We present a Gaussian uncertainty analysis of bounded curved patches that fit to local rough surfaces and are suitable for representing foothold or handhold contacts between an articulated robot and the environment. The input is a set of 3D point samples with 3×3 covariance matrices that express their Gaussian uncertainty. We first introduce uncertainty propagation of geometrical patch parameters during fitting on range samples. The output for each patch includes a covariance matrix in its parametric space. We also introduce a set of distance metrics to validate the magnitude of the propagated uncertainty and we run a set of tests on various range data. The importance of this paper lies in the uncertainty analysis for curved contact patches that can be further applied during locomotion or manipulation.