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 6 lb 5 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
6 lb 5 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 1 tbsp of an oral suspension three times a day for 10 days. Using 1 tbsp = 15 mL, how many mL V are needed for the whole course?
1 tbspthree times a day10 days1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 90 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.
90 kg10 mg/kg
D = mg
4.Dosage calculationsHard
A child weighing 12 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give? Round to one decimal place.
12 kg12.5 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
Infuse 1500 mL over 4 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1500 mL4 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
500 mg of a drug is diluted in 500 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.
500 mg/500 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 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 infusion starts at 12:30 at 75 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 mL75 mL/h · 3 h200 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 104 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg104 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 5 mcg/kg/min for a patient who weighs 81 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min81 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 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
Practice exercise (made-up values, not clinical guidance). You have 60 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 2% ointment? Round to the nearest whole gram.
60 g · 2.5%0.5%2%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.87 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
5 oz/16 = 0.3125 lb
6 + 0.3125 = 6.313 lb
Pounds to kilograms
m = 6.313/2.2 = 2.869 ≈ 2.87 kg
Answer
m = 2.87 kg
2.Nursing math & unit conversions
Answer: V = 450 mL
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 per dose
1 tbsp = 1·15 = 15 mL
Whole course
V = 15 mL × 3/day × 10 = 450 mL
Answer
V = 450 mL
3.Dosage calculations
Answer: D = 900 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
10·90 = 900 mg
Answer
D = 900 mg
4.Dosage calculations
Answer: V = 3.8 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
12.5·12 = 150 mg
Volume
V = (150/40)·1 = 3.75 ≈ 3.8 mL
Answer
V = 3.8 mL
5.IV infusion rates
Answer: R = 63 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
4·60 = 240 min
Drip rate
R = 1500·10/240 = 62.5 ≈ 63 gtt/min
Answer
R = 63 gtt/min
At the bedside you round to the nearest whole drop: 63 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
500/500 = 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: B = −175 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: 180 + 200 + 120 = 500 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1200 mL
Total output
450 + 425 + 500 = 1375 mL
Balance
B = 1200 − 1375 = −175 mL
Answer
B = −175 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: t = 6.9 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
75·3 = 225 mL
1000 − 225 = 775 mL left
Second part
775/200 = 3.875 h
Total time
t = 3 + 3.875 = 6.875 ≈ 6.9 h
Answer
t = 6.9 h
That is about 6 h 53 min, so the bag runs out at about 19:23.
9.Pediatric & critical-care dosing
Answer: V = 7.3 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
70·104 = 7 280 units
Volume
V = 7280/1000 = 7.28 ≈ 7.3 mL
Answer
V = 7.3 mL
10.Pediatric & critical-care dosing
Answer: R = 24.3 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
5·81 = 405 mcg/min
405·60 = 24300 mcg/h
Pump rate
R = 24300/1000 = 24.3 mL/h
Answer
R = 24.3 mL/h
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: m = 20 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.