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 12:30 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
12:30
112:30 AM
212:30 PM
311:30 PM
42:30 PM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 8 fl oz of juice, 3 tbsp of liquid supplement, 3 cups of tea. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tbsp = 15 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A child weighing 40 kg is prescribed 3 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
40 kg3 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 195 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
195 mcg0.5 mg/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 30 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.
30 mL/h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 2 g of a drug in 250 mL. The order is 0.5 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/250 mL0.5 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 patient weighs 98 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
98 kg8 hurine: 425 mLurine: 175 mLwound drain: 30 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 50 mL/h. At 20:00, 200 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL200 mL infused50 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 80 units/kg for a patient who weighs 67 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg67 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 15 mcg/kg/min for a patient who weighs 57 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL15 mcg/kg/min57 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.69 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.69 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 60 mg. Draw up the dose: what volume V do you give?
250 mg4.4 mL + 0.6 mL60 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 12:30 PM
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
12 → 12 PM
Answer
12:30 PM
Answer
12:30 PM
2.Nursing math & unit conversions
Answer: V = 1005 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
8 fl oz = 8·30 = 240 mL
3 tbsp = 3·15 = 45 mL
3 cups = 3·240 = 720 mL
Add
V = 240 + 45 + 720 = 1005 mL
Answer
V = 1005 mL
3.Dosage calculations
Answer: V = 6 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 = 3·40 = 120 mg
Volume
V = 120/20 = 6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 6 mL
4.Dosage calculations
Answer: V = 0.39 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.
Same units
0.5 mg/mL = 500 mcg/mL
Volume
V = 195/500 = 0.39 mL
Answer
V = 0.39 mL
5.IV infusion rates
Answer: R = 5 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
30/60 = 0.5 mL/min
Drip rate
R = 0.5·10 = 5 gtt/min
Answer
R = 5 gtt/min
6.IV infusion rates
Answer: R = 3.75 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
0.5·60 = 30 mg/h
Pump rate
R = 30/8 = 3.75 mL/h
Answer
R = 3.75 mL/h
7.IV fluids & fluid balance
Answer: U = 0.77 mL/kg/h
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 urine
425 + 175 = 600 mL
Per kilogram per hour
U = 600/(98·8) = 0.7653 ≈ 0.77 mL/kg/h
Answer
U = 0.77 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 16 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 − 200 = 800 mL
Time
t = 800/50 = 16 h
Answer
t = 16 h
That is about 16 h 00 min, so the bag runs out at about 12:00.
9.Pediatric & critical-care dosing
Answer: V = 1.1 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
80·67 = 5 360 units
Volume
V = 5360/5000 = 1.072 ≈ 1.1 mL
Answer
V = 1.1 mL
10.Pediatric & critical-care dosing
Answer: R = 32.1 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
15·57 = 855 mcg/min
855·60 = 51300 mcg/h
Pump rate
R = 51300/1600 = 32.06 ≈ 32.1 mL/h
Answer
R = 32.1 mL/h
11.Pharmacy calculations
Answer: V = 0.69 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 = 0.69/1 = 0.69 mL
Answer
V = 0.69 mL
12.Pharmacy calculations
Answer: V = 1.2 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.