Half-Life Decay
Fraction remaining after any elapsed time, from the half-life.
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The engineering
Pure exponential decay: use any time unit you like, as long as both fields share it. Activity (counts per second) falls by exactly the same factor as the atom count, so the remaining-% row reads directly as remaining activity. Rules of thumb the card makes precise: 10 half-lives leaves about 0.1% — the common 'effectively gone' threshold in radiation safety — and 7 leaves under 1%.
The model assumes a single decaying species with nothing feeding it; decay *chains* (radon from radium, daughters in-growing) need the Bateman equations instead. The same math prices drug elimination in pharmacokinetics and charge on a leaky capacitor — anything whose loss rate is proportional to what remains.
Where this math comes from
Henri Becquerel found uranium fogging photographic plates in 1896; the shape of the fading came from Ernest Rutherford and Frederick Soddy, who in 1902 showed thorium emanation losing activity geometrically — half gone in a fixed interval, whatever the starting amount — and drew the revolutionary conclusion that atoms were transmuting on a statistical schedule.
The 'half-life' framing proved to be the most practical description of the law, and Willard Libby closed the loop in 1949 by running it backwards: carbon-14's 5,730-year half-life as a clock for archaeology, a technique that won the 1960 Nobel Prize and re-dated human history.
- 1896Henri BecquerelRadioactivity discovered in uranium salts.
- 1902Rutherford & SoddyExponential decay law and transmutation theory — the half-life.
- 1949Willard LibbyRadiocarbon dating — the half-life as a clock.
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