Decay is random for one atom, predictable for billions
You can't predict when any single radioactive atom will decay — it's genuinely random, with no warning and no cause. But take a large enough sample, billions of atoms, and the group behaves with total predictability. That predictability is captured in one number per isotope: its half-life, the time it takes for exactly half of a sample to decay.
After one half-life, half the original amount remains. After two, a quarter. After three, an eighth. Each half-life only removes half of what's left, which is why the amount shrinks along a smooth curve rather than hitting zero on a schedule — mathematically it never quite reaches zero, though after enough half-lives the remainder becomes negligible.
Run the numbers on any isotope
Pick a common isotope or enter your own half-life and see exactly how much remains.
The decay formula
The relationship between starting amount, elapsed time and half-life is a simple exponential:
Plug in any starting amount and any elapsed time, expressed in multiples of the half-life, and the formula tells you what's left. It works identically whether you're measuring grams of a sample, becquerels of activity, or a percentage.
Half-lives span an extraordinary range
What makes half-life such a rich topic is the sheer range it covers — from fractions of a second to timescales longer than the age of the Earth.
| Isotope | Half-life | Notable use |
|---|---|---|
| Iodine-131 | ~8 days | Medical imaging and thyroid treatment |
| Cobalt-60 | ~5.3 years | Radiotherapy, industrial sterilisation |
| Strontium-90 | ~28.8 years | Fission product, RTG power sources |
| Caesium-137 | ~30.2 years | Fission product, calibration sources |
| Carbon-14 | ~5,730 years | Radiocarbon dating |
| Plutonium-239 | ~24,110 years | Reactor fuel and weapons material |
| Uranium-235 | ~704 million years | Fissile reactor fuel isotope |
| Uranium-238 | ~4.47 billion years | Bulk of natural uranium, roughly Earth's age |
Iodine-131's short half-life is exactly why it's useful in medicine — it does its job in the body, then clears within weeks. Uranium-238's half-life being close to the age of the Earth is why a meaningful fraction of the uranium the planet formed with is still here today.
Why half-life matters for nuclear waste
The same maths behind medical isotopes governs radioactive waste. A material with a short half-life is intensely radioactive but doesn't stay dangerous for long; one with a long half-life is less intense at any given moment but remains radioactive for a very long time, which is why waste-storage timelines are measured in thousands of years for some fission products. Fuel behind these decay chains starts life in a reactor — see the uranium enrichment calculator for how that fuel is made, and the reactor output calculator for the power it produces.
Frequently asked questions
What is a half-life in simple terms?
The time it takes for half of a radioactive substance to decay into something else. It's a fixed property of each isotope, from microseconds to billions of years.
Does a radioactive substance ever fully disappear?
Mathematically, no — each half-life only removes half of what remains. After about ten half-lives, under 0.1% remains, which is treated as effectively gone in practice.
Why do isotopes have such different half-lives?
Half-life depends on how stable an isotope's nucleus is. There's no way to speed up or slow down decay, which makes it a reliable clock for dating and medical use.