Second-Order Concentration Calculator

About this calculator

For a second-order reaction — one whose rate depends on the square of a single reactant's concentration, rate = k[A]² — the integrated rate law is 1/[A] = 1/[A]₀ + kt, which is linear in 1/[A] versus time (unlike the exponential decay of a first-order reaction). Rearranging it lets you solve for the remaining concentration [A] at any elapsed time t, given the initial concentration [A]₀ and rate constant k.

This calculator takes [A]₀, k, and t and returns [A] directly from the integrated rate law, sparing you the algebra of inverting the equation by hand. Chemistry students and researchers studying reaction kinetics use it to model how a reactant depletes over time in processes that follow second-order kinetics — such as many gas-phase decomposition and dimerization reactions — and to compare predicted concentrations against experimental data when confirming a reaction's order.