The number densities (?/V) above or below which pockets of additional-sphere excluded volume (?pe) and available volume (?pa) begin to percolate the whole volume of the system, sometimes referred to as percolation thresholds, have been determined for the equilibrium hard-sphere fluid of diameter s using a Monte Carlo (MC) approach. Values obtained are ?pes3 = 0.0785 +/- 0.01 and ?pas3 = 0.537 +/- 0.005. The present value of ?pes3 agrees with an interpolation of previous data for the percolation diameter (sp) for various densities from Heyes et al. The available volume (Va) can be resolved as a radial acceptance function (u(r)), which is easily obtained from MC acceptance ratio statistics providing a direct route to the chemical potential up to liquid-like densities. The closed-virial equation-of-state of the hard-sphere fluid is found to deviate slightly, but significantly from thermodynamic pressures at densities exceeding ?pa. Knowledge of the hard-sphere fluid percolation transitions could lead to a more formal description of the critical point and origins of the liquid state, in the spirit of van der Waals. (c) 2011 American Institute of Chemical Engineers AIChE J, 2012