Curvature is simply expressed as the second derivative of the plate deflection in prior studies of post-buckling of plates. It is shown in this paper that the higher-order terms in curvature should be retained, consistent with Koiter's post-buckling theory. This paper also solves the dilemma whether the increase of post-buckling load is proportional to the square of the ratio of the post-buckling deflection w to the plate thickness t, (w/t)2, as in most prior studies, or to the characteristic in-plane length L of the plate, (w/L)2, as discovered in some recent studies.