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 weight conversion gives 77.3158 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
77.3158 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tbsp of an oral suspension every 8 hours for 10 days. Using 1 tbsp = 15 mL, how many mL V are needed for the whole course?
½ tbspevery 8 hours10 days1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 60 kg and is prescribed 5 mg/kg as a single dose. Find the dose D in mg.
60 kg5 mg/kg
D = mg
4.Dosage calculationsHard
A child weighing 20 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give?
20 kg10 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
A drip runs at 20 gtt/min through a set of 20 gtt/mL. How many millilitres V does the patient receive in 2 hours?
20 gtt/min20 gtt/mL2 h
V = mL
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 500 mL and runs at 15 mL/h. How many milligrams per hour D does the patient receive?
200 mg/500 mL15 mL/h
D = mg/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 patient weighs 78 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 500 mL bag was started at 13:00 and runs by pump at 60 mL/h. How many mL V are left in the bag at 16:30?
500 mL60 mL/h13:00 → 16:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 16 units/kg/h for a patient who weighs 88 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL16 units/kg/h88 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 80 kg has an order for norepinephrine at 6 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL6 mcg/min80 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.35 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.35 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 250 mg. Draw up the dose: what volume V do you give?
1000 mg1.8 mL + 0.2 mL250 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 77.3 kg
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
77.3158 → 3
Only the next digit decides
77.3158 → 1
1 is 4 or less, so 3 stays.
The digits after it (58) are ignored: round once, never step by step.
Round
x = 77.3 kg
Answer
x = 77.3 kg
2.Nursing math & unit conversions
Answer: V = 225 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
½ tbsp = 0.5·15 = 7.5 mL
Whole course
V = 7.5 mL × 3/day × 10 = 225 mL
Answer
V = 225 mL
3.Dosage calculations
Answer: D = 300 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
5·60 = 300 mg
Answer
D = 300 mg
4.Dosage calculations
Answer: V = 5 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
10·20 = 200 mg
Volume
V = (200/40)·1 = 5 mL
Answer
V = 5 mL
5.IV infusion rates
Answer: V = 120 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
20·60/20 = 60 mL/h
Volume
V = 60·2 = 120 mL
Answer
V = 120 mL
6.IV infusion rates
Answer: D = 6 mg/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.
Concentration
200/500 = 0.4 mg/mL
Dose rate
D = 0.4·15 = 6 mg/h
Answer
D = 6 mg/h
7.IV fluids & fluid balance
Answer: U = 1.39 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 + 150 + 450 + 325 = 1300 mL
Per kilogram per hour
U = 1300/(78·12) = 1.389 ≈ 1.39 mL/kg/h
Answer
U = 1.39 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 290 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
13:00 → 16:30 = 3.5 h
Volume infused
60·3.5 = 210 mL
Volume left
V = 500 − 210 = 290 mL
Answer
V = 290 mL
9.Pediatric & critical-care dosing
Answer: R = 28.2 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
16·88 = 1 408 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1408/50 = 28.16 ≈ 28.2 mL/h
Answer
R = 28.2 mL/h
10.Pediatric & critical-care dosing
Answer: R = 11.3 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
6·60 = 360 mcg/h
Pump rate
R = 360/32 = 11.25 ≈ 11.3 mL/h
Answer
R = 11.3 mL/h
11.Pharmacy calculations
Answer: V = 0.35 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 = 0.35/1 = 0.35 mL
Answer
V = 0.35 mL
12.Pharmacy calculations
Answer: V = 0.5 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.