First-Order Rate Constant Calculator

About this calculator

For a first-order reaction, where the rate depends linearly on a single reactant's concentration (−d[A]/dt = k[A]), the rate constant relates directly to half-life through k = ln 2 / t½ ≈ 0.693 / t½. This calculator also derives the mean lifetime τ = 1/k = t½/ln 2 (the average time a molecule survives before reacting) and the time needed for 90% decay, t₉₀ = ln 10 / k.

This math is identical to radioactive decay kinetics, so chemists, nuclear physicists, and pharmacologists all use it — chemists for reaction-rate studies, pharmacologists to convert a drug's elimination half-life into a decay rate for dosing schedules, and chemical engineers sizing reactors where a first-order rate law governs conversion. Enter a known half-life to get k, τ, and t₉₀ instantly.