Kibble-Zurek mechanism relates the domain of nonequilibrium dynamics with the critical properties at equilibrium. It establishes a power law connection between nonequilibrium defects quenched through a continuous phase transition and the quench rate via the scaling exponent. We present a novel numerical scheme to estimate the scaling exponent wherein the notion of defects is mapped to errors, previously introduced to quantify a variety of gapped quantum phases. To demonstrate the versatility of our method we conduct numerical experiments across a broad spectrum of spin-half models hosting local and symmetry protected topological order. Furthermore, an implementation of the quench dynamics featuring a topological phase transition on a digital quantum computer is proposed to quantify the associated criticality.