Radioactive Half-Life Calculator
Calculate how much of a radioactive element remains and its remaining fraction from the initial amount, half-life, and elapsed time. You can also work backward to find the time needed to reach a given fraction.
Input
Based on the half-life law N = N₀ × (1/2)^(t/T), this estimates how much of a radioactive element remains, or how long it takes to decay to a given fraction.
Fill in a half-life from a common nuclide (optional)
Result
Amount remaining after 60 years (estimate)
252.3058
Remaining fraction
25.23 %
Amount decayed
747.6942
Half-lives elapsed
1.99 half-lives
Initial amount N₀
1,000
Mean lifetime τ (= T/ln2)
approx. 43.5694 years
Decay constant λ
7.273e-10 /s
Estimated using N = N₀ × (1/2)^(t/T). This is a theoretical value and does not account for measured data or measurement error.
Remaining fraction per elapsed half-life (reference)
| Half-lives elapsed | Remaining fraction | Amount remaining |
|---|---|---|
| 0 | 100 % | 1,000 |
| 1 | 50 % | 500 |
| 2 | 25 % | 250 |
| 3 | 12.5 % | 125 |
| 4 | 6.25 % | 62.5 |
| 5 | 3.13 % | 31.25 |
| 10 | 0.1 % | 0.9766 |
How it works
- The remaining amount is calculated with the half-life law N = N₀ × (1/2)^(t/T), where N₀ is the initial amount, T is the half-life, and t is the elapsed time; t/T is the number of half-lives that have passed.
- The remaining fraction is found as (1/2)^(t/T) × 100 (%). The amount halves with each half-life, falling to 25% after two and 12.5% after three, decreasing exponentially.
- In the mode that solves for the time needed from a remaining fraction, t = T × log₂(N₀/N) is used to find how long it takes to decay to the specified fraction.
- The decay constant λ = ln2 / T and the mean lifetime τ = T / ln2 = 1/λ are also shown. The half-life T and mean lifetime τ are different quantities, with τ being about 1.44 times longer than the half-life.
- The preset half-lives for Iodine-131, Cobalt-60, Cesium-137, Carbon-14, and others are commonly cited reference values. Input units can be switched between seconds, minutes, hours, days, and years.
- Results are estimates based on a theoretical formula. For decisions requiring expert judgment, such as radiation dose or exposure effects, always consult the latest information from official bodies or professional advice.
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Radioactive Half-Life Calculator