The generalized Born (GB) model is a simple continuum dielectric model for the calculation of molecular electrostatic solvation energies. It is a pairwise approximation to the solution of the Poisson equation for continuum electrostatic solvation. Key to the GB method is the calculation of Born radii for every atom in the system. We introduce two new methods for determining Born radii. The first is a two-parameter grid-based method that uses nearly the same molecular volume that is used in conventional Poisson calculations. The second is a five-parameter analytical method that utilizes a molecular volume built from a superposition of atomic functions. The analytical method, distinct from the grid-based algorithm, is amenable to force-based calculations, e.g., energy minimization and molecular dynamics. Unlike other Born radii methods, both algorithms employ a new empirically determined correction term that includes energetic effects beyond the Coulomb field approximation. With this correction term, the grid-based algorithm generally yields Born radii with greater than 0.99 correlation versus converged numerically derived Poisson Born radii. The analytical method reproduces Born radii with approximately 0.95 correlation versus Poisson-derived Born radii. With respect to absolute solvation energies, the grid-based method achieves an overall 1.3% error versus converged Poisson solutions for a set of 3029 single-chain proteins obtained from the Brookhaven Protein Data Bank. On the other hand, the analytic method delivers modest 2–4 % errors versus the Poisson solutions for the same data set. Results concerning absolute solvation energies of RNA and relative solvation energies in two sets of protein conformations are also presented.