Pressure ratio is the chamber pressure divided by the exit pressure. The pressure ratio, being a measure of how much the gas expands, determines how much thermal energy is converted to mecanical energy. From a thermodynamic viewpoint a rocket engine can be viewed as a very fast piston engine, with the rocket engine pressure ratio being similar to the piston engine compression ratio.

A pressure ratio of fifteen is typical for a rocket operating at sea level. A rocket operating in vacuum has a pressure ratio of infinity. Given chamber pressure and exit pressure the pressure ratio can be calculated which is in turn used to calculate area ratio and expanded velocity.

pressure ratio = chamber pressure / exit pressure

k = 1.21
mach = sqrt( 2.0 / ( k - 1.0 ) * ( pow( pressure ratio, 1.0 - 1.0 / k ) - 1.0 ) )
area ratio = pow( ( 1.0 + ( 0.5 * k - 0.5 ) * mach * mach ) / ( 0.5 * k + 0.5 ), ( k + 1.0 ) / ( 2.0 * k - 2.0 ) ) / mach

expanded change = ( 1.0 - pow( 1.0 / pressure ratio, 1.0 - 1.0 / k ) ) * k / ( k - 1 ) * 8,314 J * K / kmol * temperature change / exhaust molecular
expanded velocity = sqrt( 2.0 * expanded change * nozzle efficiency )

This is used in bipropellant rocket, tripropellant rocket, pumped rocket and rocket cost.