Accurate knowledge of spot size, an important criterion in single-mode fiber optics, is obtained by two different optimization techniques, the well-known variational method and Marcuse formulation. The later is more accurate but cannot predict fiber parameters from given spot sizes. In this study, it is shown for the first time to the best of our knowledge that using simultaneously Marcuse relations of fiber spot sizes for single-mode graded index fibers and also variational formulation, we can more accurately and easily determine the fiber parameters for a particular normalized frequency. Then it is shown with typical example of fractional power in the core that in the case of such fibers, this synthesis of these two useful approaches can also more accurately estimate propagation characteristics of practical interest. This equivalence provides an easy and useful connection between two fundamental but disjoint approaches and should find wide use. © 2015 Taylor and Francis.