A boost gauge reads gauge pressure: how far the intake manifold sits above the atmosphere around it. That is a useful thing to know and it is not the number the engine responds to.
Pressure ratio is the real quantity
What determines how much air the engine breathes is the absolute pressure in the manifold compared with atmospheric. That is the pressure ratio, and it is what compressor maps are plotted against.
At sea level, atmospheric pressure is 14.696 psi. Eight psi of boost means the manifold is at 22.70 psi absolute, a pressure ratio of 1.544. The engine is breathing roughly 54 per cent more air than it would unblown.
The rule worth carrying: one atmosphere of boost, about 14.7 psi, gives a pressure ratio of exactly 2.0 and doubles the air. A 2.0 litre engine at that boost breathes like a 4.0 litre one.
Why the same boost is not the same thing at altitude
Atmospheric pressure falls with altitude. The same 8 psi on the gauge at 2,000 metres is 8 psi above a lower baseline, so the absolute manifold pressure is lower and the engine gets less air.
A turbo can compensate by spinning faster to hold the same absolute pressure, which is why forced induction engines lose far less power at altitude than naturally aspirated ones do. But the gauge reading alone does not tell you whether that compensation is happening.
The boost and pressure ratio calculator takes atmospheric pressure as an input for this reason rather than assuming sea level.
Compressing air heats it, and hot air is thinner
The pressure ratio figure above is the ideal case. Compression raises the charge temperature, and density falls with absolute temperature, so some of the gain is handed straight back.
The loss follows the ratio of absolute temperatures, so a 60 degree rise costs roughly 17 per cent of the density gained. That is the entire reason intercoolers exist: they are not there to protect anything, they are there to recover density that heat took away.
Doubling the air is not doubling the power
Effective displacement is a measure of airflow, not of output. Fuelling has to keep up, the extra cylinder pressure has to be survivable, and a supercharger draws real power from the crank to do its work.
Power gains in practice are meaningfully less than the air gain, and the gap widens as boost rises because heat and mechanical losses both grow. Treat effective displacement as the ceiling rather than the forecast.
For the engine capacity being multiplied, see the engine displacement calculator. For the compression ratio, which forced induction constrains, see the compression ratio calculator.