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 35.7 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
35.7 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 4 mcg/kg/min for a patient who weighs 78 kg. Express the dose rate D in mg/h. Round to two decimal places.
4 mcg/kg/min78 kg
D = mg/h
3.Dosage calculationsMedium
An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.5 mg IM for anaphylaxis. What volume V do you draw up?
1:10000.5 mg
V = mL
4.Dosage calculationsHard
The prescription is 800 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
800 units5000 units/mL
V = mL
5.IV infusion ratesMedium
1000 mL was ordered over 10 hours. After 6 hours you find that 500 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
1000 mL / 10 hafter 6 h: 500 mL
R = mL/h
6.IV infusion ratesHard
A bag contains 1000 mg of a drug in 100 mL and runs at 5 mL/h. How many milligrams per hour D does the patient receive?
1000 mg/100 mL5 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 8-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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 07:00 and runs by pump at 100 mL/h. How many mL V are left in the bag at 08:00?
1000 mL100 mL/h07:00 → 08:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 1 unit/h. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL1 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 2.5 mcg/kg/min for a patient who weighs 79 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL2.5 mcg/kg/min79 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.58 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.58 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 75 mg. Draw up the dose: what volume V do you give?
500 mg9.5 mL + 0.5 mL75 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 96.3 °F
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.
Multiply by 9/5
35.7·9/5 = 64.26
Add 32
T = 64.26 + 32 = 96.26 ≈ 96.3 °F
Answer
T = 96.3 °F
2.Nursing math & unit conversions
Answer: D = 18.72 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 = 4 mcg/kg/min × 78 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 4·78·60/1000 = 18.72 mg/h
Answer
D = 18.72 mg/h
3.Dosage calculations
Answer: V = 0.5 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
1:1000 = 1 g/1000 mL = 1 mg/mL
Volume
V = 0.5/1 = 0.5 mL
Answer
V = 0.5 mL
US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.
4.Dosage calculations
Answer: V = 0.16 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.
Volume
V = 800/5000 = 0.16 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.16 mL
5.IV infusion rates
Answer: R = 125 mL/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.
Original rate
1000/10 = 100 mL/h
New rate
R = 500/4 = 125 mL/h
Answer
R = 125 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: D = 50 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
1000/100 = 10 mg/mL
Dose rate
D = 10·5 = 50 mg/h
Answer
D = 50 mg/h
7.IV fluids & fluid balance
Answer: B = 170 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: 240 + 100 + 120 = 460 mL
ice chips: 120/2 = 60 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1420 mL
Total output
150 + 350 + 275 + 475 = 1250 mL
Balance
B = 1420 − 1250 = 170 mL
Answer
B = 170 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 900 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
07:00 → 08:00 = 1 h
Volume infused
100·1 = 100 mL
Volume left
V = 1000 − 100 = 900 mL
Answer
V = 900 mL
9.Pediatric & critical-care dosing
Answer: R = 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.
Concentration
250/250 = 1 units/mL
Pump rate
R = 1/1 = 1 mL/h
Answer
R = 1 mL/h
10.Pediatric & critical-care dosing
Answer: R = 11.9 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
2.5·79 = 197.5 mcg/min
197.5·60 = 11850 mcg/h
Pump rate
R = 11850/1000 = 11.85 ≈ 11.9 mL/h
Answer
R = 11.9 mL/h
11.Pharmacy calculations
Answer: V = 0.58 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 = 0.58/1 = 0.58 mL
Answer
V = 0.58 mL
12.Pharmacy calculations
Answer: V = 1.5 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.