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 drip-rate calculation gives 168.204 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
168.204 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 2 tsp of an oral suspension twice a day for 7 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
2 tsptwice a day7 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A dose of 200 mg is needed from a 10% (w/v) solution. What volume V contains this dose?
200 mg10% w/v
V = mL
4.Dosage calculationsHard
The prescription is 2450 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2450 units5000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 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.
500 mL3 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 500 mg of a drug in 250 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
500 mg/250 mL10 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: 200 mLwater: 150 mLsoup: 250 mLIV infusion: 125 mL/h × 8 hIV antibiotic: 1 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 50 mL/h. At 07:30, 450 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL450 mL infused50 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 78 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL18 units/kg/h78 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 34 mL/h. The patient weighs 55 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL34 mL/h55 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.46 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.46 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 1.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 400 mg. Draw up the dose: what volume V do you give?
500 mg1.2 mL + 0.8 mL400 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 168 gtt/min
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 ones place
168.204 → 8
Only the next digit decides
168.204 → 2
2 is 4 or less, so 8 stays.
The digits after it (04) are ignored: round once, never step by step.
Round
x = 168 gtt/min
Answer
x = 168 gtt/min
2.Nursing math & unit conversions
Answer: V = 140 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
2 tsp = 2·5 = 10 mL
Whole course
V = 10 mL × 2/day × 7 = 140 mL
Answer
V = 140 mL
3.Dosage calculations
Answer: V = 2 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.
Concentration
10% = 100 mg/mL
Volume
V = 200/100 = 2 mL
Answer
V = 2 mL
4.Dosage calculations
Answer: V = 0.49 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.
Volume
V = 2450/5000 = 0.49 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.49 mL
5.IV infusion rates
Answer: R = 28 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 = 500·10/180 = 27.78 ≈ 28 gtt/min
Answer
R = 28 gtt/min
At the bedside you round to the nearest whole drop: 28 gtt/min.
6.IV infusion rates
Answer: D = 20 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
500/250 = 2 mg/mL
Dose rate
D = 2·10 = 20 mg/h
Answer
D = 20 mg/h
7.IV fluids & fluid balance
Answer: I = 1700 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: 200 + 150 + 250 = 600 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 1·100 = 100 mL
I = 1700 mL
Answer
I = 1700 mL
8.IV fluids & fluid balance
Answer: t = 11 h
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.
Volume left
1000 − 450 = 550 mL
Time
t = 550/50 = 11 h
Answer
t = 11 h
That is about 11 h 00 min, so the bag runs out at about 18:30.
9.Pediatric & critical-care dosing
Answer: R = 28.1 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
18·78 = 1 404 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1404/50 = 28.08 ≈ 28.1 mL/h
Answer
R = 28.1 mL/h
10.Pediatric & critical-care dosing
Answer: D = 16.5 mcg/kg/min
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
800 000/500 = 1600 mcg/mL
Micrograms per minute
34·1600 = 54400 mcg/h
54400/60 = 906.7 mcg/min
Per kilogram
D = 906.7/55 = 16.48 ≈ 16.5 mcg/kg/min
Answer
D = 16.5 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.46 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 = 0.46/1 = 0.46 mL
Answer
V = 0.46 mL
12.Pharmacy calculations
Answer: V = 1.6 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.