Answer
V = 5 mL
4.Dosage calculations
Answer: R = 20 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
50000/500 = 100 units/mL
Pump rate
R = 2000/100 = 20 mL/h
Answer
R = 20 mL/h
5.IV infusion rates
Answer: R = 13 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 = 250·15/300 = 12.5 ≈ 13 gtt/min
Answer
R = 13 gtt/min
At the bedside you round to the nearest whole drop: 13 gtt/min.
6.IV infusion rates
Answer: R = 22.5 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
4000 mg/1000 mL = 4 mg/mL
Dose per hour
1.5·60 = 90 mg/h
Pump rate
R = 90/4 = 22.5 mL/h
Answer
R = 22.5 mL/h
7.IV fluids & fluid balance
Answer: U = 1.58 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
500 + 350 + 425 = 1275 mL
Per kilogram per hour
U = 1275/(101·8) = 1.578 ≈ 1.58 mL/kg/h
Answer
U = 1.58 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 10.8 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
80·4 = 320 mL
1000 − 320 = 680 mL left
Second part
680/100 = 6.8 h
Total time
t = 4 + 6.8 = 10.8 h
Answer
t = 10.8 h
That is about 10 h 48 min, so the bag runs out at about 21:48.
9.Pediatric & critical-care dosing
Answer: V = 5.5 mL
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 needed
70·79 = 5 530 units
Volume
V = 5530/1000 = 5.53 ≈ 5.5 mL
Answer
V = 5.5 mL
10.Pediatric & critical-care dosing
Answer: D = 5.6 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
29·1000 = 29000 mcg/h
29000/60 = 483.3 mcg/min
Per kilogram
D = 483.3/87 = 5.556 ≈ 5.6 mcg/kg/min
Answer
D = 5.6 mcg/kg/min
11.Pharmacy calculations
Answer: V = 3.4 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 = 0.34/0.1 = 3.4 mL
Answer
V = 3.4 mL
12.Pharmacy calculations
Answer: m = 40 g
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.