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 weight conversion gives 25.1279 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
25.1279 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 6 fl oz of juice, ½ tbsp of liquid supplement, 1 tsp of cough syrup, 2 cups of tea. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 30 kg. The prescribed dose is 5 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
30 kg5 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
The prescription is 320 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
320 mcg0.5 mg/mL
V = mL
5.IV infusion ratesMedium
Infuse 1500 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.
1500 mL10 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
500 mg of a drug is diluted in 500 mL and given by gravity through a set of 60 gtt/mL. The order is 100 mg per hour. Find the drip rate R in drops per minute.
500 mg/500 mL100 mg/h60 gtt/mL
R = gtt/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 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 08:45 and runs by pump at 150 mL/h. How many mL V are left in the bag at 14:15?
1000 mL150 mL/h08:45 → 14:15
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 78 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg78 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 93 kg has an order for norepinephrine at 5 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL5 mcg/min93 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 800 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL800 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 60 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 4% ointment? Round to the nearest whole gram.
60 g · 10%2%4%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 25.1 kg
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
25.1279 → 1
Only the next digit decides
25.1279 → 2
2 is 4 or less, so 1 stays.
The digits after it (79) are ignored: round once, never step by step.
Round
x = 25.1 kg
Answer
x = 25.1 kg
2.Nursing math & unit conversions
Answer: V = 672.5 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
6 fl oz = 6·30 = 180 mL
½ tbsp = 0.5·15 = 7.5 mL
1 tsp = 1·5 = 5 mL
2 cups = 2·240 = 480 mL
Add
V = 180 + 7.5 + 5 + 480 = 672.5 mL
Answer
V = 672.5 mL
3.Dosage calculations
Answer: D = 50 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
5·30 = 150 mg
Per dose
D = 150/3 = 50 mg
Answer
D = 50 mg
4.Dosage calculations
Answer: V = 0.64 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
0.5 mg/mL = 500 mcg/mL
Volume
V = 320/500 = 0.64 mL
Answer
V = 0.64 mL
5.IV infusion rates
Answer: R = 38 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 = 1500·15/600 = 37.5 ≈ 38 gtt/min
Answer
R = 38 gtt/min
At the bedside you round to the nearest whole drop: 38 gtt/min.
6.IV infusion rates
Answer: R = 100 gtt/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
500/500 = 1 mg/mL
Volume per hour
100/1 = 100 mL/h
Drip rate
R = 100·60/60 = 100 gtt/min
Answer
R = 100 gtt/min
7.IV fluids & fluid balance
Answer: B = −510 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: 250 + 150 = 400 mL
IV infusion: 60·12 = 720 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1170 mL
Total output
250 + 475 + 350 + 475 + 130 = 1680 mL
Balance
B = 1170 − 1680 = −510 mL
Answer
B = −510 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: V = 175 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 → 14:15 = 5.5 h
Volume infused
150·5.5 = 825 mL
Volume left
V = 1000 − 825 = 175 mL
Answer
V = 175 mL
9.Pediatric & critical-care dosing
Answer: V = 4.7 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
60·78 = 4 680 units
Volume
V = 4680/1000 = 4.68 ≈ 4.7 mL
Answer
V = 4.7 mL
10.Pediatric & critical-care dosing
Answer: R = 18.8 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
4 000/250 = 16 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 = 300/16 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 mL/h
11.Pharmacy calculations
Answer: V = 3.2 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.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 800 000/250 000 = 3.2 mL
Answer
V = 3.2 mL
12.Pharmacy calculations
Answer: m = 180 g
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.