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 calculation for a small injection gives 0.14226 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.14226 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ cups of tea, ½ tbsp of liquid supplement, 1 tsp of cough syrup, 3 fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 tbsp = 15 mL1 tsp = 5 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A child weighing 28 kg is prescribed 5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
28 kg5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 16 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 125 mg in 5 mL. What volume V do you give?
16 kg15 mg/kg125 mg/5 mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 4 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 mL4 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 400 mg of a drug in 500 mL and runs at 20 mL/h. How many milligrams per hour D does the patient receive?
400 mg/500 mL20 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 total intake I in mL.
soup: 180 mLjuice: 120 mLwater: 350 mLIV infusion: 125 mL/h × 12 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 11:30 at 150 mL/h. After 4 hours the rate is changed to 75 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL150 mL/h · 4 h75 mL/h
t = h
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 20 units/kg/h for a patient who weighs 89 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL20 units/kg/h89 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 26 mL/h. The patient weighs 61 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL26 mL/h61 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.77 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.77 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 250 mL of 6% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
30%0%6%250 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.14 mL
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 hundredths place
0.14226 → 4
Only the next digit decides
0.14226 → 2
2 is 4 or less, so 4 stays.
The digits after it (26) are ignored: round once, never step by step.
Round
x = 0.14 mL
Answer
x = 0.14 mL
2.Nursing math & unit conversions
Answer: V = 462.5 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
1½ cups = 1.5·240 = 360 mL
½ tbsp = 0.5·15 = 7.5 mL
1 tsp = 1·5 = 5 mL
3 fl oz = 3·30 = 90 mL
Add
V = 360 + 7.5 + 5 + 90 = 462.5 mL
Answer
V = 462.5 mL
3.Dosage calculations
Answer: V = 2.8 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 = 5·28 = 140 mg
Volume
V = 140/50 = 2.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 2.8 mL
4.Dosage calculations
Answer: V = 9.6 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
15·16 = 240 mg
Volume
V = (240/125)·5 = 9.6 mL
Answer
V = 9.6 mL
5.IV infusion rates
Answer: R = 42 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
4·60 = 240 min
Drip rate
R = 1000·10/240 = 41.67 ≈ 42 gtt/min
Answer
R = 42 gtt/min
At the bedside you round to the nearest whole drop: 42 gtt/min.
6.IV infusion rates
Answer: D = 16 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
400/500 = 0.8 mg/mL
Dose rate
D = 0.8·20 = 16 mg/h
Answer
D = 16 mg/h
7.IV fluids & fluid balance
Answer: I = 2350 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.
Add the intake
oral: 180 + 120 + 350 = 650 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 2·100 = 200 mL
I = 2350 mL
Answer
I = 2350 mL
8.IV fluids & fluid balance
Answer: t = 9.3 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
150·4 = 600 mL
1000 − 600 = 400 mL left
Second part
400/75 = 5.333 h
Total time
t = 4 + 5.333 = 9.333 ≈ 9.3 h
Answer
t = 9.3 h
That is about 9 h 20 min, so the bag runs out at about 20:50.
9.Pediatric & critical-care dosing
Answer: R = 35.6 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
20·89 = 1 780 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1780/50 = 35.6 mL/h
Answer
R = 35.6 mL/h
10.Pediatric & critical-care dosing
Answer: D = 11.4 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
26·1600 = 41600 mcg/h
41600/60 = 693.3 mcg/min
Per kilogram
D = 693.3/61 = 11.37 ≈ 11.4 mcg/kg/min
Answer
D = 11.4 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.77 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/1000 mL = 1 mg/mL
Volume
V = 0.77/1 = 0.77 mL
Answer
V = 0.77 mL
12.Pharmacy calculations
Answer: V = 200 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.
Alligation parts
30%: 6 − 0 = 6 parts
0%: 30 − 6 = 24 parts
total: 30 parts
Water
V = 250·24/30 = 200 mL
Answer
V = 200 mL
Check: 50 mL of 30% contains 15 g of drug, which is 6% of 250 mL.