Half-Life Calculator

A half-life is the time it takes for a quantity to fall to exactly half its starting value. After one half-life, 50% remains. After two, 25%. After three, 12.5%. Each interval cuts what is left in half, so the decline is exponential, not linear.

The calculator uses N(t) = N0 x (1/2)^(t / h), where N0 is the initial amount, t is elapsed time, and h is the half-life. This is mathematically identical to N(t) = N0 x e^(-k x t), where the decay constant k = ln(2) / h.

The decay constant k = ln(2) / half-life measures the instantaneous decay rate per unit time. The mean lifetime is 1 / k, which equals the half-life divided by ln(2), or roughly 1.4427 half-lives. It represents the average time a single particle or molecule survives before decaying.

No. Half-life describes decay, so the remaining amount cannot exceed the starting amount. When you solve for elapsed time, the remaining value may equal the initial amount, which simply returns a time of zero. When you solve for the half-life it must be strictly smaller, since equal amounts give no decay to measure. Any remaining value above the initial amount returns no result.

Drug pharmacokinetics (how long a medication stays in the body), carbon-14 dating, capacitor discharge in RC circuits, biological clearance rates, and any process where a quantity decreases by a fixed fraction per unit time all follow the same math.