Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions ϕ ≈ 0.75, a value that is similar to close packing of equal-sized spheres. A limitation of these analyses was the use of extended atom models, rather than the more physically accurate explicit hydrogen model. The validity of the explicit hydrogen model was proved in our previous studies by its ability to predict the side chain dihedral angle distributions observed in proteins. In contrast, the extended atom model is not able to recapitulate the side chain dihedral angle distributions, and gives rise to large atomic clashes at side chain dihedral angle combinations that are highly probable in protein crystal structures. Here, we employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high-resolution protein structures. We find that these protein cores have ϕ ≈ 0.56, which is similar to results obtained from simulations of random packings of individual amino acids. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations to protein cores and interfaces of known structure.