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 1 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 1 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 1 tbsp of liquid supplement, 1 tsp of cough syrup, 3 cups of tea, ½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A child weighing 10 kg is prescribed 3 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
10 kg3 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 2100 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2100 units10000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 6 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL6 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 4 g of a drug in 500 mL. The order is 1 mg per minute. At what rate R do you set the pump, in mL/h?
4 g/500 mL1 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 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 12:15 and runs by pump at 50 mL/h. How many mL V are left in the bag at 17:45?
500 mL50 mL/h12:15 → 17:45
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 16 units/kg/h for a patient who weighs 76 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL16 units/kg/h76 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 6 mL/h. The patient weighs 84 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL6 mL/h84 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. The prescribed dose is 375 mg. What volume V do you draw up? Round to one decimal place.
750 mg7.2 mL+0.3 mL375 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1500 mL of 20% 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%20%1500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 1.85 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
1 oz/16 = 0.0625 lb
4 + 0.0625 = 4.063 lb
Pounds to kilograms
m = 4.063/2.2 = 1.847 ≈ 1.85 kg
Answer
m = 1.85 kg
2.Nursing math & unit conversions
Answer: V = 755 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
1 tbsp = 1·15 = 15 mL
1 tsp = 1·5 = 5 mL
3 cups = 3·240 = 720 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 15 + 5 + 720 + 15 = 755 mL
Answer
V = 755 mL
3.Dosage calculations
Answer: V = 3 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.
Dose from body weight
D = 3·10 = 30 mg
Volume
V = 30/10 = 3 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3 mL
4.Dosage calculations
Answer: V = 0.21 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.
Volume
V = 2100/10000 = 0.21 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.21 mL
5.IV infusion rates
Answer: R = 28 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 = 1000·10/360 = 27.78 ≈ 28 gtt/min
Answer
R = 28 gtt/min
At the bedside you round to the nearest whole drop: 28 gtt/min.
6.IV infusion rates
Answer: R = 7.5 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
4000 mg/500 mL = 8 mg/mL
Dose per hour
1·60 = 60 mg/h
Pump rate
R = 60/8 = 7.5 mL/h
Answer
R = 7.5 mL/h
7.IV fluids & fluid balance
Answer: B = 445 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: 120 + 250 + 350 = 720 mL
ice chips: 240/2 = 120 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1690 mL
Total output
250 + 375 + 350 + 70 + 200 = 1245 mL
Balance
B = 1690 − 1245 = 445 mL
Answer
B = 445 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 225 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
12:15 → 17:45 = 5.5 h
Volume infused
50·5.5 = 275 mL
Volume left
V = 500 − 275 = 225 mL
Answer
V = 225 mL
9.Pediatric & critical-care dosing
Answer: R = 24.3 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
16·76 = 1 216 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1216/50 = 24.32 ≈ 24.3 mL/h
Answer
R = 24.3 mL/h
10.Pediatric & critical-care dosing
Answer: D = 2.4 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
6·2000 = 12000 mcg/h
12000/60 = 200 mcg/min
Per kilogram
D = 200/84 = 2.381 ≈ 2.4 mcg/kg/min
Answer
D = 2.4 mcg/kg/min
11.Pharmacy calculations
Answer: V = 3.8 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
7.2 + 0.3 = 7.5 mL
Concentration
750/7.5 = 100 mg/mL
Volume to give
V = 375/100 = 3.75 ≈ 3.8 mL
Answer
V = 3.8 mL
12.Pharmacy calculations
Answer: V = 1125 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.