Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. From a single assumption follows a scaling law according to which the relaxation time is a function of h(ρ) over temperature, where ρ is the density and the function h(ρ) depends on the liquid in question. This scaling is demonstrated to work well for simulations of the Kob–Andersen binary Lennard-Jones mixture and two molecular models, as well as for the experimental results for two van der Waals liquids, dibutyl phthalate and decahydroisoquinoline. The often used power-law density scaling, h(ρ)∝ργ, is an approximation to the more general form of scaling discussed here. A thermodynamic derivation was previously given for an explicit expression for h(ρ) for liquids of particles interacting via the generalized Lennard-Jones potential. Here a statistical mechanics derivation is given, and the prediction is shown to agree very well with simulations over large density changes. Our findings effectively reduce the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.