Many applications of geometry processing and computer vision relies on geometric properties of curves, particularly their curvature. Several methods have been proposed to estimate the curvature of a planar curve, most of them for curves in digital spaces. This work proposes a new method for curvature estimation based on weighted least square fitting and local arc-length approximation. Convergence analysis of this method and noise impact on the estimator accuracy are given. Numerical robustness issues are addressed with practical solutions. The implementation of the method is compared to other curvature estimation methods.