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 dose is charted at 9:05 AM. Which entry is the same time on the 24-hour clock? Click it.
9:05 AM
110:05
209:05
321:05
408:05
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 21:00 and finishes at 07:20 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
21:0007:20
t = h
3.Dosage calculationsMedium
A child weighing 22 kg is prescribed 4 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
22 kg4 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
A patient weighs 160.6 lb. The prescription is 1 mg/kg as a single dose, and the stock contains 50 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.
160.6 lb1 mg/kg50 mg/1 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 25 mL/h, but no pump is available. It runs by gravity through a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
25 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
250 mg of a drug is diluted in 250 mL and given by gravity through a set of 60 gtt/mL. The order is 50 mg per hour. Find the drip rate R in drops per minute.
250 mg/250 mL50 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 56 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 09:30 and runs by pump at 50 mL/h. How many mL V are left in the bag at 15:00?
500 mL50 mL/h09:30 → 15:00
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 20 units/kg/h for a patient who weighs 88 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL20 units/kg/h88 kg
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 7.5 mcg/kg/min for a patient who weighs 94 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL7.5 mcg/kg/min94 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 8.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL750 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 2 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 150 mg. Draw up the dose: what volume V do you give?
250 mg2 mL + 0.5 mL150 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 09:05
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Convert the hour
9 AM → 09
Answer
09:05
Answer
09:05
2.Nursing math & unit conversions
Answer: t = 10.33 h
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Before midnight
21:00 → 24:00 = 180 min
After midnight
00:00 → 07:20 = 440 min
Total
180 + 440 = 620 min
t = 620/60 = 10.33 h
Answer
t = 10.33 h
3.Dosage calculations
Answer: V = 4.4 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 = 4·22 = 88 mg
Volume
V = 88/20 = 4.4 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 4.4 mL
4.Dosage calculations
Answer: V = 1.5 mL
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.
Weight in kg
160.6/2.2 = 73 kg
Dose
1·73 = 73 mg
Volume
V = (73/50)·1 = 1.46 ≈ 1.5 mL
Answer
V = 1.5 mL
5.IV infusion rates
Answer: R = 25 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.
Millilitres per minute
25/60 = 0.4167 mL/min
Drip rate
R = 0.4167·60 = 25 gtt/min
Answer
R = 25 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
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
250/250 = 1 mg/mL
Volume per hour
50/1 = 50 mL/h
Drip rate
R = 50·60/60 = 50 gtt/min
Answer
R = 50 gtt/min
7.IV fluids & fluid balance
Answer: U = 1.71 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
325 + 200 + 450 + 175 = 1150 mL
Per kilogram per hour
U = 1150/(56·12) = 1.711 ≈ 1.71 mL/kg/h
Answer
U = 1.71 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 225 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
09:30 → 15:00 = 5.5 h
Volume infused
50·5.5 = 275 mL
Volume left
V = 500 − 275 = 225 mL
Answer
V = 225 mL
9.Pediatric & critical-care dosing
Answer: R = 17.6 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
20·88 = 1 760 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1760/100 = 17.6 mL/h
Answer
R = 17.6 mL/h
10.Pediatric & critical-care dosing
Answer: R = 42.3 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
7.5·94 = 705 mcg/min
705·60 = 42300 mcg/h
Pump rate
R = 42300/1000 = 42.3 mL/h
Answer
R = 42.3 mL/h
11.Pharmacy calculations
Answer: V = 1.5 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.
Concentration from the label
8.2 mL → 500 000 units/mL
Volume to give
V = 750 000/500 000 = 1.5 mL
Answer
V = 1.5 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.