Half-Life Calculator
Amount remaining after radioactive decay — or the time a decay took.
Quick answer
- Formula: N = N₀ × (½)^(t ÷ t½); t = t½ × log₂(N₀ ÷ N)
- Worked example — Remaining amount: 25.00000 (full example below).
Half-Life Calculator
| 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
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
Sources & methodology
This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.
Content last reviewed by CalcHub Editorial.
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