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 97.5 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
97.5 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 19:35 and finishes at 00:25 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.
19:3500:25
t = h
3.Dosage calculationsMedium
A patient weighs 90 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.
90 kg10 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 380 micrograms. The ampoule contains 2 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
380 mcg2 mg/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 12 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL12 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 25 mg in 250 mL runs at 3 mL/h. How many micrograms per minute D does the patient receive?
25 mg/250 mL3 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 8-hour shift. The patient weighs 57 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
57 kg8 hurine: 150 mLurine: 300 mLvomit: 100 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 08:45 and runs by pump at 120 mL/h. How many mL V are left in the bag at 12:15?
500 mL120 mL/h08:45 → 12:15
V = mL
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 88 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg88 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 3 mcg/kg/min for a patient who weighs 88 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL3 mcg/kg/min88 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.12 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.12 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 750 mL of 13% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 23% solution do you need? Round to the nearest whole mL.
23%3%13%750 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 36.4 °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
97.5 − 32 = 65.5
Multiply by 5/9
T = 65.5·5/9 = 36.39 ≈ 36.4 °C
Answer
T = 36.4 °C
2.Nursing math & unit conversions
Answer: t = 4.83 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 → 00:25 = 25 min
Total
265 + 25 = 290 min
t = 290/60 = 4.833 ≈ 4.83 h
Answer
t = 4.83 h
3.Dosage calculations
Answer: D = 900 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
10·90 = 900 mg
Answer
D = 900 mg
4.Dosage calculations
Answer: V = 0.19 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
2 mg/mL = 2000 mcg/mL
Volume
V = 380/2000 = 0.19 mL
Answer
V = 0.19 mL
5.IV infusion rates
Answer: R = 10 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
12·60 = 720 min
Drip rate
R = 500·15/720 = 10.42 ≈ 10 gtt/min
Answer
R = 10 gtt/min
At the bedside you round to the nearest whole drop: 10 gtt/min.
6.IV infusion rates
Answer: D = 5 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
25000 mcg/250 mL = 100 mcg/mL
Dose per hour
3·100 = 300 mcg/h
Dose per minute
D = 300/60 = 5 mcg/min
Answer
D = 5 mcg/min
7.IV fluids & fluid balance
Answer: U = 0.99 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
150 + 300 = 450 mL
Per kilogram per hour
U = 450/(57·8) = 0.9868 ≈ 0.99 mL/kg/h
Answer
U = 0.99 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 80 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
08:45 → 12:15 = 3.5 h
Volume infused
120·3.5 = 420 mL
Volume left
V = 500 − 420 = 80 mL
Answer
V = 80 mL
9.Pediatric & critical-care dosing
Answer: V = 5.3 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
60·88 = 5 280 units
Volume
V = 5280/1000 = 5.28 ≈ 5.3 mL
Answer
V = 5.3 mL
10.Pediatric & critical-care dosing
Answer: R = 9.9 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
3·88 = 264 mcg/min
264·60 = 15840 mcg/h
Pump rate
R = 15840/1600 = 9.9 mL/h
Answer
R = 9.9 mL/h
11.Pharmacy calculations
Answer: V = 1.2 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 = 0.12/0.1 = 1.2 mL
Answer
V = 1.2 mL
12.Pharmacy calculations
Answer: V = 375 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.