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 142.855 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
142.855 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:35 and finishes at 06:05 the next morning (24-hour clock). How many minutes t did it run?
23:3506:05
t = min
3.Dosage calculationsMedium
A patient weighs 45 kg and is prescribed 5 mg/kg as a single dose. Find the dose D in mg.
45 kg5 mg/kg
D = mg
4.Dosage calculationsHard
A child weighing 16 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give?
16 kg12.5 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
A drip runs at 40 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 8 hours?
40 gtt/min15 gtt/mL8 h
V = mL
6.IV infusion ratesHard
A drip runs at 50 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?
50 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 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
juice: 150 mLmilk: 200 mLIV infusion: 50 mL/h × 8 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 10:00 and runs by pump at 50 mL/h. How many mL V are left in the bag at 16:00?
500 mL50 mL/h10:00 → 16:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 103 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg103 kg5 000 units/mL
V = mL
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 103 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min103 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. The prescribed dose is 250 mg. What volume V do you draw up? Round to one decimal place.
1000 mg9.6 mL+0.4 mL250 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 250 mg. Draw up the dose: what volume V do you give?
1000 mg1.4 mL + 0.6 mL250 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 143 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
142.855 → 2
Only the next digit decides
142.855 → 8
8 is 5 or more, so round 2 up.
The digits after it (55) are ignored: round once, never step by step.
Round
x = 143 gtt/min
Answer
x = 143 gtt/min
2.Nursing math & unit conversions
Answer: t = 390 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
23:35 → 24:00 = 25 min
After midnight
00:00 → 06:05 = 365 min
Total
t = 25 + 365 = 390 min
Answer
t = 390 min
3.Dosage calculations
Answer: D = 225 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.
Dose
5·45 = 225 mg
Answer
D = 225 mg
4.Dosage calculations
Answer: V = 5 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.
Dose from weight
12.5·16 = 200 mg
Volume
V = (200/40)·1 = 5 mL
Answer
V = 5 mL
5.IV infusion rates
Answer: V = 1280 mL
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
40·60/15 = 160 mL/h
Volume
V = 160·8 = 1280 mL
Answer
V = 1280 mL
6.IV infusion rates
Answer: t = 18 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
50·60/60 = 50 mL/h
Time left
t = 900/50 = 18 h
Answer
t = 18 h
7.IV fluids & fluid balance
Answer: I = 950 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: 150 + 200 = 350 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 2·100 = 200 mL
I = 950 mL
Answer
I = 950 mL
8.IV fluids & fluid balance
Answer: V = 200 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
10:00 → 16:00 = 6 h
Volume infused
50·6 = 300 mL
Volume left
V = 500 − 300 = 200 mL
Answer
V = 200 mL
9.Pediatric & critical-care dosing
Answer: V = 1.2 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
60·103 = 6 180 units
Volume
V = 6180/5000 = 1.236 ≈ 1.2 mL
Answer
V = 1.2 mL
10.Pediatric & critical-care dosing
Answer: R = 30.9 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
5·103 = 515 mcg/min
515·60 = 30900 mcg/h
Pump rate
R = 30900/1000 = 30.9 mL/h
Answer
R = 30.9 mL/h
11.Pharmacy calculations
Answer: V = 2.5 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
9.6 + 0.4 = 10 mL
Concentration
1000/10 = 100 mg/mL
Volume to give
V = 250/100 = 2.5 mL
Answer
V = 2.5 mL
12.Pharmacy calculations
Answer: V = 0.5 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.