Results from the numerical simulation of Stokes flow through random packings of nonoverlapping or overlapping sphers and a [ital scaling] [ital ansatz] are used to obtain universal curves for the fluid permeability. The scaling ansatz is motivated by previous analysis of rigorous bounds on the permeability. Excellent agreement was found for a variety of model microstructures of porous media in the low and high porosity regimes. Experimentally obtained permeabilities of several sandstones were found to agree well with our universal curve.