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 4 lb 6 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
4 lb 6 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 tsp of cough syrup, ½ cup of tea, 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 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.5 mg IM for anaphylaxis. What volume V do you draw up?
1:10000.5 mg
V = mL
4.Dosage calculationsHard
A patient weighs 198 lb. The prescription is 10 mg/kg as a single dose, and the stock contains 250 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
198 lb10 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
A drip runs at 30 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 4 hours?
30 gtt/min60 gtt/mL4 h
V = mL
6.IV infusion ratesHard
A drip runs at 42 gtt/min through a set of 20 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min20 gtt/mL300 mL
t = 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 110 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
110 kg8 hurine: 425 mLurine: 300 mLwound drain: 130 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 13:00 at 120 mL/h. After 2 hours the rate is changed to 80 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL120 mL/h · 2 h80 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 16 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.
20 000 units/500 mL16 units/kg/h98 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 69 kg has an order for nitroglycerin at 20 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL20 mcg/min69 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.76 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.76 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 1.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 1400 mg. Draw up the dose: what volume V do you give?
2000 mg1.8 mL + 0.2 mL1400 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 1.99 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
6 oz/16 = 0.375 lb
4 + 0.375 = 4.375 lb
Pounds to kilograms
m = 4.375/2.2 = 1.989 ≈ 1.99 kg
Answer
m = 1.99 kg
2.Nursing math & unit conversions
Answer: V = 145 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
½ cup = 0.5·240 = 120 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 10 + 120 + 15 = 145 mL
Answer
V = 145 mL
3.Dosage calculations
Answer: V = 0.5 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
1:1000 = 1 g/1000 mL = 1 mg/mL
Volume
V = 0.5/1 = 0.5 mL
Answer
V = 0.5 mL
US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.
4.Dosage calculations
Answer: V = 18 mL
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.
Weight in kg
198/2.2 = 90 kg
Dose
10·90 = 900 mg
Volume
V = (900/250)·5 = 18 mL
Answer
V = 18 mL
5.IV infusion rates
Answer: V = 120 mL
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.
Rate in mL/h
30·60/60 = 30 mL/h
Volume
V = 30·4 = 120 mL
Answer
V = 120 mL
6.IV infusion rates
Answer: t = 2.4 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.
Rate in mL/h
42·60/20 = 126 mL/h
Time left
t = 300/126 = 2.381 ≈ 2.4 h
Answer
t = 2.4 h
7.IV fluids & fluid balance
Answer: U = 0.82 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
425 + 300 = 725 mL
Per kilogram per hour
U = 725/(110·8) = 0.8239 ≈ 0.82 mL/kg/h
Answer
U = 0.82 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 5.3 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
120·2 = 240 mL
500 − 240 = 260 mL left
Second part
260/80 = 3.25 h
Total time
t = 2 + 3.25 = 5.25 ≈ 5.3 h
Answer
t = 5.3 h
That is about 5 h 15 min, so the bag runs out at about 18:15.
9.Pediatric & critical-care dosing
Answer: R = 39.2 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
16·98 = 1 568 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1568/40 = 39.2 mL/h
Answer
R = 39.2 mL/h
10.Pediatric & critical-care dosing
Answer: R = 12 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
20·60 = 1200 mcg/h
Pump rate
R = 1200/100 = 12 mL/h
Answer
R = 12 mL/h
11.Pharmacy calculations
Answer: V = 7.6 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 = 0.76/0.1 = 7.6 mL
Answer
V = 7.6 mL
12.Pharmacy calculations
Answer: V = 1.4 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.