The effects of self compression on the internal structures of planetary bodies are poorly understood. As the number of known planets increases, understanding the effects of self-compression and layering on mass and radius provides an estimate of planetary compositions, which is useful data for the study of planetary system evolution. In this study, we apply the second-order Birch-Murnaghan equation of state to a spherical body, and study the effects of the material properties (as determined from lab experiments) of the planet on astronomical observables, planetary radius and mass. The most important parameter for a single-material, single-phase body is the overall compression of the planet, i.e., the core density over the surface density. For bodies of two or more distinct layers, the location of the boundary, the ratio between the bulk moduli of the two materials and the ratio between the initial densities of the layers are also useful dimensionless parameters. The effects of these parameters are most clearly seen in the resulting changes in the moment of inertia coefficient, $\alpha$ = C/MR$^2$. Specific cases of astronomical interest are discussed, including water planets and Earth-like rocky planets with metallic cores.