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 37.3619 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
37.3619 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 4 tbsp of liquid supplement, ¾ cup of tea, 3 tsp of cough syrup, 3 fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 cup = 8 fl oz = 240 mL1 tsp = 5 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A prefilled syringe of epinephrine (adrenaline) is labelled 1:10 000 (0.1 mg/mL). The prescription is 1 mg IV in cardiac arrest. What volume V do you give?
1:10 0001 mg
V = mL
4.Dosage calculationsHard
The prescription is 1450 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1450 units5000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 8 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 mL8 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 500 mg of a drug in 50 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
500 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 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 11:30 and runs by pump at 50 mL/h. How many mL V are left in the bag at 13:30?
500 mL50 mL/h11:30 → 13:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 76 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg76 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 6 mcg/kg/min for a patient who weighs 84 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL6 mcg/kg/min84 kg
R = mL/h
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 18.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL750 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 960 mg. Draw up the dose: what volume V do you give?
1000 mg4.5 mL + 0.5 mL960 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 37.4 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
37.3619 → 3
Only the next digit decides
37.3619 → 6
6 is 5 or more, so round 3 up.
The digits after it (19) are ignored: round once, never step by step.
Round
x = 37.4 kg
Answer
x = 37.4 kg
2.Nursing math & unit conversions
Answer: V = 345 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
4 tbsp = 4·15 = 60 mL
¾ cup = 0.75·240 = 180 mL
3 tsp = 3·5 = 15 mL
3 fl oz = 3·30 = 90 mL
Add
V = 60 + 180 + 15 + 90 = 345 mL
Answer
V = 345 mL
3.Dosage calculations
Answer: V = 10 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
1:10 000 = 1 g/10000 mL = 0.1 mg/mL
Volume
V = 1/0.1 = 10 mL
Answer
V = 10 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 = 0.29 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 = 1450/5000 = 0.29 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.29 mL
5.IV infusion rates
Answer: R = 21 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 = 1000·10/480 = 20.83 ≈ 21 gtt/min
Answer
R = 21 gtt/min
At the bedside you round to the nearest whole drop: 21 gtt/min.
6.IV infusion rates
Answer: D = 100 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
500/50 = 10 mg/mL
Dose rate
D = 10·10 = 100 mg/h
Answer
D = 100 mg/h
7.IV fluids & fluid balance
Answer: B = 295 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 + 240 = 360 mL
ice chips: 120/2 = 60 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 1·100 = 100 mL
total intake = 920 mL
Total output
150 + 325 + 150 = 625 mL
Balance
B = 920 − 625 = 295 mL
Answer
B = 295 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 400 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
11:30 → 13:30 = 2 h
Volume infused
50·2 = 100 mL
Volume left
V = 500 − 100 = 400 mL
Answer
V = 400 mL
9.Pediatric & critical-care dosing
Answer: V = 6.1 mL
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 needed
80·76 = 6 080 units
Volume
V = 6080/1000 = 6.08 ≈ 6.1 mL
Answer
V = 6.1 mL
10.Pediatric & critical-care dosing
Answer: R = 18.9 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
6·84 = 504 mcg/min
504·60 = 30240 mcg/h
Pump rate
R = 30240/1600 = 18.9 mL/h
Answer
R = 18.9 mL/h
11.Pharmacy calculations
Answer: V = 3 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
18.2 mL → 250 000 units/mL
Volume to give
V = 750 000/250 000 = 3 mL
Answer
V = 3 mL
12.Pharmacy calculations
Answer: V = 4.8 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.