In the biosonar systems of bats, emitted acoustic energy and receiver sensitivity are distributed over direction and frequency through beampattern functions that have diverse and often complicated geometries. This complexity could be used by the animals to determine the direction of incoming sounds based on spectral signatures. The present study has investigated how well bat biosonar beampatterns are suited for direction finding using a measure of the smallest estimator variance that is possible for a given direction [Cramér-Rao lower bound (CRLB)]. CRLB values were estimated for numerical beampattern estimates derived from 330 individual shape samples, 157 noseleaves (used for emission), and 173 outer ears (pinnae). At an assumed 60 dB signal-to-noise ratio, the average value of the CRLB was 3.9°, which is similar to previous behavioral findings. Distribution for the CRLBs in individual beampatterns had a positive skew indicating the existence of regions where a given beampattern does not support a high accuracy. The highest supported accuracies were for direction finding in elevation (with the exception of phyllostomid emission patterns). No large, obvious differences in the CRLB (greater 2° in the mean) were found between the investigated major taxonomic groups, suggesting that different bat species have access to similar direction-finding information.