The packing densities of random close packing of equal hard spheres (RCPHS) are studied. The RCPHS is generated by a rearrangement algorithm with an optimization subroutine. Traditionally defined packing density, bulk density, is found to be 0.635 +/- 0.002 by extrapolation to infinite number of spheres. We propose that there exist a characteristic packing density without boundary effects. This interior packing density is calculated by two methods, resulting in values without statically significant difference. Interior packing density deduced from Voronoi diagram is 0.6690 +/- 0.0006. Local packing density for each sphere is defined as ratio of its volume to volume of its corresponding Voronoi cell and is sensitive to sphere's local configuration and overlapping. (C) 2003 Kluwer Academic Publishers.