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Radioactive Decay Calculator
Radioactive Decay Calculator reports the decay constant and mean lifetime alongside, since half of the literature uses those instead.
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Math & Science
Radioactive Decay Calculator
Frontend preview — no upload or external service.
Remaining
After 11,460 years — two half-lives of carbon-14 — 25% remains. The decay constant is 1.21 x 10^-4 per year, and the mean lifetime is 8,267 years.
How the Radioactive Decay Calculator works
- Enter the initial quantity and the half-life in matching time units.
- Enter elapsed time, or switch to solving for time from a measured remaining fraction.
- Read the decay constant and mean lifetime as well, since some calculations are expressed in those rather than half-life.
The method
Decay is exponential, with the fraction remaining depending only on the number of half-lives elapsed.
N = N0 x (1/2)^(t / half-life), or N = N0 x e^(-lambda t)
Two half-lives leaves a quarter, three leaves an eighth. The mean lifetime is the half-life divided by the natural log of two, so it is longer than the half-life.
FAQ
Why is the mean lifetime longer than the half-life?
Because the distribution has a long tail. Half the atoms decay within one half-life, but the survivors keep decaying over a much longer period, pulling the average up by a factor of about 1.44.
Does half-life change with conditions?
For practical purposes no — it is a property of the nucleus and unaffected by temperature, pressure or chemistry. A few decay modes involving electron capture show tiny chemical effects, which are negligible in ordinary use.
Is this how carbon dating works?
It is the arithmetic behind it. Real dating also requires calibration for atmospheric carbon-14 variation over time, contamination checks and a sample of adequate size, all of which matter more than the exponential.
How we compare
| Feature | Online Tool Store | A graphing calculator | A stats package |
|---|---|---|---|
| Solves in any direction | ✓ | ✗ | ✓ |
| Decay constant shown | ✓ | ✗ | ✓ |
| No sign-up | ✓ | ✓ | ✗ |
| Nothing uploaded | ✓ | ✓ | ✗ |
Radioactive Decay Calculator reports the decay constant and mean lifetime alongside, since half of the literature uses those instead.