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 97 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
97 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1 cup of tea, 2 tsp of cough syrup, 1½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 tsp = 5 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A child weighing 8 kg is prescribed 10 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
8 kg10 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
You must prepare 250 mL of a 1% (w/v) solution from a 50% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 50%C₂ = 1%V₂ = 250 mL
W = mL
5.IV infusion ratesMedium
An infusion is ordered at 30 mL/h, but no pump is available. It runs by gravity through a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
30 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 50 mL and runs at 20 mL/h. How many milligrams per hour D does the patient receive?
200 mg/50 mL20 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 patient weighs 98 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 11:00 at 75 mL/h. After 2 hours the rate is changed to 100 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 mL75 mL/h · 2 h100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 0.05 units/kg/h for a patient who weighs 100 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL0.05 units/kg/h100 kg
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 6 mcg/kg/min for a patient who weighs 78 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL6 mcg/kg/min78 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 8.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 155 mg. Draw up the dose: what volume V do you give?
250 mg4.4 mL + 0.6 mL155 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 36.1 °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
97 − 32 = 65
Multiply by 5/9
T = 65·5/9 = 36.11 ≈ 36.1 °C
Answer
T = 36.1 °C
2.Nursing math & unit conversions
Answer: V = 295 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 cup = 1·240 = 240 mL
2 tsp = 2·5 = 10 mL
1½ fl oz = 1.5·30 = 45 mL
Add
V = 240 + 10 + 45 = 295 mL
Answer
V = 295 mL
3.Dosage calculations
Answer: V = 3.2 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 = 10·8 = 80 mg
Volume
V = 80/25 = 3.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3.2 mL
4.Dosage calculations
Answer: W = 245 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.
Volume of stock
V₁ = 1·250/50 = 5 mL
Water to add
W = 250 − 5 = 245 mL
Answer
W = 245 mL
5.IV infusion rates
Answer: R = 30 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.
Millilitres per minute
30/60 = 0.5 mL/min
Drip rate
R = 0.5·60 = 30 gtt/min
Answer
R = 30 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
6.IV infusion rates
Answer: D = 80 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
200/50 = 4 mg/mL
Dose rate
D = 4·20 = 80 mg/h
Answer
D = 80 mg/h
7.IV fluids & fluid balance
Answer: U = 1.59 mL/kg/h
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 urine
175 + 400 + 375 + 300 = 1250 mL
Per kilogram per hour
U = 1250/(98·8) = 1.594 ≈ 1.59 mL/kg/h
Answer
U = 1.59 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 10.5 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
75·2 = 150 mL
1000 − 150 = 850 mL left
Second part
850/100 = 8.5 h
Total time
t = 2 + 8.5 = 10.5 h
Answer
t = 10.5 h
That is about 10 h 30 min, so the bag runs out at about 21:30.
9.Pediatric & critical-care dosing
Answer: R = 12.5 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
0.05·100 = 5 units/h
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 5/0.4 = 12.5 mL/h
Answer
R = 12.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 17.6 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
6·78 = 468 mcg/min
468·60 = 28080 mcg/h
Pump rate
R = 28080/1600 = 17.55 ≈ 17.6 mL/h
Answer
R = 17.6 mL/h
11.Pharmacy calculations
Answer: V = 4.8 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
8.2 mL → 500 000 units/mL
Volume to give
V = 2 400 000/500 000 = 4.8 mL
Answer
V = 4.8 mL
12.Pharmacy calculations
Answer: V = 3.1 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.