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 4 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.
4 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). A prescription reads 2 tsp of an oral suspension three times a day for 7 days. The suspension comes in 100 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?
2 tspthree times a day7 days100 mL1 tsp = 5 mL
N =
3.Dosage calculationsMedium
A dose of 10 mg is needed from a 0.5% (w/v) solution. What volume V contains this dose?
10 mg0.5% w/v
V = mL
4.Dosage calculationsHard
The prescription is 2.2 mg. The ampoule contains 4000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2.2 mg4000 mcg/mL
V = mL
5.IV infusion ratesMedium
A drip runs at 60 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 12 hours?
60 gtt/min60 gtt/mL12 h
V = mL
6.IV infusion ratesHard
A drip runs at 42 gtt/min through a set of 15 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min15 gtt/mL300 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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 12:00 and runs by pump at 150 mL/h. How many mL V are left in the bag at 15:30?
1000 mL150 mL/h12:00 → 15:30
V = mL
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 70 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
70 units/kg70 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 8 mcg/kg/min for a patient who weighs 60 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL8 mcg/kg/min60 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 8.2 mL of diluent. The prescribed dose is 300 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL300 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 20% dextrose by mixing 50% and 5% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%5%20%450 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.24 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
4 + 0.9375 = 4.938 lb
Pounds to kilograms
m = 4.938/2.2 = 2.244 ≈ 2.24 kg
Answer
m = 2.24 kg
2.Nursing math & unit conversions
Answer: N = 3
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.
Total volume
10 mL × 3 × 7 = 210 mL
Bottles
210/100 = 2.1 → N = 3
Answer
N = 3
3.Dosage calculations
Answer: V = 2 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
0.5% = 5 mg/mL
Volume
V = 10/5 = 2 mL
Answer
V = 2 mL
4.Dosage calculations
Answer: V = 0.55 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
2.2 mg = 2200 mcg
Volume
V = 2200/4000 = 0.55 mL
Answer
V = 0.55 mL
5.IV infusion rates
Answer: V = 720 mL
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
60·60/60 = 60 mL/h
Volume
V = 60·12 = 720 mL
Answer
V = 720 mL
6.IV infusion rates
Answer: t = 1.8 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 = 300/168 = 1.786 ≈ 1.8 h
Answer
t = 1.8 h
7.IV fluids & fluid balance
Answer: B = 935 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.
Total intake
oral: 240 + 200 = 440 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1740 mL
Total output
475 + 250 + 80 = 805 mL
Balance
B = 1740 − 805 = 935 mL
Answer
B = 935 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 475 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 → 15:30 = 3.5 h
Volume infused
150·3.5 = 525 mL
Volume left
V = 1000 − 525 = 475 mL
Answer
V = 475 mL
9.Pediatric & critical-care dosing
Answer: V = 0.98 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
70·70 = 4 900 units
Volume
V = 4900/5000 = 0.98 mL
Answer
V = 0.98 mL
10.Pediatric & critical-care dosing
Answer: R = 18 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
8·60 = 480 mcg/min
480·60 = 28800 mcg/h
Pump rate
R = 28800/1600 = 18 mL/h
Answer
R = 18 mL/h
11.Pharmacy calculations
Answer: V = 0.6 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 = 300 000/500 000 = 0.6 mL
Answer
V = 0.6 mL
12.Pharmacy calculations
Answer: V = 150 mL
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.