One measure of efficiency is power output/power input.

Assuming that you have in the input power to the compressor in watts, the output flow rate in liters per minute, and the output pressure in bar(absolute), then the formula for efficiency is

(V * 100 * ln (P))/Input

Where v is flow rate in liters per second referenced to atmospheric pressure, P is pressure in bar, and Input is power to the compressor in watts. This also assumes that the input air is roughly atmospheric pressure and near room temperature, and the output air has cooled back to near room temperature.

A rule of thumb is that 1 hp into a compressor will generate 4cfm at 100psi. Lets see what efficiency that is.

1 cfm = 1cu ft * 28.3 liter/cu ft * 1 minute/60 second = 0.472 liters per sec
100psig = 115psia = 7.9 bar absolute

4 cfm = 4*0.472 lps = 1.89 lps

1.89 * 100 * log-natural (7.9) = 390 watts of output power

1 horsepower = 746 watts.

390/746 = 52% efficiency