Compressible Flow Calculator

This tool works the isentropic relations for compressible flow of a perfect gas, with the ratio of specific heats and the specific gas constant entered rather than read from a built-in gas table. Give it a Mach number and it returns the stagnation to static ratios for temperature, pressure and density, the area ratio A over A star, the speed of sound, the velocity, and the Mach and Prandtl-Meyer angles above Mach 1. A second action takes a reservoir pressure and temperature with a throat area and returns the mass flow, saying whether the nozzle is choked and what back pressure would choke it. A third goes the other way, from a ratio to the Mach number, and gives both branches of the area ratio. The relations assume no friction, no heat transfer and no shock, so none of the stagnation pressures carry across a shock wave.

Calculator Type
Pressure Unit
Applies to every pressure you type in and every pressure in the answer. Absolute, not gauge, whichever you pick. Temperature stays in kelvin and the gas constant in J/kg.K.
cp/cv. 1.4 for air, nitrogen and oxygen, 1.667 for argon and helium, 1.33 for methane or hot combustion gas, 1.3 for steam.
The temperature of the moving gas itself, not of the reservoir it came from.
In whichever unit you picked above. Leave it empty for one standard atmosphere, which is 101.325 kPa, 1.01325 bar or 14.6959 psi.
8314.46 divided by the molar mass in g/mol. 287.05 for air, 2077 for helium, 461.5 for steam.
Widget
Pressure Unit
Applies to every pressure you type in and every pressure in the answer. Absolute, not gauge, whichever you pick. Temperature stays in kelvin and the gas constant in J/kg.K.
In whichever unit you picked above. The reservoir pressure, absolute rather than gauge: add one atmosphere to a gauge reading, which is 101.325 kPa, 1.01325 bar or 14.6959 psi.
The narrowest cross section. A round throat of diameter d has an area of 0.7854 x d squared.
In whichever unit you picked above. The pressure downstream. Leave at zero for discharge to vacuum, which is always choked.
1 for the ideal one-dimensional result. A well rounded nozzle runs near 0.98, a sharp edged orifice nearer 0.6.
cp/cv. 1.4 for air, nitrogen and oxygen, 1.667 for argon and helium, 1.33 for methane or hot combustion gas, 1.3 for steam.
8314.46 divided by the molar mass in g/mol. 287.05 for air, 2077 for helium, 461.5 for steam.
Widget
Every one of these ratios is 1 at Mach 0 or Mach 1 and rises from there, so it is never less than 1.
cp/cv. 1.4 for air, nitrogen and oxygen, 1.667 for argon and helium, 1.33 for methane or hot combustion gas, 1.3 for steam.
Widget