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 100.9 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
100.9 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 fl oz of juice, 1½ tbsp of liquid supplement, 1½ tsp of cough syrup, ¾ cup of tea. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 70 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.
70 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
A child weighing 10 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 200 mg in 5 mL. What volume V do you give? Round to one decimal place.
10 kg12.5 mg/kg200 mg/5 mL
V = mL
5.IV infusion ratesMedium
1000 mL was ordered over 12 hours. After 10 hours you find that 180 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
1000 mL / 12 hafter 10 h: 180 mL
R = mL/h
6.IV infusion ratesHard
A bag contains 1 g of a drug in 250 mL. The order is 3 mg per minute. At what rate R do you set the pump, in mL/h?
1 g/250 mL3 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 81 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 bag was started at 11:30 and runs by pump at 125 mL/h. How many mL V are left in the bag at 12:30?
1000 mL125 mL/h11:30 → 12:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 14 units/kg/h for a patient who weighs 109 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL14 units/kg/h109 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 2 mcg/kg/min for a patient who weighs 77 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min77 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.68 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.68 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 1840 mg. Draw up the dose: what volume V do you give?
2000 mg4.8 mL + 0.2 mL1840 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 38.3 °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
100.9 − 32 = 68.9
Multiply by 5/9
T = 68.9·5/9 = 38.28 ≈ 38.3 °C
Answer
T = 38.3 °C
2.Nursing math & unit conversions
Answer: V = 270 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
2 fl oz = 2·30 = 60 mL
1½ tbsp = 1.5·15 = 22.5 mL
1½ tsp = 1.5·5 = 7.5 mL
¾ cup = 0.75·240 = 180 mL
Add
V = 60 + 22.5 + 7.5 + 180 = 270 mL
Answer
V = 270 mL
3.Dosage calculations
Answer: D = 525 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
7.5·70 = 525 mg
Answer
D = 525 mg
4.Dosage calculations
Answer: V = 3.1 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
12.5·10 = 125 mg
Volume
V = (125/200)·5 = 3.125 ≈ 3.1 mL
Answer
V = 3.1 mL
5.IV infusion rates
Answer: R = 90 mL/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.
Original rate
1000/12 = 83.33 mL/h
New rate
R = 180/2 = 90 mL/h
Answer
R = 90 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: R = 45 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
1000 mg/250 mL = 4 mg/mL
Dose per hour
3·60 = 180 mg/h
Pump rate
R = 180/4 = 45 mL/h
Answer
R = 45 mL/h
7.IV fluids & fluid balance
Answer: U = 2.12 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
325 + 400 + 375 + 275 = 1375 mL
Per kilogram per hour
U = 1375/(81·8) = 2.122 ≈ 2.12 mL/kg/h
Answer
U = 2.12 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 875 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
11:30 → 12:30 = 1 h
Volume infused
125·1 = 125 mL
Volume left
V = 1000 − 125 = 875 mL
Answer
V = 875 mL
9.Pediatric & critical-care dosing
Answer: R = 30.5 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
14·109 = 1 526 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1526/50 = 30.52 ≈ 30.5 mL/h
Answer
R = 30.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 5.8 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
2·77 = 154 mcg/min
154·60 = 9240 mcg/h
Pump rate
R = 9240/1600 = 5.775 ≈ 5.8 mL/h
Answer
R = 5.8 mL/h
11.Pharmacy calculations
Answer: V = 0.68 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 = 0.68/1 = 0.68 mL
Answer
V = 0.68 mL
12.Pharmacy calculations
Answer: V = 4.6 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.