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 2:35 AM. Which entry is the same time on the 24-hour clock? Click it.
2:35 AM
114:35
201:35
302:35
403:35
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ tsp of cough syrup, 1½ tbsp of liquid supplement, ½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 tbsp = 15 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A child weighing 18 kg is prescribed 10 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
18 kg10 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 1.9 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1.9 mg2000 mcg/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 40 mL/h, but no pump is available. It runs by gravity through a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
40 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 4 g of a drug in 500 mL. The order is 3 mg per minute. At what rate R do you set the pump, in mL/h?
4 g/500 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 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).
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 15:30 at 150 mL/h. After 4 hours the rate is changed to 50 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 mL150 mL/h · 4 h50 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 10 000 units of heparin in 250 mL. The order is 12 units/kg/h for a patient who weighs 107 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
10 000 units/250 mL12 units/kg/h107 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 21 mL/h. The patient weighs 56 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL21 mL/h56 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.36 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.36 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 4% chlorhexidine from a 20% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
20%0%4%600 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 02:35
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 AM → 02
Answer
02:35
Answer
02:35
2.Nursing math & unit conversions
Answer: V = 40 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 tsp = 0.5·5 = 2.5 mL
1½ tbsp = 1.5·15 = 22.5 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 2.5 + 22.5 + 15 = 40 mL
Answer
V = 40 mL
3.Dosage calculations
Answer: V = 7.2 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 = 10·18 = 180 mg
Volume
V = 180/25 = 7.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.2 mL
4.Dosage calculations
Answer: V = 0.95 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
1.9 mg = 1900 mcg
Volume
V = 1900/2000 = 0.95 mL
Answer
V = 0.95 mL
5.IV infusion rates
Answer: R = 40 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
40/60 = 0.6667 mL/min
Drip rate
R = 0.6667·60 = 40 gtt/min
Answer
R = 40 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
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
4000 mg/500 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 = 75 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: 350 + 100 + 200 = 650 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1600 mL
Total output
475 + 325 + 500 + 225 = 1525 mL
Balance
B = 1600 − 1525 = 75 mL
Answer
B = 75 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 12 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
150·4 = 600 mL
1000 − 600 = 400 mL left
Second part
400/50 = 8 h
Total time
t = 4 + 8 = 12 h
Answer
t = 12 h
That is about 12 h 00 min, so the bag runs out at about 03:30.
9.Pediatric & critical-care dosing
Answer: R = 32.1 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
12·107 = 1 284 units/h
Concentration
10 000/250 = 40 units/mL
Pump rate
R = 1284/40 = 32.1 mL/h
Answer
R = 32.1 mL/h
10.Pediatric & critical-care dosing
Answer: D = 6.3 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
21·1000 = 21000 mcg/h
21000/60 = 350 mcg/min
Per kilogram
D = 350/56 = 6.25 ≈ 6.3 mcg/kg/min
Answer
D = 6.3 mcg/kg/min
11.Pharmacy calculations
Answer: V = 3.6 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 = 0.36/0.1 = 3.6 mL
Answer
V = 3.6 mL
12.Pharmacy calculations
Answer: V = 480 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Alligation parts
20%: 4 − 0 = 4 parts
0%: 20 − 4 = 16 parts
total: 20 parts
Water
V = 600·16/20 = 480 mL
Answer
V = 480 mL
Check: 120 mL of 20% contains 24 g of drug, which is 4% of 600 mL.