A new approach to the analytical solution of the 2-D Poisson equation including the inversion-charge density in undoped square gate-all-around metal-oxide-semiconductor field-effect transistors has been developed. We have obtained functions with different degrees of complexity to calculate the electric potential in the devices under study. The results obtained are compared with the data simulated by solving the Poisson equation numerically. A good fit is achieved both for the electric potential and the inversion charge, which are calculated by means of Gauss's law.