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 11:50 AM. Which entry is the same time on the 24-hour clock? Click it.
11:50 AM
112:50
210:50
323:50
411:50
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ tbsp of liquid supplement, 2 tsp of cough syrup, 1 cup of tea. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A child weighing 10 kg is prescribed 20 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
10 kg20 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 500 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/500 mL2000 units/h
R = mL/h
5.IV infusion ratesMedium
An infusion is ordered at 90 mL/h, but no pump is available. It runs by gravity through a giving set of 10 gtt/mL. Find the drip rate R in drops per minute.
90 mL/h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 200 mg in 250 mL runs at 30 mL/h. How many micrograms per minute D does the patient receive?
200 mg/250 mL30 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 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 infusion starts at 13:30 at 120 mL/h. After 3 hours the rate is changed to 60 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 · 3 h60 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 250 mL runs at 10 mL/h. How many units per hour D does the patient receive?
100 units/250 mL10 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 71 kg has an order for nitroglycerin at 20 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL20 mcg/min71 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.54 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.54 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 130 mg. Draw up the dose: what volume V do you give?
250 mg4.6 mL + 0.4 mL130 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 11:50
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
11 AM → 11
Answer
11:50
Answer
11:50
2.Nursing math & unit conversions
Answer: V = 257.5 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Each item in mL
½ tbsp = 0.5·15 = 7.5 mL
2 tsp = 2·5 = 10 mL
1 cup = 1·240 = 240 mL
Add
V = 7.5 + 10 + 240 = 257.5 mL
Answer
V = 257.5 mL
3.Dosage calculations
Answer: V = 8 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 = 20·10 = 200 mg
Volume
V = 200/25 = 8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 8 mL
4.Dosage calculations
Answer: R = 50 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
20000/500 = 40 units/mL
Pump rate
R = 2000/40 = 50 mL/h
Answer
R = 50 mL/h
5.IV infusion rates
Answer: R = 15 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.
Millilitres per minute
90/60 = 1.5 mL/min
Drip rate
R = 1.5·10 = 15 gtt/min
Answer
R = 15 gtt/min
6.IV infusion rates
Answer: D = 400 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
200000 mcg/250 mL = 800 mcg/mL
Dose per hour
30·800 = 24000 mcg/h
Dose per minute
D = 24000/60 = 400 mcg/min
Answer
D = 400 mcg/min
7.IV fluids & fluid balance
Answer: B = −295 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 + 150 + 120 = 390 mL
ice chips: 240/2 = 120 mL
IV infusion: 60·12 = 720 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1330 mL
Total output
425 + 475 + 475 + 250 = 1625 mL
Balance
B = 1330 − 1625 = −295 mL
Answer
B = −295 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: t = 5.3 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
120·3 = 360 mL
500 − 360 = 140 mL left
Second part
140/60 = 2.333 h
Total time
t = 3 + 2.333 = 5.333 ≈ 5.3 h
Answer
t = 5.3 h
That is about 5 h 20 min, so the bag runs out at about 18:50.
9.Pediatric & critical-care dosing
Answer: D = 4 units/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
100/250 = 0.4 units/mL
Units per hour
D = 10·0.4 = 4 units/h
Answer
D = 4 units/h
10.Pediatric & critical-care dosing
Answer: R = 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
20·60 = 1200 mcg/h
Pump rate
R = 1200/200 = 6 mL/h
Answer
R = 6 mL/h
11.Pharmacy calculations
Answer: V = 0.54 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 = 0.54/1 = 0.54 mL
Answer
V = 0.54 mL
12.Pharmacy calculations
Answer: V = 2.6 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.