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 dose calculation for an injection gives 7.0625 mL. The rule in this exercise is that volumes of 1 mL or more are rounded to the nearest tenth of a mL. What value x do you record?
7.0625 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A maintenance infusion runs at 20 mL/h without a break. How many litres V does it deliver in 24 hours?
20 mL/h24 h
V = L
3.Dosage calculationsMedium
A vial contains 1 g of powder. The label says: add 3.4 mL of water for injection to give a total volume of 4 mL. The prescription is 300 mg. What volume V of the reconstituted solution do you give?
1 g+ 3.4 mL → 4 mL300 mg
V = mL
4.Dosage calculationsHard
An infusion contains 50000 units of a drug in 500 mL. The prescription is 1200 units per hour. At what rate R do you set the pump, in mL/h?
50000 units/500 mL1200 units/h
R = mL/h
5.IV infusion ratesMedium
A drip runs at 75 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 3 hours?
75 gtt/min60 gtt/mL3 h
V = mL
6.IV infusion ratesHard
A bag contains 1 g of a drug in 250 mL. The order is 1.5 mg per minute. At what rate R do you set the pump, in mL/h?
1 g/250 mL1.5 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 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 500 mL bag runs by pump at 120 mL/h. At 06:00, 200 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL200 mL infused120 mL/h
t = h
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 12 units/kg/h for a patient who weighs 63 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL12 units/kg/h63 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 33 mL/h. The patient weighs 89 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL33 mL/h89 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.23 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.23 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 110 mg. Draw up the dose: what volume V do you give?
500 mg4.2 mL + 0.8 mL110 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 7.1 mL
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
7.0625 → 0
Only the next digit decides
7.0625 → 6
6 is 5 or more, so round 0 up.
The digits after it (25) are ignored: round once, never step by step.
Round
x = 7.1 mL
Answer
x = 7.1 mL
2.Nursing math & unit conversions
Answer: V = 0.48 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
20 mL/h × 24 h = 480 mL
In litres
V = 480/1000 = 0.48 L
Answer
V = 0.48 L
3.Dosage calculations
Answer: V = 1.2 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.
Concentration after mixing
1000 mg/4 mL = 250 mg/mL
Volume
V = 300/250 = 1.2 mL
Answer
V = 1.2 mL
4.Dosage calculations
Answer: R = 12 mL/h
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.
Concentration
50000/500 = 100 units/mL
Pump rate
R = 1200/100 = 12 mL/h
Answer
R = 12 mL/h
5.IV infusion rates
Answer: V = 225 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
75·60/60 = 75 mL/h
Volume
V = 75·3 = 225 mL
Answer
V = 225 mL
6.IV infusion rates
Answer: R = 22.5 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
1.5·60 = 90 mg/h
Pump rate
R = 90/4 = 22.5 mL/h
Answer
R = 22.5 mL/h
7.IV fluids & fluid balance
Answer: B = 895 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: 100 + 200 + 240 = 540 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1490 mL
Total output
300 + 225 + 70 = 595 mL
Balance
B = 1490 − 595 = 895 mL
Answer
B = 895 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 2.5 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.
Volume left
500 − 200 = 300 mL
Time
t = 300/120 = 2.5 h
Answer
t = 2.5 h
That is about 2 h 30 min, so the bag runs out at about 08:30.
9.Pediatric & critical-care dosing
Answer: R = 15.1 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
12·63 = 756 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 756/50 = 15.12 ≈ 15.1 mL/h
Answer
R = 15.1 mL/h
10.Pediatric & critical-care dosing
Answer: D = 12.4 mcg/kg/min
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
500 000/250 = 2000 mcg/mL
Micrograms per minute
33·2000 = 66000 mcg/h
66000/60 = 1100 mcg/min
Per kilogram
D = 1100/89 = 12.36 ≈ 12.4 mcg/kg/min
Answer
D = 12.4 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.23 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 = 0.23/1 = 0.23 mL
Answer
V = 0.23 mL
12.Pharmacy calculations
Answer: V = 1.1 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.