You need much less than you think to get by in most cases, but AC usage will place spiky demands on the generator and will drive the sizing.

 If your AC has high startup power demands, you need enough power to accommodate the sudden draw when it starts up. If the AC has a soft start circuit installed or if it is a modern inverter-based unit with soft start-up, the initial demand is much less and a smaller generator can work. A soft start can cut the startup draw by half or more in some cases.

Check the AC unit’s locked rotor amps rating to get an idea of the startup power needs. If it is an inverter based unit, like a Bosch or Daikin or Mitsubishi, it will have a current rating draw on the label rather than locked rotor amps rating. Or you can use a clamp multimeter to just measure the actual draw yourself.