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’s temperature is 103.1 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
103.1 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:20 and finishes at 03:05 the next morning (24-hour clock). How many minutes t did it run?
23:2003:05
t = min
3.Dosage calculationsMedium
A patient weighs 30 kg. The prescribed dose is 30 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
30 kg30 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
You must prepare 250 mL of a 1% (w/v) solution from a 50% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 50%C₂ = 1%V₂ = 250 mL
V₁ = mL
5.IV infusion ratesMedium
Infuse 500 mL over 2 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 mL2 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 50 mg in 250 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?
50 mg/250 mL24 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 69 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 11:00 at 150 mL/h. After 3 hours the rate is changed to 200 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL150 mL/h · 3 h200 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 70 units/kg for a patient who weighs 96 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg96 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 94 kg has an order for nitroglycerin at 5 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 mL5 mcg/min94 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.6 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.6 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 440 mg. Draw up the dose: what volume V do you give?
2000 mg4.8 mL + 0.2 mL440 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 39.5 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
103.1 − 32 = 71.1
Multiply by 5/9
T = 71.1·5/9 = 39.5 °C
Answer
T = 39.5 °C
2.Nursing math & unit conversions
Answer: t = 225 min
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
23:20 → 24:00 = 40 min
After midnight
00:00 → 03:05 = 185 min
Total
t = 40 + 185 = 225 min
Answer
t = 225 min
3.Dosage calculations
Answer: D = 300 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
30·30 = 900 mg
Per dose
D = 900/3 = 300 mg
Answer
D = 300 mg
4.Dosage calculations
Answer: V₁ = 5 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Volume of stock
V₁ = 1·250/50 = 5 mL
Answer
V₁ = 5 mL
5.IV infusion rates
Answer: R = 83 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
2·60 = 120 min
Drip rate
R = 500·20/120 = 83.33 ≈ 83 gtt/min
Answer
R = 83 gtt/min
At the bedside you round to the nearest whole drop: 83 gtt/min.
6.IV infusion rates
Answer: D = 80 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/250 mL = 200 mcg/mL
Dose per hour
24·200 = 4800 mcg/h
Dose per minute
D = 4800/60 = 80 mcg/min
Answer
D = 80 mcg/min
7.IV fluids & fluid balance
Answer: U = 1.6 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
475 + 200 + 325 + 325 = 1325 mL
Per kilogram per hour
U = 1325/(69·12) = 1.6 mL/kg/h
Answer
U = 1.6 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 5.8 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.
First part
150·3 = 450 mL
1000 − 450 = 550 mL left
Second part
550/200 = 2.75 h
Total time
t = 3 + 2.75 = 5.75 ≈ 5.8 h
Answer
t = 5.8 h
That is about 5 h 45 min, so the bag runs out at about 16:45.
9.Pediatric & critical-care dosing
Answer: V = 1.3 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
70·96 = 6 720 units
Volume
V = 6720/5000 = 1.344 ≈ 1.3 mL
Answer
V = 1.3 mL
10.Pediatric & critical-care dosing
Answer: R = 1.5 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.
5·60 = 300 mcg/h
Pump rate
R = 300/200 = 1.5 mL/h
Answer
R = 1.5 mL/h
11.Pharmacy calculations
Answer: V = 6 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 = 0.6/0.1 = 6 mL
Answer
V = 6 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.