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 newborn weighs 7 lb 4 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
7 lb 4 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tsp of an oral suspension twice a day for 7 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
½ tsptwice a day7 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A patient weighing 109 kg has a body surface area of 2.04 m². The prescription is 50 mg/m². Find the dose D in mg.
109 kgBSA = 2.04 m²50 mg/m²
D = mg
4.Dosage calculationsHard
The prescription is 50 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
50 mcg0.5 mg/mL
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 10 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 mL10 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 1 g of a drug in 500 mL. The order is 0.5 mg per minute. At what rate R do you set the pump, in mL/h?
1 g/500 mL0.5 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 83 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 runs by pump at 75 mL/h. At 17:30, 50 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL50 mL infused75 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 79 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg79 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 13 mL/h. The patient weighs 79 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL13 mL/h79 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL750 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 9.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 82.5 mg. Draw up the dose: what volume V do you give?
250 mg9.8 mL + 0.2 mL82.5 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 3.3 kg
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.
Ounces to pounds
4 oz/16 = 0.25 lb
7 + 0.25 = 7.25 lb
Pounds to kilograms
m = 7.25/2.2 = 3.295 ≈ 3.3 kg
Answer
m = 3.3 kg
2.Nursing math & unit conversions
Answer: V = 35 mL
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.
Volume per dose
½ tsp = 0.5·5 = 2.5 mL
Whole course
V = 2.5 mL × 2/day × 7 = 35 mL
Answer
V = 35 mL
3.Dosage calculations
Answer: D = 102 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 = 50·2.04 = 102 mg
Answer
D = 102 mg
4.Dosage calculations
Answer: V = 0.1 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
Same units
0.5 mg/mL = 500 mcg/mL
Volume
V = 50/500 = 0.1 mL
Answer
V = 0.1 mL
5.IV infusion rates
Answer: R = 8 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 = 250·20/600 = 8.333 ≈ 8 gtt/min
Answer
R = 8 gtt/min
At the bedside you round to the nearest whole drop: 8 gtt/min.
6.IV infusion rates
Answer: R = 15 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
1000 mg/500 mL = 2 mg/mL
Dose per hour
0.5·60 = 30 mg/h
Pump rate
R = 30/2 = 15 mL/h
Answer
R = 15 mL/h
7.IV fluids & fluid balance
Answer: U = 1.88 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 + 150 + 400 = 1250 mL
Per kilogram per hour
U = 1250/(83·8) = 1.883 ≈ 1.88 mL/kg/h
Answer
U = 1.88 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 12.7 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
1000 − 50 = 950 mL
Time
t = 950/75 = 12.67 ≈ 12.7 h
Answer
t = 12.7 h
That is about 12 h 40 min, so the bag runs out at about 06:10.
9.Pediatric & critical-care dosing
Answer: V = 1.1 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
70·79 = 5 530 units
Volume
V = 5530/5000 = 1.106 ≈ 1.1 mL
Answer
V = 1.1 mL
10.Pediatric & critical-care dosing
Answer: D = 2.7 mcg/kg/min
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
250 000/250 = 1000 mcg/mL
Micrograms per minute
13·1000 = 13000 mcg/h
13000/60 = 216.7 mcg/min
Per kilogram
D = 216.7/79 = 2.743 ≈ 2.7 mcg/kg/min
Answer
D = 2.7 mcg/kg/min
11.Pharmacy calculations
Answer: V = 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.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 750 000/250 000 = 3 mL
Answer
V = 3 mL
12.Pharmacy calculations
Answer: V = 3.3 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.