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 dose calculation for a small injection gives 0.82711 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.82711 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 1½ tsp of an oral suspension every 8 hours for 14 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
1½ tspevery 8 hours14 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
How many milligrams of drug m are in 20 mL of a 1% (w/v) solution?
1% w/v20 mL
m = mg
4.Dosage calculationsHard
A child weighing 28 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 200 mg in 5 mL. What volume V do you give?
28 kg20 mg/kg200 mg/5 mL
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 4 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL4 h60 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 15 gtt/mL. The order is 40 mg per hour. Find the drip rate R in drops per minute.
1000 mg/500 mL40 mg/h15 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 10:45 and runs by pump at 100 mL/h. How many mL V are left in the bag at 14:45?
500 mL100 mL/h10:45 → 14:45
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 0.1 units/kg/h for a patient who weighs 82 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.1 units/kg/h82 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 5 mcg/kg/min for a patient who weighs 101 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL5 mcg/kg/min101 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.83 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.83 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 200 mg. Draw up the dose: what volume V do you give?
2000 mg9.8 mL + 0.2 mL200 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.83 mL
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 hundredths place
0.82711 → 2
Only the next digit decides
0.82711 → 7
7 is 5 or more, so round 2 up.
The digits after it (11) are ignored: round once, never step by step.
Round
x = 0.83 mL
Answer
x = 0.83 mL
2.Nursing math & unit conversions
Answer: V = 315 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
1½ tsp = 1.5·5 = 7.5 mL
Whole course
V = 7.5 mL × 3/day × 14 = 315 mL
Answer
V = 315 mL
3.Dosage calculations
Answer: m = 200 mg
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.
Concentration
1% = 1 g/100 mL = 10 mg/mL
Mass of drug
m = 10·20 = 200 mg
Answer
m = 200 mg
4.Dosage calculations
Answer: V = 14 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.
Dose from weight
20·28 = 560 mg
Volume
V = (560/200)·5 = 14 mL
Answer
V = 14 mL
5.IV infusion rates
Answer: R = 63 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
4·60 = 240 min
Drip rate
R = 250·60/240 = 62.5 ≈ 63 gtt/min
Answer
R = 63 gtt/min
At the bedside you round to the nearest whole drop: 63 gtt/min.
6.IV infusion rates
Answer: R = 5 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
40/2 = 20 mL/h
Drip rate
R = 20·15/60 = 5 gtt/min
Answer
R = 5 gtt/min
7.IV fluids & fluid balance
Answer: B = 760 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: 240 + 250 + 240 = 730 mL
ice chips: 200/2 = 100 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1830 mL
Total output
500 + 500 + 70 = 1070 mL
Balance
B = 1830 − 1070 = 760 mL
Answer
B = 760 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 100 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
10:45 → 14:45 = 4 h
Volume infused
100·4 = 400 mL
Volume left
V = 500 − 400 = 100 mL
Answer
V = 100 mL
9.Pediatric & critical-care dosing
Answer: R = 8.2 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
0.1·82 = 8.2 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 8.2/1 = 8.2 mL/h
Answer
R = 8.2 mL/h
10.Pediatric & critical-care dosing
Answer: R = 18.9 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
5·101 = 505 mcg/min
505·60 = 30300 mcg/h
Pump rate
R = 30300/1600 = 18.94 ≈ 18.9 mL/h
Answer
R = 18.9 mL/h
11.Pharmacy calculations
Answer: V = 0.83 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/1000 mL = 1 mg/mL
Volume
V = 0.83/1 = 0.83 mL
Answer
V = 0.83 mL
12.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.