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 104.2 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
104.2 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ fl oz of juice, 1 tsp of cough syrup, 3 cups of tea, 1 tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 18 kg. The prescribed dose is 25 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?
18 kg25 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
A patient is 101 cm tall and weighs 25 kg. The prescription is 100 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
101 cm25 kg100 mg/m²
D = mg
5.IV infusion ratesMedium
Infuse 1500 mL over 10 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute.
1500 mL10 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 25 mg in 250 mL runs at 18 mL/h. How many micrograms per minute D does the patient receive?
25 mg/250 mL18 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 patient weighs 105 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
105 kg12 hurine: 250 mLurine: 225 mLurine: 225 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 150 mL/h. At 18:30, 300 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL300 mL infused150 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 1 unit/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL1 units/h
R = mL/h
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 10 mcg/kg/min for a patient who weighs 83 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL10 mcg/kg/min83 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 2000 mg as a powder. The practice label says to add 19.2 mL of sterile water; the powder adds 0.8 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg19.2 mL+0.8 mL
C = mg/mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 900 mL of 70% ethanol from a 90% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
90%0%70%900 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 40.1 °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
104.2 − 32 = 72.2
Multiply by 5/9
T = 72.2·5/9 = 40.11 ≈ 40.1 °C
Answer
T = 40.1 °C
2.Nursing math & unit conversions
Answer: V = 755 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
½ fl oz = 0.5·30 = 15 mL
1 tsp = 1·5 = 5 mL
3 cups = 3·240 = 720 mL
1 tbsp = 1·15 = 15 mL
Add
V = 15 + 5 + 720 + 15 = 755 mL
Answer
V = 755 mL
3.Dosage calculations
Answer: D = 112.5 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.
Total per day
25·18 = 450 mg
Per dose
D = 450/4 = 112.5 mg
Answer
D = 112.5 mg
4.Dosage calculations
Answer: D = 83.75 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 = √(101·25/3600) = √0.7014 = 0.8375 m²
Dose
D = 100·0.8375 = 83.75 mg
Answer
D = 83.75 mg
5.IV infusion rates
Answer: R = 25 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
10·60 = 600 min
Drip rate
R = 1500·10/600 = 25 gtt/min
Answer
R = 25 gtt/min
6.IV infusion rates
Answer: D = 30 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
18·100 = 1800 mcg/h
Dose per minute
D = 1800/60 = 30 mcg/min
Answer
D = 30 mcg/min
7.IV fluids & fluid balance
Answer: U = 0.56 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
250 + 225 + 225 = 700 mL
Per kilogram per hour
U = 700/(105·12) = 0.5556 ≈ 0.56 mL/kg/h
Answer
U = 0.56 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 1.3 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
500 − 300 = 200 mL
Time
t = 200/150 = 1.333 ≈ 1.3 h
Answer
t = 1.3 h
That is about 1 h 20 min, so the bag runs out at about 19:50.
9.Pediatric & critical-care dosing
Answer: R = 2.5 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.
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 1/0.4 = 2.5 mL/h
Answer
R = 2.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 49.8 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
10·83 = 830 mcg/min
830·60 = 49800 mcg/h
Pump rate
R = 49800/1000 = 49.8 mL/h
Answer
R = 49.8 mL/h
11.Pharmacy calculations
Answer: C = 100 mg/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.
Final volume
19.2 + 0.8 = 20 mL
Concentration
C = 2000/20 = 100 mg/mL
Answer
C = 100 mg/mL
12.Pharmacy calculations
Answer: V = 200 mL
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.
Alligation parts
90%: 70 − 0 = 70 parts
0%: 90 − 70 = 20 parts
total: 90 parts
Water
V = 900·20/90 = 200 mL
Answer
V = 200 mL
Check: 700 mL of 90% contains 630 mL of drug, which is 70% of 900 mL. This assumes the volumes simply add up; in practice ethanol is made up to volume.