Half-Life Calculator

Amount remaining after radioactive decay — or the time a decay took.

Half-Life Calculator

Worked example result

Remaining amount	25.00000
Percent remaining	25.000%
Half-lives elapsed	2.0000
Elapsed time	10.00000

Starting with 100 units and a 5-unit half-life, after 10 units of time (two half-lives) exactly 25 remain — 25%.

Half-life is the time for half of a radioactive (or otherwise exponentially decaying) sample to decay. After each half-life the amount halves again: 100% → 50% → 25% → 12.5% and so on.

Forward mode finds the amount remaining after an elapsed time. Reverse mode works out how long it took for a sample to fall from its initial amount to a measured remaining amount.

The formula

N = N₀ × (½)^(t ÷ t½); t = t½ × log₂(N₀ ÷ N)

Worked example

Starting with 100 units and a 5-unit half-life, after 10 units of time (two half-lives) exactly 25 remain — 25%.

The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.

Frequently asked questions

Does a sample ever fully decay?

Mathematically the exponential curve approaches zero but never reaches it. In practice, once only a handful of atoms remain, decay becomes a matter of individual random events rather than a smooth curve.

What are some real half-lives?

Carbon-14: about 5,730 years (used in radiocarbon dating). Iodine-131: about 8 days. Uranium-238: about 4.47 billion years.

Does half-life apply outside radioactivity?

Yes — the same mathematics describes drug elimination from the body, some chemical reactions and any process where the decay rate is proportional to the amount present.

Category: Science calculators

Half-Life Calculator