The relation between the compressibility and the radial free space distribution function (RFSDF) has been derived. This method for calculating the compressibility employing RFSDF is useful because the compressibility of any system is obtainable in a single Monte Carlo simulation without obtaining the equation of state. The compressibilities from the newly derived relation using RFSDF of hard-sphere fluids have been compared with those obtained from the equation of state and they are in good agreement. This method has been used to calculate the velocity of sound for hard spheres confined in parallel hard walls with the results showing that the velocity of sound in parallel direction to the wall is faster than that in normal direction.