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 39.8 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
39.8 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A haemoglobin result is 81 g/L. Express it in g/dL Hb.
81 g/L1 L = 10 dL
Hb = g/dL
3.Dosage calculationsMedium
A patient weighs 12 kg. The prescribed dose is 20 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
12 kg20 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
An infusion contains 40000 units of a drug in 1000 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
40000 units/1000 mL1000 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 500 mL over 8 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL8 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 50 mg in 500 mL runs at 15 mL/h. How many micrograms per minute D does the patient receive?
50 mg/500 mL15 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 8-hour shift. The patient weighs 106 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 bag was started at 09:00 and runs by pump at 50 mL/h. How many mL V are left in the bag at 11:30?
1000 mL50 mL/h09:00 → 11:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 98 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL18 units/kg/h98 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 108 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL6 mcg/kg/min108 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.54 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.54 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1000 mL of 15% dextrose by mixing 50% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
50%10%15%1000 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 103.6 °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
39.8·9/5 = 71.64
Add 32
T = 71.64 + 32 = 103.6 °F
Answer
T = 103.6 °F
2.Nursing math & unit conversions
Answer: Hb = 8.1 g/dL
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
Hb = 81 g/L × (1 L/10 dL) = 8.1 g/dL
Answer
Hb = 8.1 g/dL
3.Dosage calculations
Answer: D = 120 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
20·12 = 240 mg
Per dose
D = 240/2 = 120 mg
Answer
D = 120 mg
4.Dosage calculations
Answer: R = 25 mL/h
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.
Concentration
40000/1000 = 40 units/mL
Pump rate
R = 1000/40 = 25 mL/h
Answer
R = 25 mL/h
5.IV infusion rates
Answer: R = 10 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
8·60 = 480 min
Drip rate
R = 500·10/480 = 10.42 ≈ 10 gtt/min
Answer
R = 10 gtt/min
At the bedside you round to the nearest whole drop: 10 gtt/min.
6.IV infusion rates
Answer: D = 25 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
50000 mcg/500 mL = 100 mcg/mL
Dose per hour
15·100 = 1500 mcg/h
Dose per minute
D = 1500/60 = 25 mcg/min
Answer
D = 25 mcg/min
7.IV fluids & fluid balance
Answer: U = 1.74 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
275 + 425 + 450 + 325 = 1475 mL
Per kilogram per hour
U = 1475/(106·8) = 1.739 ≈ 1.74 mL/kg/h
Answer
U = 1.74 mL/kg/h
8.IV fluids & fluid balance
Answer: V = 875 mL
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.
Elapsed time
09:00 → 11:30 = 2.5 h
Volume infused
50·2.5 = 125 mL
Volume left
V = 1000 − 125 = 875 mL
Answer
V = 875 mL
9.Pediatric & critical-care dosing
Answer: R = 35.3 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
18·98 = 1 764 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1764/50 = 35.28 ≈ 35.3 mL/h
Answer
R = 35.3 mL/h
10.Pediatric & critical-care dosing
Answer: R = 24.3 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
6·108 = 648 mcg/min
648·60 = 38880 mcg/h
Pump rate
R = 38880/1600 = 24.3 mL/h
Answer
R = 24.3 mL/h
11.Pharmacy calculations
Answer: V = 5.4 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 = 0.54/0.1 = 5.4 mL
Answer
V = 5.4 mL
12.Pharmacy calculations
Answer: V = 875 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.