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 20:40 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
20:40
18:40 PM
27:40 PM
310:40 PM
48:40 AM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tsp of an oral suspension every 6 hours for 10 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
1 tspevery 6 hours10 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A child weighing 39 kg is prescribed 5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
39 kg5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 940 micrograms. The ampoule contains 2 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
940 mcg2 mg/mL
V = mL
5.IV infusion ratesMedium
Infuse 250 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.
250 mL3 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1000 mL was ordered over 8 hours. After 5 hours you find that 410 mL is still in the bag, and the order must still finish on time. By what percentage Δ must the original pump rate be increased?
1000 mL / 8 hafter 5 h: 410 mL
Δ = %
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 IV infusion ran at the rate shown for the whole shift. Find the fluid balance B = intake − output in mL (a negative answer means a net loss). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 11:15 and runs by pump at 120 mL/h. How many mL V are left in the bag at 18:15?
1000 mL120 mL/h11:15 → 18:15
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 83 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL18 units/kg/h83 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 23 mL/h. The patient weighs 57 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL23 mL/h57 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 3.2 mL of diluent. The prescribed dose is 800 000 units. What volume V do you draw up? Round to one decimal place.
3.2 mL → 1 000 000 units/mL800 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 250 mg. Draw up the dose: what volume V do you give?
1000 mg9.8 mL + 0.2 mL250 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 8:40 PM
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
20 − 12 = 8 → PM
Answer
8:40 PM
Answer
8:40 PM
2.Nursing math & unit conversions
Answer: V = 200 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
1 tsp = 1·5 = 5 mL
Whole course
V = 5 mL × 4/day × 10 = 200 mL
Answer
V = 200 mL
3.Dosage calculations
Answer: V = 7.8 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 = 5·39 = 195 mg
Volume
V = 195/25 = 7.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.8 mL
4.Dosage calculations
Answer: V = 0.47 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.
Same units
2 mg/mL = 2000 mcg/mL
Volume
V = 940/2000 = 0.47 mL
Answer
V = 0.47 mL
5.IV infusion rates
Answer: R = 21 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 = 250·15/180 = 20.83 ≈ 21 gtt/min
Answer
R = 21 gtt/min
At the bedside you round to the nearest whole drop: 21 gtt/min.
6.IV infusion rates
Answer: Δ = 9.333 %
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.
Original rate
1000/8 = 125 mL/h
New rate
R = 410/3 = 136.7 mL/h
Percentage change
Δ = (136.7 − 125)/125·100% = 9.333%
Answer
Δ = 9.333%
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
7.IV fluids & fluid balance
Answer: B = 575 mL
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 intake
oral: 150 + 100 + 120 = 370 mL
ice chips: 240/2 = 120 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1440 mL
Total output
425 + 150 + 40 + 250 = 865 mL
Balance
B = 1440 − 865 = 575 mL
Answer
B = 575 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 160 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
11:15 → 18:15 = 7 h
Volume infused
120·7 = 840 mL
Volume left
V = 1000 − 840 = 160 mL
Answer
V = 160 mL
9.Pediatric & critical-care dosing
Answer: R = 29.9 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
18·83 = 1 494 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1494/50 = 29.88 ≈ 29.9 mL/h
Answer
R = 29.9 mL/h
10.Pediatric & critical-care dosing
Answer: D = 10.8 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
23·1600 = 36800 mcg/h
36800/60 = 613.3 mcg/min
Per kilogram
D = 613.3/57 = 10.76 ≈ 10.8 mcg/kg/min
Answer
D = 10.8 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
3.2 mL → 1 000 000 units/mL
Volume to give
V = 800 000/1 000 000 = 0.8 mL
Answer
V = 0.8 mL
12.Pharmacy calculations
Answer: V = 2.5 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.