The prediction of hydraulic conductivity from nuclear magnetic resonance (NMR) measurements has been performed primarily in sandstones. In hydrogeological applications, however, unconsolidated material is more prevalent. Compared to sandstones, unconsolidated sediments can show pore sizes up to several millimeters. The known (semi-)empiric relations to estimate from NMR have been applied on this material, but the underlying assumptions are not valid for large pores. We formulated a new model, called the Kozeny-Godefroy model. It is based on capillary pores with a single pore radius, and accounts for bulk water relaxation and relaxation in porous media under fast- and slow-diffusion conditions. The bulk-water relaxation and slow-diffusion conditions significantly affect the NMR measurements on coarse material. If the impact of the bulk-water relaxation is well known and small, a maximum can be derived from NMR measurements by accounting for the slow-diffusion case. The model replaces the empirical factors in known relations with physical, structural, and intrinsic NMR parameters. Focusing the calibration on material-specific NMR parameters improves the prediction of for similar material. Measurements on well-sorted glass beads and natural sands with different grain sizes are used for evaluation. These measurements confirm the applicability of the new model and, for coarse material, show the limit of the fast-diffusion-based Seevers and Schlumberger-Doll-Research equations. The application of our model is limited to (1) simple pore geometries, and (2) materials with a small range of pore sizes.