Abstract Sphericity, as one of the most important shape parameter for non-spherical objects, is extensively applied in evaluating the porosity or packing density of particles. In this paper, the sphericities of common non-spherical objects are deduced and investigated. Maximum sphericities and optimum shapes of these objects are presented as well. A decreasing order of sphericity from sphere (1.0) to regular tetrahedron (0.671) for objects with constant sphericity is given. Similar trends are found in most sphericity–aspect ratio relationships, which exhibit single peak and the sphericity increases with the growth of aspect ratio before the peak point and decreases afterward. The peak loci of aspect ratio are all around 1.0 which makes the shape approaching to a sphere. The information in the paper could be useful as literature for general application.