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 patient is 178 cm tall. Using 1 in = 2.54 cm, find the height h in inches. Round to one decimal place.
178 cm1 in = 2.54 cm
h = in
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:10 and finishes at 00:50 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
23:1000:50
t = h
3.Dosage calculationsMedium
A patient weighs 90 kg. The prescribed dose is 25 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
90 kg25 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A child weighing 20 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give?
20 kg20 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
500 mL was ordered over 10 hours. After 4 hours you find that 350 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
500 mL / 10 hafter 4 h: 350 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 40 gtt/min through a set of 15 gtt/mL. There are 200 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
40 gtt/min15 gtt/mL200 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 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
jelly: 120 mLjuice: 200 mLIV infusion: 60 mL/h × 8 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 09:30 and runs by pump at 60 mL/h. How many mL V are left in the bag at 14:00?
1000 mL60 mL/h09:30 → 14:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 10 000 units of heparin in 250 mL. The order is 14 units/kg/h for a patient who weighs 107 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
10 000 units/250 mL14 units/kg/h107 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 95 kg has an order for norepinephrine at 6 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL6 mcg/min95 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.88 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.88 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 9.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 200 mg. Draw up the dose: what volume V do you give?
2000 mg9.5 mL + 0.5 mL200 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 70.1 in
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.
Centimetres to inches
h = 178/2.54 = 70.08 ≈ 70.1 in
Answer
h = 70.1 in
2.Nursing math & unit conversions
Answer: t = 1.67 h
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.
Before midnight
23:10 → 24:00 = 50 min
After midnight
00:00 → 00:50 = 50 min
Total
50 + 50 = 100 min
t = 100/60 = 1.667 ≈ 1.67 h
Answer
t = 1.67 h
3.Dosage calculations
Answer: D = 750 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.
Total per day
25·90 = 2250 mg
Per dose
D = 2250/3 = 750 mg
Answer
D = 750 mg
4.Dosage calculations
Answer: V = 10 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
20·20 = 400 mg
Volume
V = (400/40)·1 = 10 mL
Answer
V = 10 mL
5.IV infusion rates
Answer: R = 58.33 mL/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.
Original rate
500/10 = 50 mL/h
New rate
R = 350/6 = 58.33 mL/h
Answer
R = 58.33 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: t = 1.3 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
40·60/15 = 160 mL/h
Time left
t = 200/160 = 1.25 ≈ 1.3 h
Answer
t = 1.3 h
7.IV fluids & fluid balance
Answer: I = 850 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: 120 + 200 = 320 mL
IV infusion: 60·8 = 480 mL
IV antibiotic: 1·50 = 50 mL
I = 850 mL
Answer
I = 850 mL
8.IV fluids & fluid balance
Answer: V = 730 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
09:30 → 14:00 = 4.5 h
Volume infused
60·4.5 = 270 mL
Volume left
V = 1000 − 270 = 730 mL
Answer
V = 730 mL
9.Pediatric & critical-care dosing
Answer: R = 37.5 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
14·107 = 1 498 units/h
Concentration
10 000/250 = 40 units/mL
Pump rate
R = 1498/40 = 37.45 ≈ 37.5 mL/h
Answer
R = 37.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 11.3 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
6·60 = 360 mcg/h
Pump rate
R = 360/32 = 11.25 ≈ 11.3 mL/h
Answer
R = 11.3 mL/h
11.Pharmacy calculations
Answer: V = 8.8 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.88/0.1 = 8.8 mL
Answer
V = 8.8 mL
12.Pharmacy calculations
Answer: V = 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.