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 drip-rate calculation gives 142.791 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
142.791 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 2 mcg/min. Express this dose rate D in mg/h.
2 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
A dose of 125 mg is needed from a 5% (w/v) solution. What volume V contains this dose?
125 mg5% w/v
V = mL
4.Dosage calculationsHard
You must prepare 100 mL of a 5% (w/v) solution from a 25% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 25%C₂ = 5%V₂ = 100 mL
V₁ = mL
5.IV infusion ratesMedium
Infuse 250 mL over 2 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL2 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 400 mg in 500 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?
400 mg/500 mL24 mL/h
D = mcg/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 total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 08:00 at 75 mL/h. After 4 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 · 4 h200 mL/h
t = h
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 20 units/kg/h for a patient who weighs 90 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL20 units/kg/h90 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 95 kg has an order for nitroglycerin at 30 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL30 mcg/min95 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.72 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.72 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.7 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 640 mg. Draw up the dose: what volume V do you give?
1000 mg1.7 mL + 0.8 mL640 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 143 gtt/min
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 ones place
142.791 → 2
Only the next digit decides
142.791 → 7
7 is 5 or more, so round 2 up.
The digits after it (91) are ignored: round once, never step by step.
Round
x = 143 gtt/min
Answer
x = 143 gtt/min
2.Nursing math & unit conversions
Answer: D = 0.12 mg/h
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.
Set up the chain
D = 2 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 2·60/1000 = 0.12 mg/h
Answer
D = 0.12 mg/h
3.Dosage calculations
Answer: V = 2.5 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
5% = 50 mg/mL
Volume
V = 125/50 = 2.5 mL
Answer
V = 2.5 mL
4.Dosage calculations
Answer: V₁ = 20 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 = 5·100/25 = 20 mL
Answer
V₁ = 20 mL
5.IV infusion rates
Answer: R = 31 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
2·60 = 120 min
Drip rate
R = 250·15/120 = 31.25 ≈ 31 gtt/min
Answer
R = 31 gtt/min
At the bedside you round to the nearest whole drop: 31 gtt/min.
6.IV infusion rates
Answer: D = 320 mcg/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
400000 mcg/500 mL = 800 mcg/mL
Dose per hour
24·800 = 19200 mcg/h
Dose per minute
D = 19200/60 = 320 mcg/min
Answer
D = 320 mcg/min
7.IV fluids & fluid balance
Answer: I = 1320 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.
Add the intake
oral: 100 + 200 + 200 = 500 mL
ice chips: 240/2 = 120 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 1·100 = 100 mL
I = 1320 mL
Answer
I = 1320 mL
8.IV fluids & fluid balance
Answer: t = 7.5 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
75·4 = 300 mL
1000 − 300 = 700 mL left
Second part
700/200 = 3.5 h
Total time
t = 4 + 3.5 = 7.5 h
Answer
t = 7.5 h
That is about 7 h 30 min, so the bag runs out at about 15:30.
9.Pediatric & critical-care dosing
Answer: R = 36 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
20·90 = 1 800 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1800/50 = 36 mL/h
Answer
R = 36 mL/h
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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
30·60 = 1800 mcg/h
Pump rate
R = 1800/100 = 18 mL/h
Answer
R = 18 mL/h
11.Pharmacy calculations
Answer: V = 7.2 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/10 000 mL = 0.1 mg/mL
Volume
V = 0.72/0.1 = 7.2 mL
Answer
V = 7.2 mL
12.Pharmacy calculations
Answer: V = 1.6 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.