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 2:15 PM. Which entry is the same time on the 24-hour clock? Click it.
2:15 PM
113:15
215:15
314:15
402:15
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ cups of tea, 1 tsp of cough syrup, 6 fl oz of juice, 3 tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 tsp = 5 mL1 fl oz = 30 mL1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A prefilled syringe of epinephrine (adrenaline) is labelled 1:10 000 (0.1 mg/mL). The prescription is 1 mg IV in cardiac arrest. What volume V do you give?
1:10 0001 mg
V = mL
4.Dosage calculationsHard
You must prepare 1000 mL of a 5% (w/v) solution from a 50% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 50%C₂ = 5%V₂ = 1000 mL
W = mL
5.IV infusion ratesMedium
Infuse 1500 mL over 4 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1500 mL4 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 2 g of a drug in 250 mL. The order is 3 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/250 mL3 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 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 1000 mL bag runs by pump at 150 mL/h. At 14:30, 800 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL800 mL infused150 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 16 units/kg/h for a patient who weighs 98 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL16 units/kg/h98 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 10 mL/h. The patient weighs 86 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL10 mL/h86 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.66 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.66 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 135 mg. Draw up the dose: what volume V do you give?
500 mg9.4 mL + 0.6 mL135 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 14:15
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
2 PM → 2 + 12 = 14
Answer
14:15
Answer
14:15
2.Nursing math & unit conversions
Answer: V = 590 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
1½ cups = 1.5·240 = 360 mL
1 tsp = 1·5 = 5 mL
6 fl oz = 6·30 = 180 mL
3 tbsp = 3·15 = 45 mL
Add
V = 360 + 5 + 180 + 45 = 590 mL
Answer
V = 590 mL
3.Dosage calculations
Answer: V = 10 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
1:10 000 = 1 g/10000 mL = 0.1 mg/mL
Volume
V = 1/0.1 = 10 mL
Answer
V = 10 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: W = 900 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.
Volume of stock
V₁ = 5·1000/50 = 100 mL
Water to add
W = 1000 − 100 = 900 mL
Answer
W = 900 mL
5.IV infusion rates
Answer: R = 94 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
4·60 = 240 min
Drip rate
R = 1500·15/240 = 93.75 ≈ 94 gtt/min
Answer
R = 94 gtt/min
At the bedside you round to the nearest whole drop: 94 gtt/min.
6.IV infusion rates
Answer: R = 22.5 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
3·60 = 180 mg/h
Pump rate
R = 180/8 = 22.5 mL/h
Answer
R = 22.5 mL/h
7.IV fluids & fluid balance
Answer: B = −80 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: 180 + 120 + 200 = 500 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 1·50 = 50 mL
total intake = 950 mL
Total output
275 + 425 + 80 + 250 = 1030 mL
Balance
B = 950 − 1030 = −80 mL
Answer
B = −80 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: t = 1.3 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.
Volume left
1000 − 800 = 200 mL
Time
t = 200/150 = 1.333 ≈ 1.3 h
Answer
t = 1.3 h
That is about 1 h 20 min, so the bag runs out at about 15:50.
9.Pediatric & critical-care dosing
Answer: R = 15.7 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
16·98 = 1 568 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1568/100 = 15.68 ≈ 15.7 mL/h
Answer
R = 15.7 mL/h
10.Pediatric & critical-care dosing
Answer: D = 3.1 mcg/kg/min
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
400 000/250 = 1600 mcg/mL
Micrograms per minute
10·1600 = 16000 mcg/h
16000/60 = 266.7 mcg/min
Per kilogram
D = 266.7/86 = 3.101 ≈ 3.1 mcg/kg/min
Answer
D = 3.1 mcg/kg/min
11.Pharmacy calculations
Answer: V = 6.6 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.66/0.1 = 6.6 mL
Answer
V = 6.6 mL
12.Pharmacy calculations
Answer: V = 2.7 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.