Radioactivity / Half-life Calculator

Radioactive decay with N = N₀(½)^(t/t½): leave any one of N₀, N, t or the half-life blank and it is calculated from the other three.

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What it asks for

The formula

Decay law: N = N₀ e−λt

Half-life: t½ = ln 2 / λ = 0.6931 / λ

Half-life form (easiest when t is a whole number of half-lives):
N = N₀ × (1/2)n, where n = t / t½

Solving for time: t = (1/λ) × ln(N₀/N)

From the article Half-Life Formula — Radioactive Decay Calculations.

Worked example

A 100 g sample of a nuclide has t½ = 5.0 days. How much remains after 20 days?

n = t ÷ t½ = 20 ÷ 5.0 = 4 half-lives

N = 100 × (1/2)⁴ = 100 ÷ 16 = 6.25 g

and 100 − 6.25 = 93.75 g has decayed. Whenever n is a whole number, never touch the exponential — the halving form is faster and safer.

Worked in full in Half-Life Formula — Radioactive Decay Calculations.

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About this tool

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The Radioactivity / Half-life calculator above is the live tool — type your values and press its button; the answer appears in the same box. The link under it opens the full suite with this tool already selected, next to the others.

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