This page is about your compressor power supply.
Most DIY compressor owners have 120 VAC (volt alternating current) running to the outlets in their house, workshop and garage.
Some of the power outlets (plugs) are connected to the breaker panel or fuse box with 15 amp fuses or breakers to protect the line. Some are connected to 20 amp fuses or breakers.There are other fuses / breaker amperages in the panel, but most of those are specialty applications like for the stove or baseboard electric heaters. The 15 amp and 20 amp circuits are the ones that normally run to typical electric outlets and are your compressor power supply.
And that is the reason why the largest home compressor motor powered by a 120 AC power supply should be in the 1 - 1.5 HP size.
It's not rocket science then to see that a 1 HP compressor motor will draw around 12 amps of power, and a compressor motor just a little larger than 1 HP would exceed the capacity of the 15 amp breaker.
The compressor manufacturers do not know if you are going to be plugging your air compressor into a 15 amp fuse/breaker supply, or to a 20 amp supply. I expect then that they would tend to lean towards making sure that their compressors would start and run on the15 amp supply, this being the average for most homeowners, and thus limiting the compressor motor size.
When the fridge compressor first comes on, any lights on the same electrical circuit will dim briefly because the fridge motor needs a power inrush to start to get it up to designed speed. While the motor starting is happening, the fridge compressor motor sucks more current than at normal running speed, pulling power from anything else on the circuit.
Compressor motors have start capacitors (an electrical storage device) to supply a quick boost of electricity when the motor tries to start. That is why your compressor motor will start for you even though the draw of that motor is very close to, or may even exceed, the load capacity of the circuit on start up.
That's why one of the first checks for a compressor motor than will not start is to make sure the power supply to the compressor is clean.
Manufacturing plant compressors commonly run on 480 or 575 Volts, to provide enough energy for a compressor that is big enough to generate the flow required for those high-demand installations.