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 95.7 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
95.7 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tbsp of an oral suspension every 6 hours for 14 days. The suspension comes in 150 mL bottles. Using 1 tbsp = 15 mL, how many whole bottles N must be supplied so the course is complete?
½ tbspevery 6 hours14 days150 mL1 tbsp = 15 mL
N =
3.Dosage calculationsMedium
A dose of 250 mg is needed from a 10% (w/v) solution. What volume V contains this dose?
250 mg10% w/v
V = mL
4.Dosage calculationsHard
You must prepare 200 mL of a 2% (w/v) solution from a 10% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 10%C₂ = 2%V₂ = 200 mL
W = mL
5.IV infusion ratesMedium
Infuse 250 mL over 6 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL6 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 2 g of a drug in 250 mL. The order is 1.5 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/250 mL1.5 mg/min
R = mL/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 54 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
54 kg8 hurine: 325 mLurine: 450 mLwound drain: 50 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 17:30 at 150 mL/h. After 3 hours the rate is changed to 200 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 mL150 mL/h · 3 h200 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 1.5 units/h. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL1.5 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 86 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL10 mcg/kg/min86 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg11.5 mL+1 mL
C = mg/mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 8% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%8%300 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 35.4 °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
95.7 − 32 = 63.7
Multiply by 5/9
T = 63.7·5/9 = 35.39 ≈ 35.4 °C
Answer
T = 35.4 °C
2.Nursing math & unit conversions
Answer: N = 3
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.
Total volume
7.5 mL × 4 × 14 = 420 mL
Bottles
420/150 = 2.8 → N = 3
Answer
N = 3
3.Dosage calculations
Answer: V = 2.5 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.
Concentration
10% = 100 mg/mL
Volume
V = 250/100 = 2.5 mL
Answer
V = 2.5 mL
4.Dosage calculations
Answer: W = 160 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 = 2·200/10 = 40 mL
Water to add
W = 200 − 40 = 160 mL
Answer
W = 160 mL
5.IV infusion rates
Answer: R = 14 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
6·60 = 360 min
Drip rate
R = 250·20/360 = 13.89 ≈ 14 gtt/min
Answer
R = 14 gtt/min
At the bedside you round to the nearest whole drop: 14 gtt/min.
6.IV infusion rates
Answer: R = 11.25 mL/h
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
2000 mg/250 mL = 8 mg/mL
Dose per hour
1.5·60 = 90 mg/h
Pump rate
R = 90/8 = 11.25 mL/h
Answer
R = 11.25 mL/h
7.IV fluids & fluid balance
Answer: U = 1.79 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
325 + 450 = 775 mL
Per kilogram per hour
U = 775/(54·8) = 1.794 ≈ 1.79 mL/kg/h
Answer
U = 1.79 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 5.8 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
150·3 = 450 mL
1000 − 450 = 550 mL left
Second part
550/200 = 2.75 h
Total time
t = 3 + 2.75 = 5.75 ≈ 5.8 h
Answer
t = 5.8 h
That is about 5 h 45 min, so the bag runs out at about 23:15.
9.Pediatric & critical-care dosing
Answer: R = 1.5 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
250/250 = 1 units/mL
Pump rate
R = 1.5/1 = 1.5 mL/h
Answer
R = 1.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 32.3 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
10·86 = 860 mcg/min
860·60 = 51600 mcg/h
Pump rate
R = 51600/1600 = 32.25 ≈ 32.3 mL/h
Answer
R = 32.3 mL/h
11.Pharmacy calculations
Answer: C = 160 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
11.5 + 1 = 12.5 mL
Concentration
C = 2000/12.5 = 160 mg/mL
Answer
C = 160 mg/mL
12.Pharmacy calculations
Answer: V = 225 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.