Radioactive Decay Calculator

Real isotopes rarely decay directly to something stable — U-238 passes through about 14 sequential decays (through thorium, radium, radon, polonium and more) before finally reaching stable Pb-206, with half-lives ranging from billions of years down to microseconds. When an intermediate step is much shorter-lived than its parent, the chain reaches secular equilibrium: every daughter's activity locks onto the parent's decay rate, which is why a single exponential like the one graphed here still accurately describes the parent's decline even though the full chain has over a dozen steps.

Each unstable nucleus decays at a moment no one can predict — there is no countdown ticking inside it, only a fixed probability per second. Yet with trillions of atoms, that randomness averages into the smooth curve you see here. The half-life is simply the time for a sample to lose half its atoms, so after 3 half-lives only (1/2)³ = 1/8 remains, no matter how much you started with.

Textbooks say decay rates ignore temperature, pressure and chemistry — and for alpha and beta decay that's almost perfectly true. But isotopes that decay by electron capture, like beryllium-7, borrow an electron from their own atom, so their rate depends on the electron density at the nucleus. Chemists have shifted Be-7's half-life (~53 days) by around 1% just by changing its chemical compound or squeezing it under pressure.