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 dose is charted at 4:35 PM. Which entry is the same time on the 24-hour clock? Click it.
4:35 PM
117:35
204:35
316:35
415:35
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 tsp of cough syrup, 1½ cups of tea, 3 tbsp of liquid supplement, ½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 cup = 8 fl oz = 240 mL1 tbsp = 15 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 80 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.
80 kg10 mg/kg
D = mg
4.Dosage calculationsHard
A patient is 190 cm tall and weighs 87 kg. The prescription is 60 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
190 cm87 kg60 mg/m²
D = mg
5.IV infusion ratesMedium
Infuse 250 mL over 8 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 mL8 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 1000 mg of a drug in 50 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
1000 mg/50 mL10 mL/h
D = mg/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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 10:30 and runs by pump at 50 mL/h. How many mL V are left in the bag at 14:30?
500 mL50 mL/h10:30 → 14:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 250 units of regular insulin in 250 mL runs at 10 mL/h. How many units per hour D does the patient receive?
250 units/250 mL10 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 12 mL/h. The patient weighs 83 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL12 mL/h83 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 8.2 mL of diluent. The prescribed dose is 600 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL600 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 600 mg. Draw up the dose: what volume V do you give?
2000 mg3.6 mL + 0.4 mL600 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 16:35
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Convert the hour
4 PM → 4 + 12 = 16
Answer
16:35
Answer
16:35
2.Nursing math & unit conversions
Answer: V = 430 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
2 tsp = 2·5 = 10 mL
1½ cups = 1.5·240 = 360 mL
3 tbsp = 3·15 = 45 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 10 + 360 + 45 + 15 = 430 mL
Answer
V = 430 mL
3.Dosage calculations
Answer: D = 800 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.
Dose
10·80 = 800 mg
Answer
D = 800 mg
4.Dosage calculations
Answer: D = 128.6 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 = √(190·87/3600) = √4.592 = 2.143 m²
Dose
D = 60·2.143 = 128.6 mg
Answer
D = 128.6 mg
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 = 250·20/480 = 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 = 200 mg/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.
Concentration
1000/50 = 20 mg/mL
Dose rate
D = 20·10 = 200 mg/h
Answer
D = 200 mg/h
7.IV fluids & fluid balance
Answer: B = 80 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: 180 + 100 = 280 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 2·50 = 100 mL
total intake = 980 mL
Total output
150 + 425 + 275 + 50 = 900 mL
Balance
B = 980 − 900 = 80 mL
Answer
B = 80 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 300 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
10:30 → 14:30 = 4 h
Volume infused
50·4 = 200 mL
Volume left
V = 500 − 200 = 300 mL
Answer
V = 300 mL
9.Pediatric & critical-care dosing
Answer: D = 10 units/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
Units per hour
D = 10·1 = 10 units/h
Answer
D = 10 units/h
10.Pediatric & critical-care dosing
Answer: D = 3.9 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
12·1600 = 19200 mcg/h
19200/60 = 320 mcg/min
Per kilogram
D = 320/83 = 3.855 ≈ 3.9 mcg/kg/min
Answer
D = 3.9 mcg/kg/min
11.Pharmacy calculations
Answer: V = 1.2 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
8.2 mL → 500 000 units/mL
Volume to give
V = 600 000/500 000 = 1.2 mL
Answer
V = 1.2 mL
12.Pharmacy calculations
Answer: V = 1.2 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.