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 37.8 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
37.8 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tsp of an oral suspension every 6 hours for 14 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
½ tspevery 6 hours14 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.3 mg IM for anaphylaxis. What volume V do you draw up?
1:10000.3 mg
V = mL
4.Dosage calculationsHard
You must prepare 200 mL of a 2% (w/v) solution from a 10% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 10%C₂ = 2%V₂ = 200 mL
V₁ = mL
5.IV infusion ratesMedium
Infuse 500 mL over 5 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL5 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1000 mg of a drug is diluted in 250 mL and given by gravity through a set of 60 gtt/mL. The order is 200 mg per hour. Find the drip rate R in drops per minute.
1000 mg/250 mL200 mg/h60 gtt/mL
R = gtt/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 patient weighs 106 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
106 kg12 hurine: 250 mLurine: 400 mLwound drain: 110 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 11:00 and runs by pump at 150 mL/h. How many mL V are left in the bag at 12:00?
1000 mL150 mL/h11:00 → 12:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 101 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg101 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 72 kg has an order for nitroglycerin at 15 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL15 mcg/min72 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 500 mg. What volume V do you draw up? Round to one decimal place.
1000 mg3.5 mL+0.5 mL500 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 60% ethanol from a 90% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
90%0%60%600 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 100 °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
37.8·9/5 = 68.04
Add 32
T = 68.04 + 32 = 100 °F
Answer
T = 100 °F
2.Nursing math & unit conversions
Answer: V = 140 mL
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 per dose
½ tsp = 0.5·5 = 2.5 mL
Whole course
V = 2.5 mL × 4/day × 14 = 140 mL
Answer
V = 140 mL
3.Dosage calculations
Answer: V = 0.3 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 = 0.3/1 = 0.3 mL
Answer
V = 0.3 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: V₁ = 40 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 = 2·200/10 = 40 mL
Answer
V₁ = 40 mL
5.IV infusion rates
Answer: R = 17 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
5·60 = 300 min
Drip rate
R = 500·10/300 = 16.67 ≈ 17 gtt/min
Answer
R = 17 gtt/min
At the bedside you round to the nearest whole drop: 17 gtt/min.
6.IV infusion rates
Answer: R = 50 gtt/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
1000/250 = 4 mg/mL
Volume per hour
200/4 = 50 mL/h
Drip rate
R = 50·60/60 = 50 gtt/min
Answer
R = 50 gtt/min
7.IV fluids & fluid balance
Answer: U = 0.51 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 + 400 = 650 mL
Per kilogram per hour
U = 650/(106·12) = 0.511 ≈ 0.51 mL/kg/h
Answer
U = 0.51 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 850 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
11:00 → 12:00 = 1 h
Volume infused
150·1 = 150 mL
Volume left
V = 1000 − 150 = 850 mL
Answer
V = 850 mL
9.Pediatric & critical-care dosing
Answer: V = 1.2 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
60·101 = 6 060 units
Volume
V = 6060/5000 = 1.212 ≈ 1.2 mL
Answer
V = 1.2 mL
10.Pediatric & critical-care dosing
Answer: R = 4.5 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
15·60 = 900 mcg/h
Pump rate
R = 900/200 = 4.5 mL/h
Answer
R = 4.5 mL/h
11.Pharmacy calculations
Answer: V = 2 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.
Final volume
3.5 + 0.5 = 4 mL
Concentration
1000/4 = 250 mg/mL
Volume to give
V = 500/250 = 2 mL
Answer
V = 2 mL
12.Pharmacy calculations
Answer: V = 200 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Alligation parts
90%: 60 − 0 = 60 parts
0%: 90 − 60 = 30 parts
total: 90 parts
Water
V = 600·30/90 = 200 mL
Answer
V = 200 mL
Check: 400 mL of 90% contains 360 mL of drug, which is 60% of 600 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.