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 10:10 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
10:10
110:10 AM
212:10 AM
310:10 PM
49:10 AM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 4 fl oz of juice, 2 tbsp of liquid supplement, 3 tsp of cough syrup, ½ cup of tea. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A child weighing 35 kg is prescribed 2 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
35 kg2 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 14 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 125 mg in 5 mL. What volume V do you give?
14 kg15 mg/kg125 mg/5 mL
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 8 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL8 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 1 g of a drug in 250 mL. The order is 3 mg per minute. At what rate R do you set the pump, in mL/h?
1 g/250 mL3 mg/min
R = mL/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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 120 mL/h. At 18:30, 50 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL50 mL infused120 mL/h
t = h
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 70 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg70 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 12.5 mcg/kg/min for a patient who weighs 57 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL12.5 mcg/kg/min57 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 3.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
3.2 mL → 1 000 000 units/mL750 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 55 mg. Draw up the dose: what volume V do you give?
250 mg4.8 mL + 0.2 mL55 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 10:10 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
10 → 10 AM
Answer
10:10 AM
Answer
10:10 AM
2.Nursing math & unit conversions
Answer: V = 285 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
4 fl oz = 4·30 = 120 mL
2 tbsp = 2·15 = 30 mL
3 tsp = 3·5 = 15 mL
½ cup = 0.5·240 = 120 mL
Add
V = 120 + 30 + 15 + 120 = 285 mL
Answer
V = 285 mL
3.Dosage calculations
Answer: V = 7 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 = 2·35 = 70 mg
Volume
V = 70/10 = 7 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7 mL
4.Dosage calculations
Answer: V = 8.4 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.
Dose from weight
15·14 = 210 mg
Volume
V = (210/125)·5 = 8.4 mL
Answer
V = 8.4 mL
5.IV infusion rates
Answer: R = 31 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 = 250·60/480 = 31.25 ≈ 31 gtt/min
Answer
R = 31 gtt/min
At the bedside you round to the nearest whole drop: 31 gtt/min.
6.IV infusion rates
Answer: R = 45 mL/h
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
1000 mg/250 mL = 4 mg/mL
Dose per hour
3·60 = 180 mg/h
Pump rate
R = 180/4 = 45 mL/h
Answer
R = 45 mL/h
7.IV fluids & fluid balance
Answer: B = 785 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: 200 + 300 = 500 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1560 mL
Total output
150 + 150 + 475 = 775 mL
Balance
B = 1560 − 775 = 785 mL
Answer
B = 785 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 3.8 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
500 − 50 = 450 mL
Time
t = 450/120 = 3.75 ≈ 3.8 h
Answer
t = 3.8 h
That is about 3 h 45 min, so the bag runs out at about 22:15.
9.Pediatric & critical-care dosing
Answer: V = 0.84 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
60·70 = 4 200 units
Volume
V = 4200/5000 = 0.84 mL
Answer
V = 0.84 mL
10.Pediatric & critical-care dosing
Answer: R = 21.4 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
12.5·57 = 712.5 mcg/min
712.5·60 = 42750 mcg/h
Pump rate
R = 42750/2000 = 21.38 ≈ 21.4 mL/h
Answer
R = 21.4 mL/h
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 = 750 000/1 000 000 = 0.75 ≈ 0.8 mL
Answer
V = 0.8 mL
12.Pharmacy calculations
Answer: V = 1.1 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.