The radon seeping into basements across the American Midwest is decaying right now — every atom with a fixed probability of breaking apart each second, no exceptions, no slowdown. Radioactive decay follows one exponential rule: the amount remaining equals the starting amount times e raised to negative lambda times time. In symbols: N = N₀ × e^(−λt). The decay constant λ sets the pace, and the half-life — the time for half the atoms to decay — is just ln(2)/λ.

Because the rule is exponential, the drops come in clean fractions: after one half-life half remains, after two a quarter, after three an eighth. Smoke detectors exploit a 432-year half-life isotope (americium-241) so steady the current barely changes over the device's life. Doctors use iodine-131's 8-day half-life the opposite way — hot enough to treat thyroid tissue, gone fast enough to be safe within weeks.

This calculator multiplies out the decay formula's two parts. Type the starting quantity in the Variable A box — atoms, grams, or becquerels — and the decay factor e^(−λt) in the Variable B box (compute it first: raise e to the power of −λt). The Result box gives what remains. A radon test kit reading, a carbon-dating sample, and a nuclear medicine dose all answer the same multiplication.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Decay Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.