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 103.9 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
103.9 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1 tsp of cough syrup, ¼ cup of tea, 2 tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 cup = 8 fl oz = 240 mL1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A child weighing 38 kg is prescribed 2 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
38 kg2 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 100 cm tall and weighs 18 kg. The prescription is 25 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
100 cm18 kg25 mg/m²
D = mg
5.IV infusion ratesMedium
A drip runs at 50 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 4 hours?
50 gtt/min15 gtt/mL4 h
V = mL
6.IV infusion ratesHard
An infusion of 50 mg in 500 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?
50 mg/500 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 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
tea: 240 mLjelly: 120 mLIV infusion: 50 mL/h × 8 hIV antibiotic: 2 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 125 mL/h. At 21:00, 600 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL600 mL infused125 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 82 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg82 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 12.5 mcg/kg/min for a patient who weighs 95 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL12.5 mcg/kg/min95 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.74 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.74 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
1000 mg4.4 mL + 0.6 mL300 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 39.9 °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
103.9 − 32 = 71.9
Multiply by 5/9
T = 71.9·5/9 = 39.94 ≈ 39.9 °C
Answer
T = 39.9 °C
2.Nursing math & unit conversions
Answer: V = 95 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
1 tsp = 1·5 = 5 mL
¼ cup = 0.25·240 = 60 mL
2 tbsp = 2·15 = 30 mL
Add
V = 5 + 60 + 30 = 95 mL
Answer
V = 95 mL
3.Dosage calculations
Answer: V = 7.6 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 = 2·38 = 76 mg
Volume
V = 76/10 = 7.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.6 mL
4.Dosage calculations
Answer: D = 17.68 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Body surface area
BSA = √(100·18/3600) = √0.5 = 0.7071 m²
Dose
D = 25·0.7071 = 17.68 mg
Answer
D = 17.68 mg
5.IV infusion rates
Answer: V = 800 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
50·60/15 = 200 mL/h
Volume
V = 200·4 = 800 mL
Answer
V = 800 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
50000 mcg/500 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 = 860 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 + 120 = 360 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 2·50 = 100 mL
I = 860 mL
Answer
I = 860 mL
8.IV fluids & fluid balance
Answer: t = 3.2 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.
Volume left
1000 − 600 = 400 mL
Time
t = 400/125 = 3.2 h
Answer
t = 3.2 h
That is about 3 h 12 min, so the bag runs out at about 00:12.
9.Pediatric & critical-care dosing
Answer: V = 1.1 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
70·82 = 5 740 units
Volume
V = 5740/5000 = 1.148 ≈ 1.1 mL
Answer
V = 1.1 mL
10.Pediatric & critical-care dosing
Answer: R = 35.6 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
12.5·95 = 1188 mcg/min
1188·60 = 71250 mcg/h
Pump rate
R = 71250/2000 = 35.63 ≈ 35.6 mL/h
Answer
R = 35.6 mL/h
11.Pharmacy calculations
Answer: V = 7.4 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 = 0.74/0.1 = 7.4 mL
Answer
V = 7.4 mL
12.Pharmacy calculations
Answer: V = 1.5 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.