Solve exponential decay for half-life, mean lifetime, decay constant or remaining quantity.
Half-life t½ is the time for a quantity to fall to half its value. It describes any exponential decay: radioactive atoms, drug concentration in blood, carbon-14 dating, population decline. The decay constant λ = ln(2)/t½ gives the instantaneous fractional decay rate per unit time. The mean lifetime τ = 1/λ = t½/ln(2) is the average time a particle survives.
Remaining quantity
N(t) = N₀ × (1/2)^(t/t½) = N₀ × e^(−λt)
Decay constant
λ = ln(2) / t½ ≈ 0.693 / t½
Mean lifetime
τ = 1/λ = t½ / ln(2)
Half-life t½ is the time for exactly half the material to decay. Mean lifetime τ is the average time a single atom survives before decaying. They are related by τ = t½ / ln(2) ≈ 1.4427 × t½. The mean lifetime is always longer because a small fraction of atoms survive much longer than average.
(1/2)³ = 1/8 = 12.5% of the original. After n half-lives, the fraction remaining is (1/2)ⁿ.
Yes. Drug elimination in pharmacokinetics, attenuation of a signal, population decline, and compound interest all follow the same exponential model. The calculator works with any unit of time and any unit of quantity.