How to use this calculator

Choose isentropic flow or a normal shock and enter the Mach number, or for isentropic flow an area, pressure or temperature ratio. Add the stagnation state to get static values, the speed and the choked mass flow.

Formulas

TemperatureT₀/T = 1 + (k − 1)M²/2

PressureP₀/P = [1 + (k − 1)M²/2]^k/(k−1)

AreaA/A* = (1/M)[(2/(k+1))(1 + (k−1)M²/2)]^{(k+1)/(2(k−1))}

Normal shockM₂² = (M₁² + 2/(k−1))/(2kM₁²/(k−1) − 1), P₂/P₁ = 1 + 2k(M₁² − 1)/(k+1)

Worked example

Air (k = 1.4) at M = 2 (the default)

T/T₀ = 1/(1 + 0.2 × 4) = 0.5556, P/P₀ = 0.5556^3.5 = 0.1278.
A/A* = (1/2)(1.8/1.2)³ = 1.6875, Mach angle 30°.
Across a normal shock at M₁ = 2: M₂ = 0.5774, P₂/P₁ = 4.5, P₀₂/P₀₁ = 0.7209.

Frequently asked questions

Why two answers for one area ratio?

A nozzle area larger than the throat can carry either subsonic or supersonic flow; the back pressure decides which. Pick the branch that matches the problem.