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 36.1 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
36.1 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A maintenance infusion runs at 100 mL/h without a break. How many litres V does it deliver in 24 hours?
100 mL/h24 h
V = L
3.Dosage calculationsMedium
A child weighing 38 kg is prescribed 5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
38 kg5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 0.7 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
0.7 mg1000 mcg/mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 8 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL8 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
250 mg of a drug is diluted in 250 mL and given by gravity through a set of 20 gtt/mL. The order is 60 mg per hour. Find the drip rate R in drops per minute.
250 mg/250 mL60 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 12-hour shift. The patient weighs 110 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 12:00 and runs by pump at 60 mL/h. How many mL V are left in the bag at 14:30?
1000 mL60 mL/h12:00 → 14:30
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 16 units/kg/h for a patient who weighs 60 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL16 units/kg/h60 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 12.5 mcg/kg/min for a patient who weighs 96 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL12.5 mcg/kg/min96 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 375 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL375 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 580 mg. Draw up the dose: what volume V do you give?
1000 mg4.5 mL + 0.5 mL580 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 97 °F
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.
Multiply by 9/5
36.1·9/5 = 64.98
Add 32
T = 64.98 + 32 = 96.98 ≈ 97 °F
Answer
T = 97 °F
2.Nursing math & unit conversions
Answer: V = 2.4 L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Volume in a day
100 mL/h × 24 h = 2400 mL
In litres
V = 2400/1000 = 2.4 L
Answer
V = 2.4 L
3.Dosage calculations
Answer: V = 7.6 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 = 5·38 = 190 mg
Volume
V = 190/25 = 7.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.6 mL
4.Dosage calculations
Answer: V = 0.7 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.
Same units
0.7 mg = 700 mcg
Volume
V = 700/1000 = 0.7 mL
Answer
V = 0.7 mL
5.IV infusion rates
Answer: R = 21 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
8·60 = 480 min
Drip rate
R = 1000·10/480 = 20.83 ≈ 21 gtt/min
Answer
R = 21 gtt/min
At the bedside you round to the nearest whole drop: 21 gtt/min.
6.IV infusion rates
Answer: R = 20 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
250/250 = 1 mg/mL
Volume per hour
60/1 = 60 mL/h
Drip rate
R = 60·20/60 = 20 gtt/min
Answer
R = 20 gtt/min
7.IV fluids & fluid balance
Answer: U = 0.64 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
375 + 475 = 850 mL
Per kilogram per hour
U = 850/(110·12) = 0.6439 ≈ 0.64 mL/kg/h
Answer
U = 0.64 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 850 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
12:00 → 14:30 = 2.5 h
Volume infused
60·2.5 = 150 mL
Volume left
V = 1000 − 150 = 850 mL
Answer
V = 850 mL
9.Pediatric & critical-care dosing
Answer: R = 19.2 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.
Units per hour
16·60 = 960 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 960/50 = 19.2 mL/h
Answer
R = 19.2 mL/h
10.Pediatric & critical-care dosing
Answer: R = 36 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
12.5·96 = 1200 mcg/min
1200·60 = 72000 mcg/h
Pump rate
R = 72000/2000 = 36 mL/h
Answer
R = 36 mL/h
11.Pharmacy calculations
Answer: V = 3.8 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.
Final volume
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 375/100 = 3.75 ≈ 3.8 mL
Answer
V = 3.8 mL
12.Pharmacy calculations
Answer: V = 2.9 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.