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 drip-rate calculation gives 42.859 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
42.859 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ tsp of cough syrup, ¼ cup of tea, 3 tbsp of liquid supplement, 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 tbsp = 15 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 15 kg. The prescribed dose is 20 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
15 kg20 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
The prescription is 380 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
380 units1000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 10 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL10 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 1 g of a drug in 500 mL. The order is 1.5 mg per minute. At what rate R do you set the pump, in mL/h?
1 g/500 mL1.5 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 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 09:45 and runs by pump at 120 mL/h. How many mL V are left in the bag at 13:45?
1000 mL120 mL/h09:45 → 13:45
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 16 units/kg/h for a patient who weighs 95 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL16 units/kg/h95 kg
R = mL/h
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 2 mcg/kg/min for a patient who weighs 61 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min61 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.12 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.12 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 15% dextrose by mixing 50% and 5% dextrose. How many mL V of the 5% solution do you need? Round to the nearest whole mL.
50%5%15%450 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 43 gtt/min
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 ones place
42.859 → 2
Only the next digit decides
42.859 → 8
8 is 5 or more, so round 2 up.
The digits after it (59) are ignored: round once, never step by step.
Round
x = 43 gtt/min
Answer
x = 43 gtt/min
2.Nursing math & unit conversions
Answer: V = 127.5 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 tsp = 1.5·5 = 7.5 mL
¼ cup = 0.25·240 = 60 mL
3 tbsp = 3·15 = 45 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 7.5 + 60 + 45 + 15 = 127.5 mL
Answer
V = 127.5 mL
3.Dosage calculations
Answer: D = 150 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
20·15 = 300 mg
Per dose
D = 300/2 = 150 mg
Answer
D = 150 mg
4.Dosage calculations
Answer: V = 0.38 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 = 380/1000 = 0.38 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.38 mL
5.IV infusion rates
Answer: R = 8 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
10·60 = 600 min
Drip rate
R = 250·20/600 = 8.333 ≈ 8 gtt/min
Answer
R = 8 gtt/min
At the bedside you round to the nearest whole drop: 8 gtt/min.
6.IV infusion rates
Answer: R = 45 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
1000 mg/500 mL = 2 mg/mL
Dose per hour
1.5·60 = 90 mg/h
Pump rate
R = 90/2 = 45 mL/h
Answer
R = 45 mL/h
7.IV fluids & fluid balance
Answer: I = 1630 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 + 200 + 200 = 580 mL
ice chips: 200/2 = 100 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·50 = 50 mL
I = 1630 mL
Answer
I = 1630 mL
8.IV fluids & fluid balance
Answer: V = 520 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
09:45 → 13:45 = 4 h
Volume infused
120·4 = 480 mL
Volume left
V = 1000 − 480 = 520 mL
Answer
V = 520 mL
9.Pediatric & critical-care dosing
Answer: R = 30.4 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
16·95 = 1 520 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1520/50 = 30.4 mL/h
Answer
R = 30.4 mL/h
10.Pediatric & critical-care dosing
Answer: R = 4.6 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
2·61 = 122 mcg/min
122·60 = 7320 mcg/h
Pump rate
R = 7320/1600 = 4.575 ≈ 4.6 mL/h
Answer
R = 4.6 mL/h
11.Pharmacy calculations
Answer: V = 1.2 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 = 0.12/0.1 = 1.2 mL
Answer
V = 1.2 mL
12.Pharmacy calculations
Answer: V = 350 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.