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 13:05 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
13:05
11:05 PM
21:05 AM
33:05 PM
412:05 PM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A maintenance infusion runs at 60 mL/h without a break. How many litres V does it deliver in 24 hours?
60 mL/h24 h
V = L
3.Dosage calculationsMedium
A patient weighs 12 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.
12 kg10 mg/kg
D = mg
4.Dosage calculationsHard
A patient is 138 cm tall and weighs 36 kg. The prescription is 135 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
138 cm36 kg135 mg/m²
D = mg
5.IV infusion ratesMedium
An infusion is ordered at 200 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.
200 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 40 gtt/min through a set of 60 gtt/mL. There are 450 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
40 gtt/min60 gtt/mL450 mL
t = 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 19:30 at 100 mL/h. After 4 hours the rate is changed to 75 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 mL100 mL/h · 4 h75 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 50 units of regular insulin in 50 mL runs at 12 mL/h. How many units per hour D does the patient receive?
50 units/50 mL12 mL/h
D = units/h
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 12 mcg/kg/min for a patient who weighs 108 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL12 mcg/kg/min108 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg11.5 mL+1 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 700 mg. Draw up the dose: what volume V do you give?
2000 mg9.2 mL + 0.8 mL700 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 1:05 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
13 − 12 = 1 → PM
Answer
1:05 PM
Answer
1:05 PM
2.Nursing math & unit conversions
Answer: V = 1.44 L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Volume in a day
60 mL/h × 24 h = 1440 mL
In litres
V = 1440/1000 = 1.44 L
Answer
V = 1.44 L
3.Dosage calculations
Answer: D = 120 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.
Dose
10·12 = 120 mg
Answer
D = 120 mg
4.Dosage calculations
Answer: D = 158.6 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Body surface area
BSA = √(138·36/3600) = √1.38 = 1.175 m²
Dose
D = 135·1.175 = 158.6 mg
Answer
D = 158.6 mg
5.IV infusion rates
Answer: R = 200 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
200/60 = 3.333 mL/min
Drip rate
R = 3.333·60 = 200 gtt/min
Answer
R = 200 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
6.IV infusion rates
Answer: t = 11.3 h
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
40·60/60 = 40 mL/h
Time left
t = 450/40 = 11.25 ≈ 11.3 h
Answer
t = 11.3 h
7.IV fluids & fluid balance
Answer: B = −210 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: 250 + 120 + 120 = 490 mL
ice chips: 200/2 = 100 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1590 mL
Total output
425 + 500 + 400 + 375 + 100 = 1800 mL
Balance
B = 1590 − 1800 = −210 mL
Answer
B = −210 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
100·4 = 400 mL
500 − 400 = 100 mL left
Second part
100/75 = 1.333 h
Total time
t = 4 + 1.333 = 5.333 ≈ 5.3 h
Answer
t = 5.3 h
That is about 5 h 20 min, so the bag runs out at about 00:50.
9.Pediatric & critical-care dosing
Answer: D = 12 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
50/50 = 1 units/mL
Units per hour
D = 12·1 = 12 units/h
Answer
D = 12 units/h
10.Pediatric & critical-care dosing
Answer: R = 48.6 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
12·108 = 1296 mcg/min
1296·60 = 77760 mcg/h
Pump rate
R = 77760/1600 = 48.6 mL/h
Answer
R = 48.6 mL/h
11.Pharmacy calculations
Answer: C = 160 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
11.5 + 1 = 12.5 mL
Concentration
C = 2000/12.5 = 160 mg/mL
Answer
C = 160 mg/mL
12.Pharmacy calculations
Answer: V = 3.5 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.