The free energy is analysed of a spherical interface generated in a fluid described by a local free energy density functional that features square-gradient and square-Laplacian terms. The bulk, the surface tension and the bending rigidity terms are investigated, and the position is found for the dividing surface that satisfies the generalized Laplace equation that incorporates bending terms. The results agree with those obtained previously from the general expression for the stress tensor of an interface of arbitrary shape (Romero-Rochín, V., Varea, C., and Robledo, A., 1991, Phys. Rev. A, 44, 8417; 1993, Phys. Rev. E, 46, 1600). Also, when a comparison is made between spherical and planar interfaces the expressions obtained are those derived by Gompper, G., and Zschocke, S. (1991, Europhys. Lett., 18, 731) and by Blokhuis, E. M., and Bedeaux, D. (1993, Molec, Phys., 80, 705). These expressions correspond to the length of Tolman and to similar higher-order correction terms.