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 6 lb 15 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
6 lb 15 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tbsp of an oral suspension every 6 hours for 5 days. Using 1 tbsp = 15 mL, how many mL V are needed for the whole course?
½ tbspevery 6 hours5 days1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A child weighing 9 kg is prescribed 10 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
9 kg10 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 250 mL. The prescription is 1500 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/250 mL1500 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 1000 mL over 3 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL3 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
1000 mg of a drug is diluted in 500 mL and given by gravity through a set of 60 gtt/mL. The order is 200 mg per hour. Find the drip rate R in drops per minute.
1000 mg/500 mL200 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 patient weighs 72 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
72 kg12 hurine: 500 mLurine: 400 mLvomit: 200 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 11:15 and runs by pump at 120 mL/h. How many mL V are left in the bag at 15:15?
1000 mL120 mL/h11:15 → 15:15
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 89 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg89 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 7.5 mcg/kg/min for a patient who weighs 74 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL7.5 mcg/kg/min74 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.1 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.1 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.9 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 680 mg. Draw up the dose: what volume V do you give?
1000 mg1.9 mL + 0.6 mL680 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 3.15 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
15 oz/16 = 0.9375 lb
6 + 0.9375 = 6.938 lb
Pounds to kilograms
m = 6.938/2.2 = 3.153 ≈ 3.15 kg
Answer
m = 3.15 kg
2.Nursing math & unit conversions
Answer: V = 150 mL
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Volume per dose
½ tbsp = 0.5·15 = 7.5 mL
Whole course
V = 7.5 mL × 4/day × 5 = 150 mL
Answer
V = 150 mL
3.Dosage calculations
Answer: V = 1.8 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.
Dose from body weight
D = 10·9 = 90 mg
Volume
V = 90/50 = 1.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 1.8 mL
4.Dosage calculations
Answer: R = 18.75 mL/h
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
20000/250 = 80 units/mL
Pump rate
R = 1500/80 = 18.75 mL/h
Answer
R = 18.75 mL/h
5.IV infusion rates
Answer: R = 56 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
3·60 = 180 min
Drip rate
R = 1000·10/180 = 55.56 ≈ 56 gtt/min
Answer
R = 56 gtt/min
At the bedside you round to the nearest whole drop: 56 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
1000/500 = 2 mg/mL
Volume per hour
200/2 = 100 mL/h
Drip rate
R = 100·60/60 = 100 gtt/min
Answer
R = 100 gtt/min
7.IV fluids & fluid balance
Answer: U = 1.04 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
500 + 400 = 900 mL
Per kilogram per hour
U = 900/(72·12) = 1.042 ≈ 1.04 mL/kg/h
Answer
U = 1.04 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 520 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
11:15 → 15:15 = 4 h
Volume infused
120·4 = 480 mL
Volume left
V = 1000 − 480 = 520 mL
Answer
V = 520 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
60·89 = 5 340 units
Volume
V = 5340/1000 = 5.34 ≈ 5.3 mL
Answer
V = 5.3 mL
10.Pediatric & critical-care dosing
Answer: R = 33.3 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
7.5·74 = 555 mcg/min
555·60 = 33300 mcg/h
Pump rate
R = 33300/1000 = 33.3 mL/h
Answer
R = 33.3 mL/h
11.Pharmacy calculations
Answer: V = 1 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 = 0.1/0.1 = 1 mL
Answer
V = 1 mL
12.Pharmacy calculations
Answer: V = 1.7 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.