Mach Number Formula
Calculate an object's speed relative to the speed of sound.
Classify flight as subsonic, transonic, or supersonic.
The Formula
M = v / a
The Mach number compares an object's speed to the local speed of sound. Mach 1 is exactly the speed of sound. Above Mach 1 is supersonic flight.
Variables
| Symbol | Meaning |
|---|---|
| M | Mach number (unitless) |
| v | Speed of the object (m/s) |
| a | Speed of sound in the surrounding medium (m/s) |
Flight regimes: Subsonic (M < 0.8), Transonic (0.8-1.2), Supersonic (1.2-5.0), Hypersonic (M > 5.0)
Example 1
A jet flies at 680 m/s at altitude where speed of sound is 295 m/s
M = 680 / 295
M ≈ 2.31 (supersonic)
Example 2
A commercial airplane flies at 250 m/s at sea level (a = 343 m/s)
M = 250 / 343
M ≈ 0.73 (subsonic)
When to Use It
Use the Mach number when:
- Classifying the speed regime of aircraft or projectiles
- Designing aircraft and wind tunnels
- Predicting shock wave formation at high speeds
- Calculating compressibility effects on aerodynamic forces