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Estimating permeability from grain-size distributions or from well logs is attractive but difficult. In this paper we present a new, generally applicable, and relatively inexpensive approach which yields information on permeability on the core sample and on the borehole scale. The approach is theoretically based on a fractal model for the internal structure of a porous medium. It yields a general and petrophysically justified relation linking porosity to permeability, which may be calculated either from porosity or from the pore radius distribution. This general relation can be tuned to the entire spectrum of sandstones ranging from clean to shaly sandstones. The resulting expressions for the different rock types are calibrated to a comprehensive data set of petrophysical and petrographical rock properties measured on 640 sandstone core samples of the Rotliegend (Lower Permian) in northeast Germany. Permeability calculated with this procedure from industry porosity logs compares very well with permeability measured on sedimentary and metamorphic rock samples.