Compression ratio and theoretical pressure
For an isothermal ideal gas, Boyle's law gives P2 = P1 x CR. For ideal adiabatic compression, P2 = P1 x CR^gamma; dry air near standard conditions is commonly approximated with gamma = 1.4. Both starting and final values in these equations are absolute pressures.
Absolute versus gauge pressure
Absolute pressure includes atmospheric pressure. Gauge pressure is the final absolute pressure minus the starting atmospheric pressure. The calculator reports both so a theoretical pressure is not mistaken for a compression-gauge reading.
Why real cranking PSI differs
This is an ideal-gas comparison, not a prediction of measured engine compression. Intake-valve closing, cranking speed, leakage, temperature change, altitude, cam timing, ring seal, valve seal, and gauge behavior all affect a real test. Use measured compression for diagnosis and compare cylinders under the same test conditions.