The effects of varying the radius of an ion on the Born theory of ionic solvation are examined using molecular dynamics and Monte Carlo simulations and a simple quasi-continuum theory of ionic solvation (Hyun, J.-K.; Babu, C. S.; Ichiye, T. J. Phys. Chem. 1995, 99, 5187), referred to here as the HBI theory. In particular, the relationship in aqueous solution between the effective radius used to calculate the Born solvation free energy, often termed the Born radius, and the radius of the ion is examined. It has been observed empirically that the relationship is approximately linear, giving rise to the Latimer-Pitzer-Slansky (LPS) equation for the Born radius, which is a linear function of the Pauling radius. Here, the radius that gives the same solvation energy calculated for a given ion using the Born expression as that calculated from simulations of that ion in water, referred to as the simulation Born radius, is calculated for ions of different radii. In addition, the radius that gives the same solvation energy using the HBI expression as that calculated from simulations, referred to as the simulation HBI radius, is also calculated for the same ions. Linear fits of the simulation Born and HBI radii as functions of the Lennard-Jones radii are made, which allow prediction of the Born or HBI solvation energy, respectively, from the Lennard-Jones radius alone and are thus analogous to the LPS relation. Since the linear fits of the simulation Born and HBI radii to the Lennard-Jones radii are not perfect, they give rise to systematic deviations of the predicted solvation energies from the simulation solvation energies. The Born solvation energy expression with the linear fit for the Born radius is reasonably successful for predicting the simulation solvation energy for cations and anions in water, while it fails to predict the solvation energy for ions in a Stockmayer fluid. On the other hand, the HBI solvation energy equation with the linear fit for the HBI radius gives the best prediction of the simulation solvation energy for cations in water and ions in a Stockmayer fluid, while it produces the large deviations in the solvation energy for anions in water. The relationships of the simulation Born and HBI radii to the cavity radii are also examined.