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 0.68197 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?
0.68197 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 20:35 and finishes at 06:50 the next morning (24-hour clock). How many minutes t did it run?
20:3506:50
t = min
3.Dosage calculationsMedium
A child weighing 32 kg is prescribed 2.5 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?
32 kg2.5 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
You must prepare 250 mL of a 1% (w/v) solution from a 25% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 25%C₂ = 1%V₂ = 250 mL
W = mL
5.IV infusion ratesMedium
Infuse 1500 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.
1500 mL8 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 28 gtt/min through a set of 20 gtt/mL. There are 900 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
28 gtt/min20 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 total intake I in mL.
water: 120 mLsoup: 200 mLIV infusion: 80 mL/h × 12 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 08:30 at 120 mL/h. After 2 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.
500 mL120 mL/h · 2 h75 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 100 mL. The order is 6 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL6 units/h
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 4 mcg/kg/min for a patient who weighs 104 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL4 mcg/kg/min104 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.34 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.34 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 100 mL of 25% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%25%100 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.68 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
0.68197 → 8
Only the next digit decides
0.68197 → 1
1 is 4 or less, so 8 stays.
The digits after it (97) are ignored: round once, never step by step.
Round
x = 0.68 mL
Answer
x = 0.68 mL
2.Nursing math & unit conversions
Answer: t = 615 min
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
20:35 → 24:00 = 205 min
After midnight
00:00 → 06:50 = 410 min
Total
t = 205 + 410 = 615 min
Answer
t = 615 min
3.Dosage calculations
Answer: V = 2 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 = 2.5·32 = 80 mg
Volume
V = 80/40 = 2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 2 mL
4.Dosage calculations
Answer: W = 240 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.
Volume of stock
V₁ = 1·250/25 = 10 mL
Water to add
W = 250 − 10 = 240 mL
Answer
W = 240 mL
5.IV infusion rates
Answer: R = 31 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 = 1500·10/480 = 31.25 ≈ 31 gtt/min
Answer
R = 31 gtt/min
At the bedside you round to the nearest whole drop: 31 gtt/min.
6.IV infusion rates
Answer: t = 10.7 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
28·60/20 = 84 mL/h
Time left
t = 900/84 = 10.71 ≈ 10.7 h
Answer
t = 10.7 h
7.IV fluids & fluid balance
Answer: I = 1330 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: 120 + 200 = 320 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 1·50 = 50 mL
I = 1330 mL
Answer
I = 1330 mL
8.IV fluids & fluid balance
Answer: t = 5.5 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
120·2 = 240 mL
500 − 240 = 260 mL left
Second part
260/75 = 3.467 h
Total time
t = 2 + 3.467 = 5.467 ≈ 5.5 h
Answer
t = 5.5 h
That is about 5 h 28 min, so the bag runs out at about 13:58.
9.Pediatric & critical-care dosing
Answer: R = 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.
Concentration
100/100 = 1 units/mL
Pump rate
R = 6/1 = 6 mL/h
Answer
R = 6 mL/h
10.Pediatric & critical-care dosing
Answer: R = 15.6 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
4·104 = 416 mcg/min
416·60 = 24960 mcg/h
Pump rate
R = 24960/1600 = 15.6 mL/h
Answer
R = 15.6 mL/h
11.Pharmacy calculations
Answer: V = 3.4 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 = 0.34/0.1 = 3.4 mL
Answer
V = 3.4 mL
12.Pharmacy calculations
Answer: V = 25 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.