The time required for half of a radioactive substance to decay. After n half-lives, a fraction (1/2)^n remains.

Half-Life & Radioactive Decay Calculator

Remaining quantity, decay constant and a live decay curve.

Initial quantity N₀

Half-life T (any time unit)

Time elapsed t (same unit)

Results

Formulas

N(t) = N₀ · (1/2)^(t/T)
Equivalently: N = N₀ · e^(−λt), λ = ln 2 / T

Physics behind radioactive decay

Radioactive decay is a quintessentially quantum process: each unstable nucleus has a fixed probability per unit time of decaying, independent of its history. Averaged over many nuclei, this produces the familiar exponential law. The half-life is the interval in which half of any remaining sample decays — irrespective of how much is left. Same math applies to drug elimination pharmacokinetics, capacitor discharge and carbon-14 dating.

Worked example

N₀ = 100, T = 10 days, t = 20 days

N = 100 · (1/2)² = 25  (25% remaining)

FAQs

What is half-life?

The time for half of a radioactive sample to decay.

Decay constant?

λ = ln 2 / T.