Radioactive Decay Calculator
Every radioactive isotope decays at a characteristic rate described by its half-life — the time for half the atoms to decay. Enter the initial quantity, the half-life, and the elapsed time to find how much remains, how much has decayed, and the decay constant λ.
Isotope preset
Amount of the original sample remaining after elapsed time
- 1
Decay constant λ
ln(2) ÷ 5,730 = 0.000121 - 2
Exponent (−λ × t)
−0.000121 × 5,730 = -0.693147 - 3
Remaining quantity N(t)
1,000 × e^(-0.6931) = 500N(t) = N₀ × e^(−λt) — exponential decay formula
How does this calculator work?
Radioactive decay follows N(t) = N₀ × e^(−λt) where λ = ln(2)/t½. Enter the initial quantity, half-life, and elapsed time to find the remaining amount, fraction decayed, and decay constant. Presets for Carbon-14, Iodine-131, Radium-226, and Uranium-238 are included.
Formula
How this is calculated
Radioactive decay is a random quantum process: each nucleus has a fixed probability per unit time of decaying. Summing over a large ensemble of nuclei gives the smooth exponential law N(t) = N₀ × e^(−λt), where λ = ln(2)/t½ is the decay constant. After one half-life exactly half the original nuclei remain; after two half-lives, one quarter; after n half-lives, 1/2ⁿ of the original.
The same formula applies to any quantity proportional to the number of nuclei — mass in grams, activity in becquerels, or an abstract "units" count. Simply enter N₀ in whichever unit you use and read the result in the same unit.
Built-in presets for Carbon-14 (5730 yr), Uranium-238 (4.47 Gy), Iodine-131 (8.02 d) and Radium-226 (1600 yr) are editable estimates based on standard nuclear-physics tables (NUBASE2020). Use the Custom option for any other isotope.
Frequently asked questions
The half-life (t½) is the time after which, on average, exactly half of a radioactive sample has decayed into a daughter product. It is constant for a given isotope regardless of how much sample you start with or the temperature and pressure.
Yes — select the Carbon-14 preset (t½ ≈ 5730 years). If you know the fraction of C-14 remaining compared to the original, you can rearrange the formula to find time: t = −ln(N/N₀)/λ. The calculator works in the forward direction (find remaining amount given time); rearranging for t requires logarithms.
The amount approaches zero exponentially but never reaches exactly zero mathematically. In practice, after 10 half-lives less than 0.1% of the original remains; after 20 half-lives, less than 1 ppm. The calculator handles any number of elapsed half-lives.
Also known as
TG we-Calculate Editorial Team. (2026). Radioactive Decay Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/radioactive-decay-calculator
TG we-Calculate Editorial Team. "Radioactive Decay Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/radioactive-decay-calculator.
TG we-Calculate Editorial Team, "Radioactive Decay Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/radioactive-decay-calculator
@misc{wecalculate_radioactive_decay_calculator, title = {Radioactive Decay Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/radioactive-decay-calculator}}, year = {2026}, note = {TG we-Calculate} }
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