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 a small injection gives 0.41606 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.41606 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tsp of an oral suspension three times a day for 5 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?
½ tspthree times a day5 days100 mL1 tsp = 5 mL
N =
3.Dosage calculationsMedium
A patient weighs 30 kg and is prescribed 30 mg/kg as a single dose. Find the dose D in mg.
30 kg30 mg/kg
D = mg
4.Dosage calculationsHard
You must prepare 250 mL of a 2.5% (w/v) solution from a 25% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 25%C₂ = 2.5%V₂ = 250 mL
V₁ = mL
5.IV infusion ratesMedium
A drip runs at 30 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 4 hours?
30 gtt/min15 gtt/mL4 h
V = mL
6.IV infusion ratesHard
A bag contains 1 g of a drug in 250 mL. The order is 3 mg per minute. At what rate R do you set the pump, in mL/h?
1 g/250 mL3 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 patient weighs 102 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
102 kg12 hurine: 250 mLurine: 250 mLwound drain: 30 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 11:30 at 100 mL/h. After 4 hours the rate is changed to 80 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 mL100 mL/h · 4 h80 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 78 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL18 units/kg/h78 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 2 mcg/kg/min for a patient who weighs 89 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min89 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 18.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 780 mg. Draw up the dose: what volume V do you give?
1000 mg4.8 mL + 0.2 mL780 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.42 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 hundredths place
0.41606 → 1
Only the next digit decides
0.41606 → 6
6 is 5 or more, so round 1 up.
The digits after it (06) are ignored: round once, never step by step.
Round
x = 0.42 mL
Answer
x = 0.42 mL
2.Nursing math & unit conversions
Answer: N = 1
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
2.5 mL × 3 × 5 = 37.5 mL
Bottles
37.5/100 = 0.375 → N = 1
Answer
N = 1
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
30·30 = 900 mg
Answer
D = 900 mg
4.Dosage calculations
Answer: V₁ = 25 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.
Volume of stock
V₁ = 2.5·250/25 = 25 mL
Answer
V₁ = 25 mL
5.IV infusion rates
Answer: V = 480 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
30·60/15 = 120 mL/h
Volume
V = 120·4 = 480 mL
Answer
V = 480 mL
6.IV infusion rates
Answer: R = 45 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
3·60 = 180 mg/h
Pump rate
R = 180/4 = 45 mL/h
Answer
R = 45 mL/h
7.IV fluids & fluid balance
Answer: U = 0.41 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
250 + 250 = 500 mL
Per kilogram per hour
U = 500/(102·12) = 0.4085 ≈ 0.41 mL/kg/h
Answer
U = 0.41 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 11.5 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.
First part
100·4 = 400 mL
1000 − 400 = 600 mL left
Second part
600/80 = 7.5 h
Total time
t = 4 + 7.5 = 11.5 h
Answer
t = 11.5 h
That is about 11 h 30 min, so the bag runs out at about 23:00.
9.Pediatric & critical-care dosing
Answer: R = 35.1 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
18·78 = 1 404 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1404/40 = 35.1 mL/h
Answer
R = 35.1 mL/h
10.Pediatric & critical-care dosing
Answer: R = 6.7 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
2·89 = 178 mcg/min
178·60 = 10680 mcg/h
Pump rate
R = 10680/1600 = 6.675 ≈ 6.7 mL/h
Answer
R = 6.7 mL/h
11.Pharmacy calculations
Answer: V = 9.6 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
18.2 mL → 250 000 units/mL
Volume to give
V = 2 400 000/250 000 = 9.6 mL
Answer
V = 9.6 mL
12.Pharmacy calculations
Answer: V = 3.9 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.