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 patient’s temperature is 105.2 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
105.2 °F
T = °C
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 14 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
2 tsptwice a day14 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 22 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.
22 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 1.52 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1.52 mg2000 mcg/mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 4 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL4 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 40 gtt/min through a set of 15 gtt/mL. There are 200 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
40 gtt/min15 gtt/mL200 mL
t = 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 total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 08:00 at 120 mL/h. After 2 hours the rate is changed to 50 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL120 mL/h · 2 h50 mL/h
t = h
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 63 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg63 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 85 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/min85 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.23 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.23 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 60 mg. Draw up the dose: what volume V do you give?
250 mg4.5 mL + 0.5 mL60 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 40.7 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
105.2 − 32 = 73.2
Multiply by 5/9
T = 73.2·5/9 = 40.67 ≈ 40.7 °C
Answer
T = 40.7 °C
2.Nursing math & unit conversions
Answer: V = 280 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 × 14 = 280 mL
Answer
V = 280 mL
3.Dosage calculations
Answer: D = 165 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
7.5·22 = 165 mg
Answer
D = 165 mg
4.Dosage calculations
Answer: V = 0.76 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
1.52 mg = 1520 mcg
Volume
V = 1520/2000 = 0.76 mL
Answer
V = 0.76 mL
5.IV infusion rates
Answer: R = 83 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 = 1000·20/240 = 83.33 ≈ 83 gtt/min
Answer
R = 83 gtt/min
At the bedside you round to the nearest whole drop: 83 gtt/min.
6.IV infusion rates
Answer: t = 1.3 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.
Rate in mL/h
40·60/15 = 160 mL/h
Time left
t = 200/160 = 1.25 ≈ 1.3 h
Answer
t = 1.3 h
7.IV fluids & fluid balance
Answer: I = 1790 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: 240 + 240 + 100 = 580 mL
ice chips: 100/2 = 50 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 2·100 = 200 mL
I = 1790 mL
Answer
I = 1790 mL
8.IV fluids & fluid balance
Answer: t = 7.2 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.
First part
120·2 = 240 mL
500 − 240 = 260 mL left
Second part
260/50 = 5.2 h
Total time
t = 2 + 5.2 = 7.2 h
Answer
t = 7.2 h
That is about 7 h 12 min, so the bag runs out at about 15:12.
9.Pediatric & critical-care dosing
Answer: V = 4.4 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
70·63 = 4 410 units
Volume
V = 4410/1000 = 4.41 ≈ 4.4 mL
Answer
V = 4.4 mL
10.Pediatric & critical-care dosing
Answer: R = 38.3 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
7.5·85 = 637.5 mcg/min
637.5·60 = 38250 mcg/h
Pump rate
R = 38250/1000 = 38.25 ≈ 38.3 mL/h
Answer
R = 38.3 mL/h
11.Pharmacy calculations
Answer: V = 0.23 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 = 0.23/1 = 0.23 mL
Answer
V = 0.23 mL
12.Pharmacy calculations
Answer: V = 1.2 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.