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 0.98977 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?
0.98977 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 22:10 and finishes at 00:55 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.
22:1000:55
t = h
3.Dosage calculationsMedium
A vial contains 1 g of powder. The label says: add 3.4 mL of water for injection to give a total volume of 4 mL. The prescription is 300 mg. What volume V of the reconstituted solution do you give?
1 g+ 3.4 mL → 4 mL300 mg
V = mL
4.Dosage calculationsHard
An infusion contains 25000 units of a drug in 1000 mL. The prescription is 1500 units per hour. At what rate R do you set the pump, in mL/h?
25000 units/1000 mL1500 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 1500 mL over 5 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute.
1500 mL5 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 50 mg in 250 mL runs at 9 mL/h. How many micrograms per minute D does the patient receive?
50 mg/250 mL9 mL/h
D = mcg/min
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.
milk: 100 mLsoup: 180 mLice chips: 240 mLIV infusion: 60 mL/h × 12 hIV antibiotic: 1 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 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 12:30?
1000 mL50 mL/h11:30 → 12:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 83 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL0.1 units/kg/h83 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 5 mcg/kg/min for a patient who weighs 105 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min105 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 2000 mg as a powder. The practice label says to add 19.2 mL of sterile water; the powder adds 0.8 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg19.2 mL+0.8 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 390 mg. Draw up the dose: what volume V do you give?
1000 mg9.2 mL + 0.8 mL390 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.99 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
0.98977 → 8
Only the next digit decides
0.98977 → 9
9 is 5 or more, so round 8 up.
The digits after it (77) are ignored: round once, never step by step.
Round
x = 0.99 mL
Answer
x = 0.99 mL
2.Nursing math & unit conversions
Answer: t = 2.75 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
22:10 → 24:00 = 110 min
After midnight
00:00 → 00:55 = 55 min
Total
110 + 55 = 165 min
t = 165/60 = 2.75 h
Answer
t = 2.75 h
3.Dosage calculations
Answer: V = 1.2 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.
Concentration after mixing
1000 mg/4 mL = 250 mg/mL
Volume
V = 300/250 = 1.2 mL
Answer
V = 1.2 mL
4.Dosage calculations
Answer: R = 60 mL/h
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.
Concentration
25000/1000 = 25 units/mL
Pump rate
R = 1500/25 = 60 mL/h
Answer
R = 60 mL/h
5.IV infusion rates
Answer: R = 100 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
5·60 = 300 min
Drip rate
R = 1500·20/300 = 100 gtt/min
Answer
R = 100 gtt/min
6.IV infusion rates
Answer: D = 30 mcg/min
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
50000 mcg/250 mL = 200 mcg/mL
Dose per hour
9·200 = 1800 mcg/h
Dose per minute
D = 1800/60 = 30 mcg/min
Answer
D = 30 mcg/min
7.IV fluids & fluid balance
Answer: I = 1220 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: 100 + 180 = 280 mL
ice chips: 240/2 = 120 mL
IV infusion: 60·12 = 720 mL
IV antibiotic: 1·100 = 100 mL
I = 1220 mL
Answer
I = 1220 mL
8.IV fluids & fluid balance
Answer: V = 950 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 → 12:30 = 1 h
Volume infused
50·1 = 50 mL
Volume left
V = 1000 − 50 = 950 mL
Answer
V = 950 mL
9.Pediatric & critical-care dosing
Answer: R = 20.8 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
0.1·83 = 8.3 units/h
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 8.3/0.4 = 20.75 ≈ 20.8 mL/h
Answer
R = 20.8 mL/h
10.Pediatric & critical-care dosing
Answer: R = 31.5 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
5·105 = 525 mcg/min
525·60 = 31500 mcg/h
Pump rate
R = 31500/1000 = 31.5 mL/h
Answer
R = 31.5 mL/h
11.Pharmacy calculations
Answer: C = 100 mg/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.
Final volume
19.2 + 0.8 = 20 mL
Concentration
C = 2000/20 = 100 mg/mL
Answer
C = 100 mg/mL
12.Pharmacy calculations
Answer: V = 3.9 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.