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 patient’s temperature is 95.7 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
95.7 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 5 mcg/kg/min for a patient who weighs 97 kg. Express the dose rate D in mg/h. Round to two decimal places.
5 mcg/kg/min97 kg
D = mg/h
3.Dosage calculationsMedium
A child weighing 6 kg is prescribed 10 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
6 kg10 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
You must prepare 100 mL of a 0.5% (w/v) solution from a 25% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 25%C₂ = 0.5%V₂ = 100 mL
V₁ = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 12 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL12 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1000 mL was ordered over 6 hours. After 3 hours you find that 550 mL is still in the bag, and the order must still finish on time. By what percentage Δ must the original pump rate be increased?
1000 mL / 6 hafter 3 h: 550 mL
Δ = %
7.IV fluids & fluid balanceMedium
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 8-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 500 mL bag was started at 06:00 and runs by pump at 100 mL/h. How many mL V are left in the bag at 09:30?
500 mL100 mL/h06:00 → 09:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 64 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg64 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 88 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/min88 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.38 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.38 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 200 mg. Draw up the dose: what volume V do you give?
500 mg4.4 mL + 0.6 mL200 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 35.4 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
95.7 − 32 = 63.7
Multiply by 5/9
T = 63.7·5/9 = 35.39 ≈ 35.4 °C
Answer
T = 35.4 °C
2.Nursing math & unit conversions
Answer: D = 29.1 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 = 5 mcg/kg/min × 97 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 5·97·60/1000 = 29.1 mg/h
Answer
D = 29.1 mg/h
3.Dosage calculations
Answer: V = 3 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
Dose from body weight
D = 10·6 = 60 mg
Volume
V = 60/20 = 3 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3 mL
4.Dosage calculations
Answer: V₁ = 2 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 = 0.5·100/25 = 2 mL
Answer
V₁ = 2 mL
5.IV infusion rates
Answer: R = 21 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
12·60 = 720 min
Drip rate
R = 1000·15/720 = 20.83 ≈ 21 gtt/min
Answer
R = 21 gtt/min
At the bedside you round to the nearest whole drop: 21 gtt/min.
6.IV infusion rates
Answer: Δ = 10 %
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.
Original rate
1000/6 = 166.7 mL/h
New rate
R = 550/3 = 183.3 mL/h
Percentage change
Δ = (183.3 − 166.7)/166.7·100% = 10%
Answer
Δ = 10%
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
7.IV fluids & fluid balance
Answer: I = 1750 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: 200 + 200 + 250 = 650 mL
ice chips: 200/2 = 100 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 2·100 = 200 mL
I = 1750 mL
Answer
I = 1750 mL
8.IV fluids & fluid balance
Answer: V = 150 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
06:00 → 09:30 = 3.5 h
Volume infused
100·3.5 = 350 mL
Volume left
V = 500 − 350 = 150 mL
Answer
V = 150 mL
9.Pediatric & critical-care dosing
Answer: V = 1 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
80·64 = 5 120 units
Volume
V = 5120/5000 = 1.024 ≈ 1 mL
Answer
V = 1 mL
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 = 3.8 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 = 0.38/0.1 = 3.8 mL
Answer
V = 3.8 mL
12.Pharmacy calculations
Answer: V = 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.