Half-Life Calculator
Exponential decay by half-life: the amount left after a time, the time to reach an amount, or the half-life from two measurements, plus λ and the mean lifetime.
Remaining and decayed amounts, elapsed half-lives, the decay constant and mean lifetime, and a table of the first ten half-lives — the half-life is yours, no isotope table.
Example: 100 units with a 5,730-year half-life leave 29.8 after 10,000 years (1.75 half-lives; λ = 1.21 × 10⁻⁴ per year). 100 → 12.5 in 30 minutes means a 10-minute half-life.
One law,
three ways round.
The decay law, the three quantities it links, and what the page does not know.
The law
A quantity that loses a fixed fraction per unit time follows N(t) = N₀ (½)^(t/T½): after one half-life half remains, after two a quarter, after ten about a thousandth. The same curve written with the decay constant is N₀e^(−λt), with λ = ln 2 / T½; the mean lifetime of a single nucleus or molecule is τ = 1/λ = T½ / ln 2.
Solving
Given N₀, T½ and t the remaining amount follows directly; given N₀, N and T½ the time is t = T½ · log₂(N₀/N); given N₀, N and t the half-life is T½ = t · ln 2 / ln(N₀/N). Any amount unit works (grams, becquerels, counts) and any time unit, as long as the half-life and the time share it.
Limits
The law describes a large population of independent events — radioactive nuclei, a first-order reaction, a discharging capacitor. It is not a model of a living body or of any process with feedback. No half-life is suggested: the value belongs to your isotope or reaction and comes from a reference, not this page. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- N(t) = N₀ (½)^(t/T½) = N₀ e^(−λt), λ = ln 2 / T½, mean lifetime τ = 1/λ (first-order decay law)
Last reviewed 20 September 2026. How results are checked: How we verify.