The advances in manufacturing methods such as Additive manufacturing provide more flexibility in fabrication of complex geometries. Meanwhile, design tools such as aesthetic design and topology optimization algorithms have been implemented in industrial applications mostly due to the provided flexibility to manufacture freeform surfaces. Computational time and efficiency of the developed algorithms for design, manufacturing and inspection are heavily dependent on the geometric complexity of surfaces. In this paper a measure to estimate the geometric complexity is introduced based on the inherent property of a surface which is curvature. A quantitative value for the geometric complexity is defined through normalization and integration of the mean curvatures. Case studies of the implementation of the proposed measure of complexity verifies the ability of the method to predict the convergence of a surface fitting algorithm based on the geometric complexity of the input model.