Free volume ideas have been employed extensively in the interpretation of equilibrium processes and as a measure of molecular mobility. More recently, the vacancy fraction h, defined in our hole theory, has served to provide a link between diverse processes. This raises a question regarding the relation between the van der Waals type of free volume and h. As an important and useful result, valid for polymers and low molar mass fluids, simple relations are obtained between the van der Waals volume V-w, computed according to Bondi’s structural rules, and the scaling volume V* in the hole theory. This is defined by the intersegmental potential and extracted from the equation of state. In turn, this result enables us to compute the corresponding scaling temperature T*. In this manner the theory predicts the volume-temperature function for a melt, based on a single experimental datum. Corresponding considerations are presented for the glassy state. The quantitative relation between the van der Waals type of free volume v(f) and h derived makes it possible to reconsider various empirical correlations involving the former.