Not compressor related but I have an e-bike with a nominal 48 volt, 12 amp-hour Lipo battery. Nominally its 12 amp x 48 volt = 576 watt-hour. In the real world a LiPo battery is good for about 80% of it's nominal wh so mine is good for 461 watt-hour. IOW it will supply 461 watts for one hour. AFter 80% the voltage drop off is significant. That particular battery is about 15 inch long, 2.5 inch deep and 6 inch wide, weighs about 8 lbs.
My first ebike battery was an honest 1 kwhr battery. That was 12" long x 7" square, 20 lbs. Honest 80 mile range on the bike.
For a compressor it depends on how many amps it draws at whatever voltage. You also have to be aware of the battery's "C rating". It represents the multiplication factor that determines the amperage that can be drawn from the battery without excessive overheating or voltage dip. Example a 10C rated battery that is rated for 10 amp-hours storage can provide a maximum 100 amps current, a 20C battery 200 amps, etc.
First thing to determine is the amps or watts the compressor draws and go from there. Regards.
