Compressible Aerodynamics Calculator

Solve isentropic flow, normal shock, oblique shock, Fanno flow, and Rayleigh flow relations quickly and easily. See sample implementations in Python, JavaScript, MATLAB, and C++. This calculator is based on Virginia Tech’s Compressible Aerodynamics Calculator.

Isentropic Flow Relations

Information about isentropic flow relations.

$ \gamma $ =

$ M $ =

$ \mu $ =

$ \nu $ =

$ \frac{p}{p_0} $ =

$ \frac{\rho}{\rho_0} $ =

$ \frac{T}{T_0} $ =

$ \frac{p}{p^*} $ =

$ \frac{\rho}{\rho^*} $ =

$ \frac{T}{T^*} $ =

$ \frac{A}{A^*} $ =

$$ \mu = \frac{1}{\sin^{-1}(M)} $$ $$ \nu = \sqrt{\frac{\gamma + 1}{\gamma - 1}} \cdot \tan^{-1}\left( \sqrt{\frac{\gamma - 1}{\gamma + 1} (M^2 - 1) } \right) - \tan^{-1}\left( \sqrt{ (M^2 - 1) } \right) $$ $$ \frac{p}{p_0} = \left( 1 + \frac{\gamma - 1}{2} M^2 \right) ^ {-\frac{\gamma}{\gamma - 1}} $$ $$ \frac{\rho}{\rho_0} = \left( 1 + \frac{\gamma - 1}{2} M^2 \right) ^ {-\frac{1}{\gamma - 1}} $$ $$ \frac{T}{T_0} = \left( 1 + \frac{\gamma - 1}{2} M^2 \right) ^ {-1} $$ $$ \frac{p}{p^*} = \left( \frac{2 + (\gamma - 1) M^2}{\gamma + 1} \right) ^ {-\frac{\gamma}{\gamma - 1}} $$ $$ \frac{\rho}{\rho^*} = \left( \frac{2 + (\gamma - 1) M^2}{\gamma + 1} \right) ^ {-\frac{1}{\gamma - 1}} $$ $$ \frac{T}{T^*} = \frac{\gamma + 1}{2 + (\gamma - 1) M^2} $$ $$ \frac{A}{A^*} = \left( \frac{\gamma + 1}{2} \right) ^ {-\frac{\gamma + 1}{2(\gamma - 1)}} \cdot \left( \frac{1 + \frac{\gamma - 1}{2} M^2}{M} \right) ^ {\frac{\gamma + 1}{2(\gamma - 1)}} $$

import math

M = 2.0  # Mach Number

mach_angle = math.degrees(math.asin(1 / M))
print(f'The Mach angle at M = { M } is { mach_angle } degrees.')

var M = 2.0;  // Mach Number

mach_angle = Math.asin(1 / M) * 180 / Math.PI;
console.log('The Mach angle at M = ' + M + ' is ' + mach_angle + ' degrees.');

M = 2.0;  % Mach Number

mach_angle = asind(1 / M);
fprintf('The Mach angle at M = %f is %f degrees.', M, mach_angle)

#include <stdio.h>      /* printf */
#include <math.h>       /* asin */

#define PI 3.14159265

int main ()
{
  double M = 0.5;  // Mach Number
  double mach_angle = asin(1 / M) * 180.0 / PI;
  printf ("The Mach angle at M = %f is %f degrees.\n", M, mach_angle);
  return 0;
}