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 an injection gives 12.7557 mL. The rule in this exercise is that volumes of 1 mL or more are rounded to the nearest tenth of a mL. What value x do you record?
12.7557 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:35 and finishes at 01:15 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
23:3501:15
t = h
3.Dosage calculationsMedium
How many milligrams of drug m are in 10 mL of a 5% (w/v) solution?
5% w/v10 mL
m = mg
4.Dosage calculationsHard
The prescription is 3300 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?
3300 units10000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 1000 mL over 3 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 mL3 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 42 gtt/min through a set of 60 gtt/mL. There are 900 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min60 gtt/mL900 mL
t = 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 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 13:15 and runs by pump at 150 mL/h. How many mL V are left in the bag at 14:45?
500 mL150 mL/h13:15 → 14:45
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 94 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg94 kg5 000 units/mL
V = mL
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 10 mcg/kg/min for a patient who weighs 83 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL10 mcg/kg/min83 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.48 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.48 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 2.3 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 110 mg. Draw up the dose: what volume V do you give?
250 mg2.3 mL + 0.2 mL110 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 12.8 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 tenths place
12.7557 → 7
Only the next digit decides
12.7557 → 5
5 is 5 or more, so round 7 up.
The digits after it (57) are ignored: round once, never step by step.
Round
x = 12.8 mL
Answer
x = 12.8 mL
2.Nursing math & unit conversions
Answer: t = 1.67 h
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Before midnight
23:35 → 24:00 = 25 min
After midnight
00:00 → 01:15 = 75 min
Total
25 + 75 = 100 min
t = 100/60 = 1.667 ≈ 1.67 h
Answer
t = 1.67 h
3.Dosage calculations
Answer: m = 500 mg
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
5% = 5 g/100 mL = 50 mg/mL
Mass of drug
m = 50·10 = 500 mg
Answer
m = 500 mg
4.Dosage calculations
Answer: V = 0.33 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 = 3300/10000 = 0.33 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.33 mL
5.IV infusion rates
Answer: R = 56 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
3·60 = 180 min
Drip rate
R = 1000·10/180 = 55.56 ≈ 56 gtt/min
Answer
R = 56 gtt/min
At the bedside you round to the nearest whole drop: 56 gtt/min.
6.IV infusion rates
Answer: t = 21.4 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.
Rate in mL/h
42·60/60 = 42 mL/h
Time left
t = 900/42 = 21.43 ≈ 21.4 h
Answer
t = 21.4 h
7.IV fluids & fluid balance
Answer: B = 1100 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: 240 + 100 + 200 = 540 mL
ice chips: 120/2 = 60 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1900 mL
Total output
300 + 225 + 275 = 800 mL
Balance
B = 1900 − 800 = 1100 mL
Answer
B = 1100 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 275 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
13:15 → 14:45 = 1.5 h
Volume infused
150·1.5 = 225 mL
Volume left
V = 500 − 225 = 275 mL
Answer
V = 275 mL
9.Pediatric & critical-care dosing
Answer: V = 1.5 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
80·94 = 7 520 units
Volume
V = 7520/5000 = 1.504 ≈ 1.5 mL
Answer
V = 1.5 mL
10.Pediatric & critical-care dosing
Answer: R = 31.1 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
10·83 = 830 mcg/min
830·60 = 49800 mcg/h
Pump rate
R = 49800/1600 = 31.13 ≈ 31.1 mL/h
Answer
R = 31.1 mL/h
11.Pharmacy calculations
Answer: V = 0.48 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 = 0.48/1 = 0.48 mL
Answer
V = 0.48 mL
12.Pharmacy calculations
Answer: V = 1.1 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.