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 37.5 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
37.5 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 cups of tea, 3 fl oz of juice, 1½ tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 fl oz = 30 mL1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 18 kg and is prescribed 20 mg/kg as a single dose. Find the dose D in mg.
18 kg20 mg/kg
D = mg
4.Dosage calculationsHard
An infusion contains 40000 units of a drug in 500 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
40000 units/500 mL2000 units/h
R = mL/h
5.IV infusion ratesMedium
A drip runs at 50 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 3 hours?
50 gtt/min60 gtt/mL3 h
V = mL
6.IV infusion ratesHard
An infusion of 25 mg in 250 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?
25 mg/250 mL24 mL/h
D = mcg/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 total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 06:30 at 100 mL/h. After 4 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.
1000 mL100 mL/h · 4 h50 mL/h
t = h
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 8 units/h. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL8 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 2 mcg/kg/min for a patient who weighs 99 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min99 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 300 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL300 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 3% ointment? Round to the nearest whole gram.
30 g · 5%1%3%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: T = 99.5 °F
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.
Multiply by 9/5
37.5·9/5 = 67.5
Add 32
T = 67.5 + 32 = 99.5 °F
Answer
T = 99.5 °F
2.Nursing math & unit conversions
Answer: V = 592.5 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
2 cups = 2·240 = 480 mL
3 fl oz = 3·30 = 90 mL
1½ tbsp = 1.5·15 = 22.5 mL
Add
V = 480 + 90 + 22.5 = 592.5 mL
Answer
V = 592.5 mL
3.Dosage calculations
Answer: D = 360 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
20·18 = 360 mg
Answer
D = 360 mg
4.Dosage calculations
Answer: R = 25 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
40000/500 = 80 units/mL
Pump rate
R = 2000/80 = 25 mL/h
Answer
R = 25 mL/h
5.IV infusion rates
Answer: V = 150 mL
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
50·60/60 = 50 mL/h
Volume
V = 50·3 = 150 mL
Answer
V = 150 mL
6.IV infusion rates
Answer: D = 40 mcg/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
25000 mcg/250 mL = 100 mcg/mL
Dose per hour
24·100 = 2400 mcg/h
Dose per minute
D = 2400/60 = 40 mcg/min
Answer
D = 40 mcg/min
7.IV fluids & fluid balance
Answer: I = 1610 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: 100 + 150 + 100 = 350 mL
ice chips: 200/2 = 100 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 2·100 = 200 mL
I = 1610 mL
Answer
I = 1610 mL
8.IV fluids & fluid balance
Answer: t = 16 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
100·4 = 400 mL
1000 − 400 = 600 mL left
Second part
600/50 = 12 h
Total time
t = 4 + 12 = 16 h
Answer
t = 16 h
That is about 16 h 00 min, so the bag runs out at about 22:30.
9.Pediatric & critical-care dosing
Answer: R = 8 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.
Concentration
50/50 = 1 units/mL
Pump rate
R = 8/1 = 8 mL/h
Answer
R = 8 mL/h
10.Pediatric & critical-care dosing
Answer: R = 7.4 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
2·99 = 198 mcg/min
198·60 = 11880 mcg/h
Pump rate
R = 11880/1600 = 7.425 ≈ 7.4 mL/h
Answer
R = 7.4 mL/h
11.Pharmacy calculations
Answer: V = 1.2 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 = 300 000/250 000 = 1.2 mL
Answer
V = 1.2 mL
12.Pharmacy calculations
Answer: m = 30 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.