Half-Life Calculator
Calculate radioactive decay or any process with a half-life.
Tip: After each half-life, half the quantity remains — after 10 half-lives, ~0.1% remains.
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About this digital tool
The half-life calculator shows how much of a quantity remains after a given time, when it decreases exponentially, as in radioactive decay. Enter the initial quantity, the half-life, the elapsed time and the unit (seconds, minutes, hours, days or years).
The formula is N = N₀ × (1/2)^(t ÷ T), where T is the half-life. For 100 g with a half-life of 5 years, after 10 years 2 half-lives have passed and 100 × 0.25 = 25 g remain. The calculator also gives the percentage remaining, the quantity decayed, the number of half-lives and the decay constant λ = ln 2 ÷ T. It is used in nuclear physics, in medicine, in archaeology (carbon dating) and in pharmacology.
How to use
- Enter the initial quantity N₀.
- Enter the substance's half-life and the elapsed time in the same unit.
- Choose the time unit: seconds, minutes, hours, days or years.
- Read the remaining quantity, the percentage, the decayed quantity and λ.
Frequently asked questions
What is a half-life?
The time it takes for half the quantity to decay or decrease. E.g. if the half-life = 5 years, after 5 years 50% remains, after 10 years 25%.
How do I calculate the quantity remaining after several half-lives?
Each half-life halves the quantity. E.g. 80 g with T = 3 years after 9 years: 3 half-lives, so 80 × (1/2)³ = 10 g.
What percentage remains after 3 half-lives?
12.5%, because (1/2)³ = 1/8. After 1 half-life 50% remains, after 2 it is 25%.
How is the decay constant λ calculated?
λ = ln 2 ÷ T ≈ 0.693 ÷ T. E.g. for T = 5 years, λ ≈ 0.1386 per year.