The magnitudes of the magnetic interactions in crystalline Cs2CrO4 have been described using the plane wave DFT treatment. A good level of agreement between the calculated and measured data has been found, and its relevance for structural studies of cesium-containing compounds has been discussed. This computational approach has been also used to reveal the absolute orientations in the Cs2CrO4 crystal frame of the Cs-133 NMR chemical shielding and EFG tensors of all the crystallographically and magnetically distinct sites, and the results have been compared to the findings of several experimental investigations. The related tensorial transformations have been described in detail. (C) 2017 Elsevier B.V. All rights reserved.