Abstract A new equation of state for the hard sphere and hard disc fluids is derived from the assumption that the correlation function g( r, ∅), for the density of particles at a point ∅ on the surface of a pair of cavities separated by r, has the same density dependence as an arbitrary linear combination of g(σ) and ( g(σ)) 2. This assumption provides a closure on the YBG hierarchy at the level of g (3). The equation is accurate over the entire fluid range and becomes unphysical a little beyond the freezing density. It predicts that the isothermal compressibility goes to zero, at a finite pressure, at a density z s = 0.75 (relative to close packing). This observation accounts for the computer simulation results which indicate that the fluid becomes kinetically unstable with respect to freezing at z = 0.76 and that a diffuse fluid-amorphous solid transition occurs near z s in the finite time experiments.