The hard sphere system exhibits a fluid-solid phase transition between the volume fractions of freezing η η f ≈ ≈ 0.494 and melting η η m ≈ ≈ 0.545 . The pressure diverges at random close packing η η r c p ≈ ≈ 0.644 for the metastable liquid branch and at close packing η η c p = 2 π π / 6 ≈ ≈ 0.74048 for the stable solid branch.