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 38.3 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
38.3 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 4 tbsp of liquid supplement, 8 fl oz of juice, 1½ tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 fl oz = 30 mL1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A patient weighing 28 kg has a body surface area of 1 m². The prescription is 75 mg/m². Find the dose D in mg.
28 kgBSA = 1 m²75 mg/m²
D = mg
4.Dosage calculationsHard
You must prepare 1000 mL of a 5% (w/v) solution from a 10% (w/v) stock solution. What volume of stock V₁ do you need?
C₁ = 10%C₂ = 5%V₂ = 1000 mL
V₁ = mL
5.IV infusion ratesMedium
1500 mL was ordered over 8 hours. After 4 hours you find that 810 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
1500 mL / 8 hafter 4 h: 810 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 50 gtt/min through a set of 20 gtt/mL. There are 900 mL left in the bag. How many hours t until it is empty?
50 gtt/min20 gtt/mL900 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 1000 mL infusion starts at 08:00 at 125 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 mL125 mL/h · 4 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 500 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 96 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL10 mcg/kg/min96 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 225 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL225 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 190 mg. Draw up the dose: what volume V do you give?
500 mg9.4 mL + 0.6 mL190 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 100.9 °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
38.3·9/5 = 68.94
Add 32
T = 68.94 + 32 = 100.9 °F
Answer
T = 100.9 °F
2.Nursing math & unit conversions
Answer: V = 307.5 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
4 tbsp = 4·15 = 60 mL
8 fl oz = 8·30 = 240 mL
1½ tsp = 1.5·5 = 7.5 mL
Add
V = 60 + 240 + 7.5 = 307.5 mL
Answer
V = 307.5 mL
3.Dosage calculations
Answer: D = 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).
Dose
D = 75·1 = 75 mg
Answer
D = 75 mg
4.Dosage calculations
Answer: V₁ = 500 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 = 5·1000/10 = 500 mL
Answer
V₁ = 500 mL
5.IV infusion rates
Answer: R = 202.5 mL/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.
Original rate
1500/8 = 187.5 mL/h
New rate
R = 810/4 = 202.5 mL/h
Answer
R = 202.5 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: t = 6 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
50·60/20 = 150 mL/h
Time left
t = 900/150 = 6 h
Answer
t = 6 h
7.IV fluids & fluid balance
Answer: I = 2060 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 + 200 + 150 = 450 mL
ice chips: 120/2 = 60 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 1·50 = 50 mL
I = 2060 mL
Answer
I = 2060 mL
8.IV fluids & fluid balance
Answer: t = 14 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
125·4 = 500 mL
1000 − 500 = 500 mL left
Second part
500/50 = 10 h
Total time
t = 4 + 10 = 14 h
Answer
t = 14 h
That is about 14 h 00 min, so the bag runs out at about 22:00.
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 = 28.8 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
10·96 = 960 mcg/min
960·60 = 57600 mcg/h
Pump rate
R = 57600/2000 = 28.8 mL/h
Answer
R = 28.8 mL/h
11.Pharmacy calculations
Answer: V = 2.3 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
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 225/100 = 2.25 ≈ 2.3 mL
Answer
V = 2.3 mL
12.Pharmacy calculations
Answer: V = 3.8 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.