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 38.2 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
38.2 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 19:35 and finishes at 01:50 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.
19:3501:50
t = h
3.Dosage calculationsMedium
A patient weighs 25 kg and is prescribed 25 mg/kg as a single dose. Find the dose D in mg.
25 kg25 mg/kg
D = mg
4.Dosage calculationsHard
A child weighing 28 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 200 mg in 5 mL. What volume V do you give?
28 kg10 mg/kg200 mg/5 mL
V = mL
5.IV infusion ratesMedium
500 mL was ordered over 10 hours. After 7 hours you find that 190 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 7 h: 190 mL
R = mL/h
6.IV infusion ratesHard
A bag contains 2 g of a drug in 500 mL. The order is 4 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/500 mL4 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 8-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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 13:30 and runs by pump at 100 mL/h. How many mL V are left in the bag at 17:00?
1000 mL100 mL/h13:30 → 17:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 12 units/kg/h for a patient who weighs 53 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL12 units/kg/h53 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 62 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/min62 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 800 mg. What volume V do you draw up? Round to one decimal place.
1000 mg4.5 mL+0.5 mL800 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 30% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%30%200 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 100.8 °F
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.
Multiply by 9/5
38.2·9/5 = 68.76
Add 32
T = 68.76 + 32 = 100.8 °F
Answer
T = 100.8 °F
2.Nursing math & unit conversions
Answer: t = 6.25 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
19:35 → 24:00 = 265 min
After midnight
00:00 → 01:50 = 110 min
Total
265 + 110 = 375 min
t = 375/60 = 6.25 h
Answer
t = 6.25 h
3.Dosage calculations
Answer: D = 625 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
25·25 = 625 mg
Answer
D = 625 mg
4.Dosage calculations
Answer: V = 7 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
10·28 = 280 mg
Volume
V = (280/200)·5 = 7 mL
Answer
V = 7 mL
5.IV infusion rates
Answer: R = 63.33 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 = 190/3 = 63.33 mL/h
Answer
R = 63.33 mL/h
This is more than a 25% increase: most hospitals require you to contact the prescriber instead of catching up, and to assess the patient for fluid overload.
6.IV infusion rates
Answer: R = 60 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
2000 mg/500 mL = 4 mg/mL
Dose per hour
4·60 = 240 mg/h
Pump rate
R = 240/4 = 60 mL/h
Answer
R = 60 mL/h
7.IV fluids & fluid balance
Answer: B = 330 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: 240 + 120 = 360 mL
ice chips: 100/2 = 50 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1260 mL
Total output
450 + 350 + 130 = 930 mL
Balance
B = 1260 − 930 = 330 mL
Answer
B = 330 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 650 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
13:30 → 17:00 = 3.5 h
Volume infused
100·3.5 = 350 mL
Volume left
V = 1000 − 350 = 650 mL
Answer
V = 650 mL
9.Pediatric & critical-care dosing
Answer: R = 12.7 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
12·53 = 636 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 636/50 = 12.72 ≈ 12.7 mL/h
Answer
R = 12.7 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 = 4 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
4.5 + 0.5 = 5 mL
Concentration
1000/5 = 200 mg/mL
Volume to give
V = 800/200 = 4 mL
Answer
V = 4 mL
12.Pharmacy calculations
Answer: V = 100 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.