Excluded volume of the system of hard-core spheres revisited: New insights from computer simulations

•The role of excluded volume in the equation of state of hard-sphere system is examined.•A number of approximations are considered for the excluded-volume parameter b(ρ) introduced in the van der Waals equation.•Partial contributions of two- and three-sphere intersections to b(ρ) are analyzed.•An approximation is identified based on Pade approximants that offers best accuracy at the lowest cost.