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 08:40 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
08:40
18:40 AM
27:40 AM
310:40 AM
48:40 PM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1 tsp of cough syrup, 2 fl oz of juice, 3 cups of tea. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 fl oz = 30 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 80 kg and is prescribed 2 mg/kg as a single dose. Find the dose D in mg.
80 kg2 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 1.2 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1.2 mg2000 mcg/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 60 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.
60 mL/h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 50 mg in 500 mL runs at 10 mL/h. How many micrograms per minute D does the patient receive?
50 mg/500 mL10 mL/h
D = mcg/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 48 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
48 kg12 hurine: 325 mLurine: 325 mLurine: 375 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 09:00 and runs by pump at 120 mL/h. How many mL V are left in the bag at 11:00?
500 mL120 mL/h09:00 → 11:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 250 mL runs at 20 mL/h. How many units per hour D does the patient receive?
100 units/250 mL20 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 4 mL/h. The patient weighs 65 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL4 mL/h65 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.94 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.94 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 900 mg. Draw up the dose: what volume V do you give?
1000 mg1.6 mL + 0.4 mL900 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 8:40 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
08 → 8 AM
Answer
8:40 AM
Answer
8:40 AM
2.Nursing math & unit conversions
Answer: V = 785 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Each item in mL
1 tsp = 1·5 = 5 mL
2 fl oz = 2·30 = 60 mL
3 cups = 3·240 = 720 mL
Add
V = 5 + 60 + 720 = 785 mL
Answer
V = 785 mL
3.Dosage calculations
Answer: D = 160 mg
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.
Dose
2·80 = 160 mg
Answer
D = 160 mg
4.Dosage calculations
Answer: V = 0.6 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.
Same units
1.2 mg = 1200 mcg
Volume
V = 1200/2000 = 0.6 mL
Answer
V = 0.6 mL
5.IV infusion rates
Answer: R = 20 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
60/60 = 1 mL/min
Drip rate
R = 1·20 = 20 gtt/min
Answer
R = 20 gtt/min
6.IV infusion rates
Answer: D = 16.67 mcg/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
50000 mcg/500 mL = 100 mcg/mL
Dose per hour
10·100 = 1000 mcg/h
Dose per minute
D = 1000/60 = 16.67 mcg/min
Answer
D = 16.67 mcg/min
7.IV fluids & fluid balance
Answer: U = 1.78 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 + 325 + 375 = 1025 mL
Per kilogram per hour
U = 1025/(48·12) = 1.78 mL/kg/h
Answer
U = 1.78 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 260 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
09:00 → 11:00 = 2 h
Volume infused
120·2 = 240 mL
Volume left
V = 500 − 240 = 260 mL
Answer
V = 260 mL
9.Pediatric & critical-care dosing
Answer: D = 8 units/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.
Concentration
100/250 = 0.4 units/mL
Units per hour
D = 20·0.4 = 8 units/h
Answer
D = 8 units/h
10.Pediatric & critical-care dosing
Answer: D = 1.6 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
4·1600 = 6400 mcg/h
6400/60 = 106.7 mcg/min
Per kilogram
D = 106.7/65 = 1.641 ≈ 1.6 mcg/kg/min
Answer
D = 1.6 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.94 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.94/1 = 0.94 mL
Answer
V = 0.94 mL
12.Pharmacy calculations
Answer: V = 1.8 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.