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 102.8 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
102.8 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A serum creatinine result is 2.1 mg/dL. Using 1 mg/dL = 88.4 µmol/L for creatinine, find c in µmol/L to the nearest whole number.
2.1 mg/dL1 mg/dL = 88.4 µmol/L
c = µmol/L
3.Dosage calculationsMedium
How many milligrams of drug m are in 10 mL of a 1% (w/v) solution?
1% w/v10 mL
m = mg
4.Dosage calculationsHard
A patient is 127 cm tall and weighs 29 kg. The prescription is 250 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
127 cm29 kg250 mg/m²
D = mg
5.IV infusion ratesMedium
1500 mL was ordered over 12 hours. After 2 hours you find that 1480 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 / 12 hafter 2 h: 1480 mL
R = mL/h
6.IV infusion ratesHard
250 mg of a drug is diluted in 250 mL and given by gravity through a set of 15 gtt/mL. The order is 20 mg per hour. Find the drip rate R in drops per minute.
250 mg/250 mL20 mg/h15 gtt/mL
R = gtt/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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 13:30 at 80 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 mL80 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 60 units/kg for a patient who weighs 99 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg99 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 52 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL10 mcg/kg/min52 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.8 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.8 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 250 mg. Draw up the dose: what volume V do you give?
2000 mg3.2 mL + 0.8 mL250 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 39.3 °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
102.8 − 32 = 70.8
Multiply by 5/9
T = 70.8·5/9 = 39.33 ≈ 39.3 °C
Answer
T = 39.3 °C
2.Nursing math & unit conversions
Answer: c = 186 µmol/L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Convert
c = 2.1·88.4 = 185.6 ≈ 186 µmol/L
Answer
c = 186 µmol/L
3.Dosage calculations
Answer: m = 100 mg
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.
Concentration
1% = 1 g/100 mL = 10 mg/mL
Mass of drug
m = 10·10 = 100 mg
Answer
m = 100 mg
4.Dosage calculations
Answer: D = 252.9 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 = √(127·29/3600) = √1.023 = 1.011 m²
Dose
D = 250·1.011 = 252.9 mg
Answer
D = 252.9 mg
5.IV infusion rates
Answer: R = 148 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
1500/12 = 125 mL/h
New rate
R = 1480/10 = 148 mL/h
Answer
R = 148 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: R = 5 gtt/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
250/250 = 1 mg/mL
Volume per hour
20/1 = 20 mL/h
Drip rate
R = 20·15/60 = 5 gtt/min
Answer
R = 5 gtt/min
7.IV fluids & fluid balance
Answer: B = 355 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.
Total intake
oral: 200 + 200 + 100 = 500 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1000 mL
Total output
300 + 275 + 70 = 645 mL
Balance
B = 1000 − 645 = 355 mL
Answer
B = 355 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 17.6 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
80·4 = 320 mL
1000 − 320 = 680 mL left
Second part
680/50 = 13.6 h
Total time
t = 4 + 13.6 = 17.6 h
Answer
t = 17.6 h
That is about 17 h 36 min, so the bag runs out at about 07:06.
9.Pediatric & critical-care dosing
Answer: V = 5.9 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
60·99 = 5 940 units
Volume
V = 5940/1000 = 5.94 ≈ 5.9 mL
Answer
V = 5.9 mL
10.Pediatric & critical-care dosing
Answer: R = 15.6 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
10·52 = 520 mcg/min
520·60 = 31200 mcg/h
Pump rate
R = 31200/2000 = 15.6 mL/h
Answer
R = 15.6 mL/h
11.Pharmacy calculations
Answer: V = 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.8/0.1 = 8 mL
Answer
V = 8 mL
12.Pharmacy calculations
Answer: V = 0.5 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.