27Al quadrupolar parameters are determined for the three aluminium sites in β-Ba3AlF9 from the reconstruction of experimental SATRAS and MQ-MAS NMR spectra. These quadrupolar parameters are then computed using the DFT linearized augmented plane wave method implemented in the WIEN2k code. A fine agreement between experimental and calculated values is obtained only after optimizing the β-Ba3AlF9 structure. The optimized structure is more satisfactory than the previously published one from a crystallographic point of view (bond lengths and angles). This approach which allows to refine crystallographic structures especially when they lack accuracy may be extendable to other compounds containing quadrupolar nuclei.