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 11:25 AM. Which entry is the same time on the 24-hour clock? Click it.
11:25 AM
112:25
211:25
323:25
410:25
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 8 mcg/min. Express this dose rate D in mg/h.
8 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
A child weighing 12 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
12 kg7.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
You must prepare 200 mL of a 0.5% (w/v) solution from a 50% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 50%C₂ = 0.5%V₂ = 200 mL
V₁ = mL
5.IV infusion ratesMedium
Infuse 250 mL over 8 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL8 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 28 gtt/min through a set of 20 gtt/mL. There are 450 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
28 gtt/min20 gtt/mL450 mL
t = 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 12-hour shift. The patient weighs 103 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 was started at 13:15 and runs by pump at 120 mL/h. How many mL V are left in the bag at 15:45?
1000 mL120 mL/h13:15 → 15:45
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 69 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg69 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 21 mL/h. The patient weighs 78 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL21 mL/h78 kg
D = mcg/kg/min
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 400 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL400 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 150 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 2% ointment? Round to the nearest whole gram.
150 g · 2.5%0.5%2%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: 11:25
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
11 AM → 11
Answer
11:25
Answer
11:25
2.Nursing math & unit conversions
Answer: D = 0.48 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 = 8 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 8·60/1000 = 0.48 mg/h
Answer
D = 0.48 mg/h
3.Dosage calculations
Answer: V = 3.6 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 = 7.5·12 = 90 mg
Volume
V = 90/25 = 3.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3.6 mL
4.Dosage calculations
Answer: V₁ = 2 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 = 0.5·200/50 = 2 mL
Answer
V₁ = 2 mL
5.IV infusion rates
Answer: R = 10 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
8·60 = 480 min
Drip rate
R = 250·20/480 = 10.42 ≈ 10 gtt/min
Answer
R = 10 gtt/min
At the bedside you round to the nearest whole drop: 10 gtt/min.
6.IV infusion rates
Answer: t = 5.4 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.
Rate in mL/h
28·60/20 = 84 mL/h
Time left
t = 450/84 = 5.357 ≈ 5.4 h
Answer
t = 5.4 h
7.IV fluids & fluid balance
Answer: U = 0.85 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 + 225 + 450 = 1050 mL
Per kilogram per hour
U = 1050/(103·12) = 0.8495 ≈ 0.85 mL/kg/h
Answer
U = 0.85 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 700 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
13:15 → 15:45 = 2.5 h
Volume infused
120·2.5 = 300 mL
Volume left
V = 1000 − 300 = 700 mL
Answer
V = 700 mL
9.Pediatric & critical-care dosing
Answer: V = 4.1 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
60·69 = 4 140 units
Volume
V = 4140/1000 = 4.14 ≈ 4.1 mL
Answer
V = 4.1 mL
10.Pediatric & critical-care dosing
Answer: D = 4.5 mcg/kg/min
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
250 000/250 = 1000 mcg/mL
Micrograms per minute
21·1000 = 21000 mcg/h
21000/60 = 350 mcg/min
Per kilogram
D = 350/78 = 4.487 ≈ 4.5 mcg/kg/min
Answer
D = 4.5 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.8 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 = 400 000/500 000 = 0.8 mL
Answer
V = 0.8 mL
12.Pharmacy calculations
Answer: m = 50 g
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.