In this paper, the performance of focused lamellar anti-scatter grids, which are currently used in fluoroscopy, is studied in order to determine guidelines of grid usage for flat detector based cone beam CT. The investigation aims at obtaining the signal to noise ratio improvement factor by the use of anti-scatter grids. First, the results of detailed Monte Carlo simulations as well as measurements are presented. From these the general characteristics of the impinging field of scattered and primary photons are derived. Phantoms modeling the head, thorax and pelvis regions have been studied for various imaging geometries with varying phantom size, cone and fan angles and patient-detector distances. Second, simulation results are shown for ideally focused and vacuum spaced grids as best case approach as well as for grids with realistic spacing materials. The grid performance is evaluated by means of the primary and scatter transmission and the signal to noise ratio improvement factor as function of imaging geometry and grid parameters. For a typical flat detector cone beam CT setup, the grid selectivity and thus the performance of anti-scatter grids is much lower compared to setups where the grid is located directly behind the irradiated object. While for small object-to-grid distances a standard grid improves the SNR, the SNR for geometries as used in flat detector based cone beam CT is deteriorated by the use of an anti-scatter grid for many application scenarios. This holds even for the pelvic region. Standard fluoroscopy anti-scatter grids were found to decrease the SNR in many application scenarios of cone beam CT due to the large patient-detector distance and have, therefore, only a limited benefit in flat detector based cone beam CT.