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 weight conversion gives 139.6634 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
139.6634 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 fl oz of juice, 2 tsp of cough syrup, ¼ cup of tea. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 60 kg. The prescribed dose is 30 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
60 kg30 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
A child weighing 28 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give? Round to one decimal place.
28 kg12.5 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 8 hours. After 5 hours you find that 680 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
1500 mL / 8 hafter 5 h: 680 mL
R = mL/h
6.IV infusion ratesHard
An infusion of 50 mg in 250 mL runs at 15 mL/h. How many micrograms per minute D does the patient receive?
50 mg/250 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 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 08:00 at 100 mL/h. After 3 hours the rate is changed to 125 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 mL100 mL/h · 3 h125 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 14 units/kg/h for a patient who weighs 59 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL14 units/kg/h59 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 15 mcg/kg/min for a patient who weighs 70 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL15 mcg/kg/min70 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.84 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.84 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 20 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 2% ointment? Round to the nearest whole gram.
20 g · 5%1%2%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 139.7 kg
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
139.6634 → 6
Only the next digit decides
139.6634 → 6
6 is 5 or more, so round 6 up.
The digits after it (34) are ignored: round once, never step by step.
Round
x = 139.7 kg
Answer
x = 139.7 kg
2.Nursing math & unit conversions
Answer: V = 130 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 fl oz = 2·30 = 60 mL
2 tsp = 2·5 = 10 mL
¼ cup = 0.25·240 = 60 mL
Add
V = 60 + 10 + 60 = 130 mL
Answer
V = 130 mL
3.Dosage calculations
Answer: D = 900 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
30·60 = 1800 mg
Per dose
D = 1800/2 = 900 mg
Answer
D = 900 mg
4.Dosage calculations
Answer: V = 8.8 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.
Dose from weight
12.5·28 = 350 mg
Volume
V = (350/40)·1 = 8.75 ≈ 8.8 mL
Answer
V = 8.8 mL
5.IV infusion rates
Answer: R = 226.7 mL/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.
Original rate
1500/8 = 187.5 mL/h
New rate
R = 680/3 = 226.7 mL/h
Answer
R = 226.7 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: D = 50 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/250 mL = 200 mcg/mL
Dose per hour
15·200 = 3000 mcg/h
Dose per minute
D = 3000/60 = 50 mcg/min
Answer
D = 50 mcg/min
7.IV fluids & fluid balance
Answer: B = 500 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: 150 + 200 + 100 = 450 mL
ice chips: 100/2 = 50 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1750 mL
Total output
325 + 175 + 300 + 450 = 1250 mL
Balance
B = 1750 − 1250 = 500 mL
Answer
B = 500 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 4.6 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
100·3 = 300 mL
500 − 300 = 200 mL left
Second part
200/125 = 1.6 h
Total time
t = 3 + 1.6 = 4.6 h
Answer
t = 4.6 h
That is about 4 h 36 min, so the bag runs out at about 12:36.
9.Pediatric & critical-care dosing
Answer: R = 20.7 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
14·59 = 826 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 826/40 = 20.65 ≈ 20.7 mL/h
Answer
R = 20.7 mL/h
10.Pediatric & critical-care dosing
Answer: R = 39.4 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
15·70 = 1050 mcg/min
1050·60 = 63000 mcg/h
Pump rate
R = 63000/1600 = 39.38 ≈ 39.4 mL/h
Answer
R = 39.4 mL/h
11.Pharmacy calculations
Answer: V = 8.4 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 = 0.84/0.1 = 8.4 mL
Answer
V = 8.4 mL
12.Pharmacy calculations
Answer: m = 60 g
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.