Half-life / decay
Calculate remaining atoms and activity, explore the exponential decay curve.
About this tool
Choose an isotope or enter a half-life, initial atom count and elapsed time. Results update as you type. Changing the unit converts both times. Choosing an isotope preserves the elapsed number of half-lives.
Click or tap the plot to choose a time. The slider and table buttons also move the marker. Animate advances one half-life per second and Pause holds the current time. Enter a later time to extend the plot up to 100 half-lives. The calculator also accepts later times. Reset restores the carbon-14 example.
For a closed sample of one radioactive parent species, N(t) = N₀ · 2−t/t½, λ = ln(2)/t½, τ = 1/λ and A(t) = λN(t). Activity is in becquerels (Bq), meaning decays per second. N₀ is a number of atoms, not a mass or an activity. The curve is an expected value; small samples fluctuate randomly. Daughter activity, decay chains and replenishment are not included.
Presets are approximate teaching values; a year is 365.25 days. This is not a calibrated radiometric dating method. Very small remaining values can underflow to zero in floating-point arithmetic.