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
211:50
309:50
422:50
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ¼ cup of tea, 4 fl oz of juice, 3 tbsp of liquid supplement, 1½ tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 fl oz = 30 mL1 tbsp = 15 mL1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 12 kg. The prescribed dose is 2 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?
12 kg2 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
An infusion contains 50000 units of a drug in 500 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
50000 units/500 mL1000 units/h
R = mL/h
5.IV infusion ratesMedium
A drip runs at 30 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 8 hours?
30 gtt/min15 gtt/mL8 h
V = mL
6.IV infusion ratesHard
A bag contains 2 g of a drug in 250 mL. The order is 1 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/250 mL1 mg/min
R = mL/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: 150 mLjuice: 150 mLIV infusion: 60 mL/h × 12 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 14:00 at 120 mL/h. After 3 hours the rate is changed to 125 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL120 mL/h · 3 h125 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 60 units/kg for a patient who weighs 85 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg85 kg5 000 units/mL
V = mL
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 6 mcg/kg/min for a patient who weighs 92 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL6 mcg/kg/min92 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg4.5 mL+0.5 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 550 mg. Draw up the dose: what volume V do you give?
2000 mg3.4 mL + 0.6 mL550 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: V = 232.5 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
¼ cup = 0.25·240 = 60 mL
4 fl oz = 4·30 = 120 mL
3 tbsp = 3·15 = 45 mL
1½ tsp = 1.5·5 = 7.5 mL
Add
V = 60 + 120 + 45 + 7.5 = 232.5 mL
Answer
V = 232.5 mL
3.Dosage calculations
Answer: D = 6 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.
Total per day
2·12 = 24 mg
Per dose
D = 24/4 = 6 mg
Answer
D = 6 mg
4.Dosage calculations
Answer: R = 10 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
50000/500 = 100 units/mL
Pump rate
R = 1000/100 = 10 mL/h
Answer
R = 10 mL/h
5.IV infusion rates
Answer: V = 960 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
30·60/15 = 120 mL/h
Volume
V = 120·8 = 960 mL
Answer
V = 960 mL
6.IV infusion rates
Answer: R = 7.5 mL/h
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
2000 mg/250 mL = 8 mg/mL
Dose per hour
1·60 = 60 mg/h
Pump rate
R = 60/8 = 7.5 mL/h
Answer
R = 7.5 mL/h
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: 150 + 150 = 300 mL
IV infusion: 60·12 = 720 mL
IV antibiotic: 2·100 = 200 mL
I = 1220 mL
Answer
I = 1220 mL
8.IV fluids & fluid balance
Answer: t = 8.1 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
1000 − 360 = 640 mL left
Second part
640/125 = 5.12 h
Total time
t = 3 + 5.12 = 8.12 ≈ 8.1 h
Answer
t = 8.1 h
That is about 8 h 07 min, so the bag runs out at about 22:07.
9.Pediatric & critical-care dosing
Answer: V = 1 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
60·85 = 5 100 units
Volume
V = 5100/5000 = 1.02 ≈ 1 mL
Answer
V = 1 mL
10.Pediatric & critical-care dosing
Answer: R = 20.7 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
6·92 = 552 mcg/min
552·60 = 33120 mcg/h
Pump rate
R = 33120/1600 = 20.7 mL/h
Answer
R = 20.7 mL/h
11.Pharmacy calculations
Answer: C = 200 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
4.5 + 0.5 = 5 mL
Concentration
C = 1000/5 = 200 mg/mL
Answer
C = 200 mg/mL
12.Pharmacy calculations
Answer: V = 1.1 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.