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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)

Nuclide preset
Unit
Bq, g, etc. (any unit)
Unit

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 elapsedRemaining fractionAmount remaining
0100 %1,000
150 %500
225 %250
312.5 %125
46.25 %62.5
53.13 %31.25
100.1 %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.