Science & engineering
Half-life and decay calculator
Solve for remaining amount, elapsed time or half-life in exponential decay.
A clear answer. Here’s how.
For exponential decay N = N₀ × (½)^(t ÷ T½). Remaining amount uses that directly; elapsed time is T½ × log₂(N₀ ÷ N); half-life is t × ln 2 ÷ ln(N₀ ÷ N). The decay constant is λ = ln 2 ÷ T½ and mean lifetime τ = 1 ÷ λ. Use one time unit for the half-life and elapsed time. The model has a single decay path and no ingrowth from a parent nuclide.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Solve for
- Amount remaining (needs initial, half-life, elapsed)
- Initial amount
- 100
- Remaining amount
- 25
- Half-life
- 5730
- Elapsed time
- 11460
Example result
- Initial amount
- 100
- Remaining amount
- 25
- Fraction remaining
- 0.25
- Percent decayed
- 75
- Half-lives elapsed
- 2
- Half-life
- 5,730
- Elapsed time
- 11,460
- Decay constant λ (per time unit)
- 0.000120968094339
- Mean lifetime τ
- 8,266.64258429
Exponential decay: N = N₀ × (½)^(t ÷ T½), so λ = ln 2 ÷ T½ and τ = 1 ÷ λ. Use one time unit throughout. It assumes a single decay path and no ingrowth from a parent, and individual decays are random, so small samples scatter around the average.