Estimation of curvature from noisy sampled data is a fundamental problem in digital arc segmentation. The facet approach in curvature estimation involves least square fitting the observed data points to a parametric cubic polynomial and calculating the curvature analytically from the fitted parametric coefficients. Due to the fitting, there exists systematic error or bias between curvature calculated analytically from the parameterization of a circle and one calculated analytically based on the coefficients of the fitted cubic polynomial, even when the data is sampled from noiseless circle. We show how to compensate this bias by estimating it with the coefficients of the fitted cubic polynomial, which gives more accurate curvature value. We introduce small perturbations to the sampled data from a noiseless circle, and we analytically trace how the perturbation propagates through coefficients of the fitted polynomials and results in perturbation error of the curvature.