Leave one field empty to solve for it. Amounts can be in any unit (g, mg, atoms, %, Bq) as long as both use the same one.
Remaining amount = 29.639
- Half-lives elapsed
- 1.754
- Remaining
- 29.64%
- Decayed
- 70.36%
- Decay constant λ
- 1.216 × 10⁻⁴ y⁻¹
Horizontal axis: half-lives elapsed. Each half-life halves whatever is left.
How it works
Radioactive decay is exponential: in every half-life, half of the remaining nuclei decay. The calculator solves N = N₀ · (½)t/t½ for whichever quantity is missing, and also reports the decay constant λ = ln 2 / t½. Isotope half-lives come from the IAEA's nuclear data (NUBASE evaluation), the same data used on each element's isotope table — which is why carbon-14 shows 5,700 years, the current evaluated value, rather than the older 5,730 or 5,568 often quoted in textbooks.
Frequently asked questions
- What is half-life?
- The time it takes for half of the atoms in a sample of a radioactive isotope to decay. It is constant for each isotope: after one half-life 50% remains, after two 25%, after three 12.5%, and so on, no matter how much you start with.
- What is the half-life formula?
- N = N₀ × (1/2)^(t / t½), where N₀ is the starting amount, N the amount left after time t, and t½ the half-life. Solving for time gives t = t½ × log₂(N₀ / N).
- How does carbon dating use half-life?
- Living things keep a steady level of carbon-14. After death it decays with a half-life of about 5,700 years, so measuring the fraction left gives the time since death. If 25% remains, two half-lives — about 11,400 years — have passed.
- Does a radioactive sample ever fully decay?
- Mathematically the amount only approaches zero, but a real sample has a finite number of atoms. After about 10 half-lives less than 0.1% remains, which is a common rule of thumb for when an isotope is effectively gone.
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