Half-Life Calculator

Model exponential decay — the amount of a substance that remains after a given time when it decays at a fixed half-life. The same law governs radioactive isotopes (carbon-14 dating, uranium-238), drug metabolism (caffeine's ~5.7-hour half-life), and many first-order processes. Compute the amount remaining N(t) = N₀·2^−t∕t½, the decay constant λ = ln 2 ∕ t½, the mean lifetime τ = t½ ∕ ln 2, the time to reach any target fraction, and plot the decay curve. Presets for common isotopes and caffeine are built in. Everything runs locally in your browser.

Initial amount N₀

Half-life t½

Elapsed time t

Decay

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Time to reach a target

Target fraction remaining

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Decay curve (amount over time)

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Exponential decay. A substance with half-life t½ leaves a fraction 2^−t∕t½ after time t, so N(t) = N₀·2^−t∕t½ = N₀·e^−λt where the decay constant λ = ln 2 ∕ t½. After each half-life exactly half remains: one half-life → 50%, two → 25%, three → 12.5%. The mean lifetime τ = 1∕λ = t½ ∕ ln 2 ≈ 1.443·t½ is the average time a single particle survives (and the time at which N has fallen to 1∕e ≈ 36.8%). To invert — find how long to reach a fraction f — use t = t½·log₂(1∕f). Carbon-14's half-life of 5730 years is the basis of radiocarbon dating; uranium-238's 4.468 billion years dates rocks; caffeine's 5.7 hours tells you how long until half the dose is out of your bloodstream. Pairs with the Exponential Distribution tool. Everything runs locally — nothing leaves your browser.