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 00:40 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
00:40
111:40 AM
212:40 AM
32:40 AM
412:40 PM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 1½ tsp of an oral suspension every 6 hours for 14 days. The suspension comes in 50 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?
1½ tspevery 6 hours14 days50 mL1 tsp = 5 mL
N =
3.Dosage calculationsMedium
A vial contains 2 g of powder. The label says: add 7.4 mL of water for injection to give a total volume of 8 mL. The prescription is 100 mg. What volume V of the reconstituted solution do you give?
2 g+ 7.4 mL → 8 mL100 mg
V = mL
4.Dosage calculationsHard
An infusion contains 50000 units of a drug in 250 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
50000 units/250 mL2000 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 500 mL over 5 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL5 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 100 mL and runs at 5 mL/h. How many milligrams per hour D does the patient receive?
200 mg/100 mL5 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 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 08:30 and runs by pump at 60 mL/h. How many mL V are left in the bag at 16:00?
500 mL60 mL/h08:30 → 16:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 14 units/kg/h for a patient who weighs 59 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL14 units/kg/h59 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 81 kg has an order for nitroglycerin at 15 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL15 mcg/min81 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. The prescribed dose is 500 mg. What volume V do you draw up? Round to one decimal place.
1000 mg9.6 mL+0.4 mL500 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 2.1 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 230 mg. Draw up the dose: what volume V do you give?
250 mg2.1 mL + 0.4 mL230 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 12:40 AM
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
00 → 12 AM
Answer
12:40 AM
Answer
12:40 AM
2.Nursing math & unit conversions
Answer: N = 9
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.
Total volume
7.5 mL × 4 × 14 = 420 mL
Bottles
420/50 = 8.4 → N = 9
Answer
N = 9
3.Dosage calculations
Answer: V = 0.4 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.
Concentration after mixing
2000 mg/8 mL = 250 mg/mL
Volume
V = 100/250 = 0.4 mL
Answer
V = 0.4 mL
4.Dosage calculations
Answer: R = 10 mL/h
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.
Concentration
50000/250 = 200 units/mL
Pump rate
R = 2000/200 = 10 mL/h
Answer
R = 10 mL/h
5.IV infusion rates
Answer: R = 33 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
5·60 = 300 min
Drip rate
R = 500·20/300 = 33.33 ≈ 33 gtt/min
Answer
R = 33 gtt/min
At the bedside you round to the nearest whole drop: 33 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
200/100 = 2 mg/mL
Dose rate
D = 2·5 = 10 mg/h
Answer
D = 10 mg/h
7.IV fluids & fluid balance
Answer: I = 2350 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.
Add the intake
oral: 200 + 200 + 150 = 550 mL
ice chips: 200/2 = 100 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 2·100 = 200 mL
I = 2350 mL
Answer
I = 2350 mL
8.IV fluids & fluid balance
Answer: V = 50 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
08:30 → 16:00 = 7.5 h
Volume infused
60·7.5 = 450 mL
Volume left
V = 500 − 450 = 50 mL
Answer
V = 50 mL
9.Pediatric & critical-care dosing
Answer: R = 20.7 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
14·59 = 826 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 826/40 = 20.65 ≈ 20.7 mL/h
Answer
R = 20.7 mL/h
10.Pediatric & critical-care dosing
Answer: R = 4.5 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
15·60 = 900 mcg/h
Pump rate
R = 900/200 = 4.5 mL/h
Answer
R = 4.5 mL/h
11.Pharmacy calculations
Answer: V = 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.
Final volume
9.6 + 0.4 = 10 mL
Concentration
1000/10 = 100 mg/mL
Volume to give
V = 500/100 = 5 mL
Answer
V = 5 mL
12.Pharmacy calculations
Answer: V = 2.3 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.