Calculators/Physics/Radioactive decay

Radioactive decay

Half-life · decay curve

Radioactive decay — illustration
Remaining N
125
Percent
12.5%
Decayed
875
Half-lives T
3
Decay curve N(t)

Decay law: N = N₀·(½)^(t/T). After each half-life T half of the nuclei remain. The dashed horizontal line = half of N₀.

Radioactive decay is governed by the decay law:

N=N0(12)t/TN=N_0\left(\tfrac{1}{2}\right)^{t/T}

where N0N_0 is the initial number of nuclei, TT is the half-life (the time after which half of the nuclei decay), and tt is time. After each TT half remains: after one 12\tfrac12, after two 14\tfrac14, after three 18\tfrac18…

Enter N0N_0, TT and tt (in the same time units) — the calculator finds the number and percentage of remaining nuclei and draws the decay curve.

Examples

N₀ = 1000, T = 5 days, t = 15 days
→ 3 half-lives → 1000·(½)³ = 125 remain (12.5%)
After one half-life
→ exactly 50% of the nuclei always remain

Frequently asked questions

What is the half-life?+

The time after which half of the radioactive nuclei decay. It is constant for a given isotope — independent of how many nuclei are left.

After how long does almost everything decay?+

After about 10 half-lives less than 0.1% of the nuclei remain. Decay is exponential — it never reaches exactly zero.

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