Frictional sliding dilates gouge or increases the separation of sliding surfaces. A common hypothesis is that the rate of dilatational strain scales linearly with the rate of shear strain. The proportionality constant is called the dilatancy coefficient. Real contact theory of friction may explain this feature. Moving contact asperities produce damaged regions with elastic strains scaling to the ratio of the real strength of asperities to the elastic modulus. Balance between this local strain-energy production rate and macroscopic work against normal traction indicates that the dilatancy coefficient scales with this ratio. So do the average slopes on a mature rough sliding surface if opening-mode cracks are unimportant. The result is compatible with the observed dilatancy coefficient of quartz gouge, ~4%.