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 103.5 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
103.5 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 3 mcg/kg/min for a patient who weighs 52 kg. Express the dose rate D in mg/h. Round to two decimal places.
3 mcg/kg/min52 kg
D = mg/h
3.Dosage calculationsMedium
A patient weighs 80 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.
80 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 2200 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2200 units10000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 3 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL3 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 250 mg of a drug in 250 mL and runs at 12 mL/h. How many milligrams per hour D does the patient receive?
250 mg/250 mL12 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 patient weighs 96 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
96 kg8 hurine: 200 mLurine: 225 mLwound drain: 40 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 06:15 and runs by pump at 75 mL/h. How many mL V are left in the bag at 14:15?
1000 mL75 mL/h06:15 → 14:15
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 16 units/kg/h for a patient who weighs 69 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL16 units/kg/h69 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 97 kg has an order for nitroglycerin at 5 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 mL5 mcg/min97 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. The prescribed dose is 300 mg. What volume V do you draw up? Round to one decimal place.
500 mg1.8 mL+0.2 mL300 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 250 mL of 45% 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%45%250 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 39.7 °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
103.5 − 32 = 71.5
Multiply by 5/9
T = 71.5·5/9 = 39.72 ≈ 39.7 °C
Answer
T = 39.7 °C
2.Nursing math & unit conversions
Answer: D = 9.36 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 = 3 mcg/kg/min × 52 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 3·52·60/1000 = 9.36 mg/h
Answer
D = 9.36 mg/h
3.Dosage calculations
Answer: D = 600 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
7.5·80 = 600 mg
Answer
D = 600 mg
4.Dosage calculations
Answer: V = 0.22 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 = 2200/10000 = 0.22 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.22 mL
5.IV infusion rates
Answer: R = 42 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
3·60 = 180 min
Drip rate
R = 500·15/180 = 41.67 ≈ 42 gtt/min
Answer
R = 42 gtt/min
At the bedside you round to the nearest whole drop: 42 gtt/min.
6.IV infusion rates
Answer: D = 12 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
250/250 = 1 mg/mL
Dose rate
D = 1·12 = 12 mg/h
Answer
D = 12 mg/h
7.IV fluids & fluid balance
Answer: U = 0.55 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
200 + 225 = 425 mL
Per kilogram per hour
U = 425/(96·8) = 0.5534 ≈ 0.55 mL/kg/h
Answer
U = 0.55 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 400 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
06:15 → 14:15 = 8 h
Volume infused
75·8 = 600 mL
Volume left
V = 1000 − 600 = 400 mL
Answer
V = 400 mL
9.Pediatric & critical-care dosing
Answer: R = 11 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
16·69 = 1 104 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1104/100 = 11.04 ≈ 11 mL/h
Answer
R = 11 mL/h
10.Pediatric & critical-care dosing
Answer: R = 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
5·60 = 300 mcg/h
Pump rate
R = 300/100 = 3 mL/h
Answer
R = 3 mL/h
11.Pharmacy calculations
Answer: V = 1.2 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
1.8 + 0.2 = 2 mL
Concentration
500/2 = 250 mg/mL
Volume to give
V = 300/250 = 1.2 mL
Answer
V = 1.2 mL
12.Pharmacy calculations
Answer: V = 125 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%: 45 − 0 = 45 parts
0%: 90 − 45 = 45 parts
total: 90 parts
Water
V = 250·45/90 = 125 mL
Answer
V = 125 mL
Check: 125 mL of 90% contains 112.5 mL of drug, which is 45% of 250 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.