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 1:35 AM. Which entry is the same time on the 24-hour clock? Click it.
1:35 AM
113:35
200:35
302:35
401:35
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 21:10 and finishes at 08:55 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.
21:1008:55
t = h
3.Dosage calculationsMedium
A child weighing 30 kg is prescribed 4 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
30 kg4 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A patient weighs 85.8 lb. The prescription is 10 mg/kg as a single dose, and the stock contains 40 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.
85.8 lb10 mg/kg40 mg/1 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 150 mL/h, but no pump is available. It runs by gravity through a giving set of 20 gtt/mL. Find the drip rate R in drops per minute.
150 mL/h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 100 mg of a drug in 100 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
100 mg/100 mL10 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 80 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 1000 mL bag runs by pump at 120 mL/h. At 13:00, 650 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL650 mL infused120 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 15 units/kg/h for a patient who weighs 55 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL15 units/kg/h55 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 95 kg has an order for norepinephrine at 8 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL8 mcg/min95 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 1 200 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL1 200 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 500 mL of 2% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
20%0%2%500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 01:35
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
1 AM → 01
Answer
01:35
Answer
01:35
2.Nursing math & unit conversions
Answer: t = 11.75 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
21:10 → 24:00 = 170 min
After midnight
00:00 → 08:55 = 535 min
Total
170 + 535 = 705 min
t = 705/60 = 11.75 h
Answer
t = 11.75 h
3.Dosage calculations
Answer: V = 4.8 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 = 4·30 = 120 mg
Volume
V = 120/25 = 4.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 4.8 mL
4.Dosage calculations
Answer: V = 9.8 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
85.8/2.2 = 39 kg
Dose
10·39 = 390 mg
Volume
V = (390/40)·1 = 9.75 ≈ 9.8 mL
Answer
V = 9.8 mL
5.IV infusion rates
Answer: R = 50 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
150/60 = 2.5 mL/min
Drip rate
R = 2.5·20 = 50 gtt/min
Answer
R = 50 gtt/min
6.IV infusion rates
Answer: D = 10 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
100/100 = 1 mg/mL
Dose rate
D = 1·10 = 10 mg/h
Answer
D = 10 mg/h
7.IV fluids & fluid balance
Answer: U = 2.19 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
375 + 250 + 300 + 475 = 1400 mL
Per kilogram per hour
U = 1400/(80·8) = 2.188 ≈ 2.19 mL/kg/h
Answer
U = 2.19 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 2.9 h
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.
Volume left
1000 − 650 = 350 mL
Time
t = 350/120 = 2.917 ≈ 2.9 h
Answer
t = 2.9 h
That is about 2 h 55 min, so the bag runs out at about 15:55.
9.Pediatric & critical-care dosing
Answer: R = 16.5 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
15·55 = 825 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 825/50 = 16.5 mL/h
Answer
R = 16.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 30 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
8·60 = 480 mcg/h
Pump rate
R = 480/16 = 30 mL/h
Answer
R = 30 mL/h
11.Pharmacy calculations
Answer: V = 2.4 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 = 1 200 000/500 000 = 2.4 mL
Answer
V = 2.4 mL
12.Pharmacy calculations
Answer: V = 450 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
20%: 2 − 0 = 2 parts
0%: 20 − 2 = 18 parts
total: 20 parts
Water
V = 500·18/20 = 450 mL
Answer
V = 450 mL
Check: 50 mL of 20% contains 10 g of drug, which is 2% of 500 mL.