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 7 lb 10 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
7 lb 10 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 tbsp of liquid supplement, 8 fl oz of juice, ½ cup of tea, 1½ tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 fl oz = 30 mL1 cup = 8 fl oz = 240 mL1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 15 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.
15 kg10 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 1640 micrograms. The ampoule contains 2 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1640 mcg2 mg/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 10 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 mL10 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 100 mg of a drug in 500 mL and runs at 15 mL/h. How many milligrams per hour D does the patient receive?
100 mg/500 mL15 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 12-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).
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 13:00 and runs by pump at 80 mL/h. How many mL V are left in the bag at 19:30?
1000 mL80 mL/h13:00 → 19:30
V = mL
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 69 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg69 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 97 kg has an order for norepinephrine at 12 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 mL12 mcg/min97 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.18 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.18 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 4% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
20%0%4%300 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 3.47 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
10 oz/16 = 0.625 lb
7 + 0.625 = 7.625 lb
Pounds to kilograms
m = 7.625/2.2 = 3.466 ≈ 3.47 kg
Answer
m = 3.47 kg
2.Nursing math & unit conversions
Answer: V = 397.5 mL
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.
Each item in mL
2 tbsp = 2·15 = 30 mL
8 fl oz = 8·30 = 240 mL
½ cup = 0.5·240 = 120 mL
1½ tsp = 1.5·5 = 7.5 mL
Add
V = 30 + 240 + 120 + 7.5 = 397.5 mL
Answer
V = 397.5 mL
3.Dosage calculations
Answer: D = 150 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
10·15 = 150 mg
Answer
D = 150 mg
4.Dosage calculations
Answer: V = 0.82 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 = 1640/2000 = 0.82 mL
Answer
V = 0.82 mL
5.IV infusion rates
Answer: R = 13 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
10·60 = 600 min
Drip rate
R = 500·15/600 = 12.5 ≈ 13 gtt/min
Answer
R = 13 gtt/min
At the bedside you round to the nearest whole drop: 13 gtt/min.
6.IV infusion rates
Answer: D = 3 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
100/500 = 0.2 mg/mL
Dose rate
D = 0.2·15 = 3 mg/h
Answer
D = 3 mg/h
7.IV fluids & fluid balance
Answer: B = 1180 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: 200 + 120 = 320 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1920 mL
Total output
250 + 150 + 90 + 250 = 740 mL
Balance
B = 1920 − 740 = 1180 mL
Answer
B = 1180 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 480 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
13:00 → 19:30 = 6.5 h
Volume infused
80·6.5 = 520 mL
Volume left
V = 1000 − 520 = 480 mL
Answer
V = 480 mL
9.Pediatric & critical-care dosing
Answer: V = 4.8 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
70·69 = 4 830 units
Volume
V = 4830/1000 = 4.83 ≈ 4.8 mL
Answer
V = 4.8 mL
10.Pediatric & critical-care dosing
Answer: R = 22.5 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
12·60 = 720 mcg/h
Pump rate
R = 720/32 = 22.5 mL/h
Answer
R = 22.5 mL/h
11.Pharmacy calculations
Answer: V = 1.8 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 = 0.18/0.1 = 1.8 mL
Answer
V = 1.8 mL
12.Pharmacy calculations
Answer: V = 240 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
20%: 4 − 0 = 4 parts
0%: 20 − 4 = 16 parts
total: 20 parts
Water
V = 300·16/20 = 240 mL
Answer
V = 240 mL
Check: 60 mL of 20% contains 12 g of drug, which is 4% of 300 mL.