How long I can use if I want to run 1000w air conditioner?

Q: My air conditioner is 1000w, how long I can use it?

A: That's need see how big battery bank you have, watt=volt x amp, 

1000w/12v=83amp, bank need 4-5 times to turn it on, means 83ax5=415amp

Otherwise, your battery bank will be very easy to low down the voltage when turn on the air conditioner , remember, this is not about inverter, it's about your battery bank has enough power or not.