Exponential decay
The half-life of a substance is the time it takes for half of it to decay or disappear. It applies to radioactive elements, medicines leaving the body, and any quantity that shrinks by the same fraction in equal time steps.
This calculator solves for any one of the four quantities in the decay formula: the amount remaining, the time elapsed, the half-life or the starting amount. It also gives the decay constant and the mean lifetime.
How it is calculated
N(t) = N₀ × (1/2)^(t ÷ T½)
Decay constant λ = ln 2 ÷ T½
Mean lifetime τ = 1 ÷ λ
Worked example
100 g of a substance with a half-life of 10 years, after 25 years
- Half-lives elapsed
- 2.5
- Amount remaining
- 17.68 g
- Fraction left
- 17.68%
What you can read from the numbers
| Half-lives passed | Fraction remaining |
|---|---|
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 5 | 3.1% |
| 10 | 0.1% |