Half-Life Calculator
Visualizer
\[ N(t) = N_0 \cdot e^{-\lambda t} \qquad t_{1/2} = \frac{\ln 2}{\lambda} \]
where N, N₀, λ, t, and t½ denote, respectively, the remaining quantity, initial quantity, decay constant (in units of inverse time), elapsed time, and time for half the sample to decay.
Decay Calculator
Result
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Common Isotopes

Select an isotope to load its half-life into the calculator above.

Decay Curve

Enter N₀ and t½ above to plot the curve. The marked point shows your current t value.

About This Tool

Radioactive decay follows first-order kinetics described by N(t) = N₀·e^(−λt), where λ is the decay constant and t½ = ln(2)/λ is the half-life — the time for exactly half of any sample to decay. This calculator lets you solve for any one of the four variables: remaining quantity N, initial quantity N₀, elapsed time t, or half-life t½. Supporting quantities — the decay constant, fraction remaining, number of half-lives elapsed, and percentage decayed — are shown automatically. The decay curve plots N against time across five half-lives, with your current time point marked. A selection of common isotopes is provided as presets, covering radiometric dating (carbon-14, uranium-235, potassium-40), nuclear medicine (iodine-131, technetium-99m, fluorine-18), and industrial applications. Note that all time units are relative — the half-life and elapsed time must be in the same units for correct results.