A self-consistent electron theory of solids is shown to lead to the formula for the vacancy formation volume in terms of defect forces which are the forces exerted on the positive charge representing ions or nuclei by the missing charge density. For the jellium model of a metal vacancy, the above relation becomes a sum rule analogous to that of Budd and Vannimenus (1973) for a surface. Self-consistent calculations of the electron density using the density-functional formalism have been performed on jellium with a vacancy, for which the sum role provides a check on numerical accuracy and a 'jellium' value for the vacancy formation volume. For jellium densities appropriated to thirteen metals this falls in the range 0.5 Omega - Omega ( Omega =atomic volume) and can be used as the basis of a perturbation theory. First-order corrections due to the discreet lattice of pseudoions have been evaluated and are mostly less than 0.3 Omega .