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 newborn weighs 4 lb 9 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
4 lb 9 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:10 and finishes at 06:55 the next morning (24-hour clock). How many minutes t did it run?
18:1006:55
t = min
3.Dosage calculationsMedium
A vial contains 1 g of powder. The label says: add 4.2 mL of water for injection to give a total volume of 5 mL. The prescription is 600 mg. What volume V of the reconstituted solution do you give?
1 g+ 4.2 mL → 5 mL600 mg
V = mL
4.Dosage calculationsHard
You must prepare 200 mL of a 2.5% (w/v) solution from a 50% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 50%C₂ = 2.5%V₂ = 200 mL
W = mL
5.IV infusion ratesMedium
A drip runs at 30 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 6 hours?
30 gtt/min60 gtt/mL6 h
V = mL
6.IV infusion ratesHard
A bag contains 500 mg of a drug in 100 mL and runs at 25 mL/h. How many milligrams per hour D does the patient receive?
500 mg/100 mL25 mL/h
D = mg/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.
juice: 100 mLsoup: 200 mLjelly: 100 mLIV infusion: 125 mL/h × 8 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 12:00 and runs by pump at 120 mL/h. How many mL V are left in the bag at 17:00?
1000 mL120 mL/h12:00 → 17:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 20 units/kg/h for a patient who weighs 79 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL20 units/kg/h79 kg
R = mL/h
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 2 mcg/kg/min for a patient who weighs 107 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL2 mcg/kg/min107 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
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 60% ethanol from a 90% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
90%0%60%300 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.07 kg
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.
Ounces to pounds
9 oz/16 = 0.5625 lb
4 + 0.5625 = 4.563 lb
Pounds to kilograms
m = 4.563/2.2 = 2.074 ≈ 2.07 kg
Answer
m = 2.07 kg
2.Nursing math & unit conversions
Answer: t = 765 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
18:10 → 24:00 = 350 min
After midnight
00:00 → 06:55 = 415 min
Total
t = 350 + 415 = 765 min
Answer
t = 765 min
3.Dosage calculations
Answer: V = 3 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.
Concentration after mixing
1000 mg/5 mL = 200 mg/mL
Volume
V = 600/200 = 3 mL
Answer
V = 3 mL
4.Dosage calculations
Answer: W = 190 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 = 2.5·200/50 = 10 mL
Water to add
W = 200 − 10 = 190 mL
Answer
W = 190 mL
5.IV infusion rates
Answer: V = 180 mL
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
30·60/60 = 30 mL/h
Volume
V = 30·6 = 180 mL
Answer
V = 180 mL
6.IV infusion rates
Answer: D = 125 mg/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.
Concentration
500/100 = 5 mg/mL
Dose rate
D = 5·25 = 125 mg/h
Answer
D = 125 mg/h
7.IV fluids & fluid balance
Answer: I = 1600 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: 100 + 200 + 100 = 400 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 2·100 = 200 mL
I = 1600 mL
Answer
I = 1600 mL
8.IV fluids & fluid balance
Answer: V = 400 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
12:00 → 17:00 = 5 h
Volume infused
120·5 = 600 mL
Volume left
V = 1000 − 600 = 400 mL
Answer
V = 400 mL
9.Pediatric & critical-care dosing
Answer: R = 31.6 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
20·79 = 1 580 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1580/50 = 31.6 mL/h
Answer
R = 31.6 mL/h
10.Pediatric & critical-care dosing
Answer: R = 8 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
2·107 = 214 mcg/min
214·60 = 12840 mcg/h
Pump rate
R = 12840/1600 = 8.025 ≈ 8 mL/h
Answer
R = 8 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 = 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.
Alligation parts
90%: 60 − 0 = 60 parts
0%: 90 − 60 = 30 parts
total: 90 parts
Water
V = 300·30/90 = 100 mL
Answer
V = 100 mL
Check: 200 mL of 90% contains 180 mL of drug, which is 60% of 300 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.