Exponential Decay Calculator

About this calculator

Exponential decay describes a quantity that shrinks at a rate proportional to its current value, following N = N₀·e^(−kt), where N₀ is the initial amount, k is the decay constant, and t is elapsed time. This same equation underlies radioactive decay (where k relates to a substance's half-life via k = ln(2)/t½), drug elimination from the bloodstream in pharmacokinetics, capacitor discharge in RC circuits, and cooling of a hot object toward ambient temperature (Newton's law of cooling).

Physicists, chemists, pharmacologists, and engineers use this calculation to find how much of a radioactive isotope remains after a given time (used in carbon dating and nuclear medicine dosing), how much medication remains active in the body, or how a signal or voltage fades over time. Enter the initial amount, decay constant, and elapsed time to find the remaining amount.