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 is charted at 10:50 AM. Which entry is the same time on the 24-hour clock? Click it.
10:50 AM
110:50
222:50
309:50
411:50
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 10 mcg/min. Express this dose rate D in mg/h.
10 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.5 mg IM for anaphylaxis. What volume V do you draw up?
1:10000.5 mg
V = mL
4.Dosage calculationsHard
An infusion contains 50000 units of a drug in 1000 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
50000 units/1000 mL1000 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 500 mL over 12 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL12 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 250 mL and runs at 25 mL/h. How many milligrams per hour D does the patient receive?
200 mg/250 mL25 mL/h
D = mg/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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 125 mL/h. At 21:30, 200 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL200 mL infused125 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 70 units/kg for a patient who weighs 51 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
70 units/kg51 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 55 kg has an order for norepinephrine at 4 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL4 mcg/min55 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 400 mg. Draw up the dose: what volume V do you give?
2000 mg4.6 mL + 0.4 mL400 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 10:50
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.
Convert the hour
10 AM → 10
Answer
10:50
Answer
10:50
2.Nursing math & unit conversions
Answer: D = 0.6 mg/h
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Set up the chain
D = 10 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 10·60/1000 = 0.6 mg/h
Answer
D = 0.6 mg/h
3.Dosage calculations
Answer: V = 0.5 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.
Concentration
1:1000 = 1 g/1000 mL = 1 mg/mL
Volume
V = 0.5/1 = 0.5 mL
Answer
V = 0.5 mL
US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.
4.Dosage calculations
Answer: R = 20 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
50000/1000 = 50 units/mL
Pump rate
R = 1000/50 = 20 mL/h
Answer
R = 20 mL/h
5.IV infusion rates
Answer: R = 42 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
12·60 = 720 min
Drip rate
R = 500·60/720 = 41.67 ≈ 42 gtt/min
Answer
R = 42 gtt/min
At the bedside you round to the nearest whole drop: 42 gtt/min.
6.IV infusion rates
Answer: D = 20 mg/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.
Concentration
200/250 = 0.8 mg/mL
Dose rate
D = 0.8·25 = 20 mg/h
Answer
D = 20 mg/h
7.IV fluids & fluid balance
Answer: B = 510 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: 120 + 120 + 200 = 440 mL
IV infusion: 75·8 = 600 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1090 mL
Total output
250 + 250 + 80 = 580 mL
Balance
B = 1090 − 580 = 510 mL
Answer
B = 510 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 2.4 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.
Volume left
500 − 200 = 300 mL
Time
t = 300/125 = 2.4 h
Answer
t = 2.4 h
That is about 2 h 24 min, so the bag runs out at about 23:54.
9.Pediatric & critical-care dosing
Answer: V = 0.71 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
70·51 = 3 570 units
Volume
V = 3570/5000 = 0.714 ≈ 0.71 mL
Answer
V = 0.71 mL
10.Pediatric & critical-care dosing
Answer: R = 7.5 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
4·60 = 240 mcg/h
Pump rate
R = 240/32 = 7.5 mL/h
Answer
R = 7.5 mL/h
11.Pharmacy calculations
Answer: V = 9.6 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.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 2 400 000/250 000 = 9.6 mL
Answer
V = 9.6 mL
12.Pharmacy calculations
Answer: V = 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.