The ability to fly opens up ecological opportunities but flight mechanics and muscle energetics impose constraints, one of which is that the maximum body size must be kept below a rather low limit. The muscle power available for flight increases in proportion to flight muscle mass and wingbeat frequency. The maximum wingbeat frequency attainable among increasingly large animals decreases faster than the minimum frequency required, so eventually they coincide, thereby defining the maximum body mass at which the available power just matches up to the power required for sustained aerobic flight. Here, we report new wingbeat frequency data for 27 morphologically diverse bat species representing nine families, and additional data from the literature for another 38 species, together spanning a range from 2.0 to 870 g. For these species, wingbeat frequency decreases with increasing body mass as Mb–0.26. We filmed 25 of our 27 species in free flight outdoors, and for these the wingbeat frequency varies as Mb–0.30. These exponents are strikingly similar to the body mass dependency Mb–0.27 among birds, but the wingbeat frequency is higher in birds than in bats for any given body mass. The downstroke muscle mass is also a larger proportion of the body mass in birds. We applied these empirically based scaling functions for wingbeat frequency in bats to biomechanical theories about how the power required for flight and the power available converge as animal size increases. To this end we estimated the muscle mass-specific power required for the largest flying extant bird (12–16 kg) and assumed that the largest potential bat would exert similar muscle mass-specific power. Given the observed scaling of wingbeat frequency and the proportion of the body mass that is made up by flight muscles in birds and bats, we estimated the maximum potential body mass for bats to be 1.1–2.3 kg. The largest bats, extinct or extant, weigh 1.6 kg. This is within the range expected if it is the bat characteristic flight muscle mass and wingbeat frequency that limit the maximum body mass in bats. It is only a tenth the mass of the largest flying extant bird.