Estimation of a digital curve’s curvature at any given point is needed for many tasks in computer vision, be it differential invariants or curvature scale space. However, curvature estimation is known to be very susceptible to noise on the contour. We shall show how noise on the contour affects the relative accuracy of the curvature computation. One interesting result is that, contrary to intuition, the accurate calculation of the curvature for low-curvature regions is in fact impossible for common image-sizes, while reasonable results may under favourable conditions be obtained for higher-curvature regions.