Mach Number Calculator
Calculate Mach number from speed and temperature.
Find the speed of sound at any temperature and identify the flight regime from subsonic to hypersonic.
The Mach number is the ratio of an object’s speed to the speed of sound in the surrounding medium. Named after Ernst Mach, who in 1887 photographed the shock waves from a supersonic bullet — one of the first images of a shock wave ever taken.
Speed of sound in air
v_sound = 331.3 x sqrt(T / 273.15) m/s
where T is absolute temperature in Kelvin. At 20°C (293.15 K): v_sound ≈ 343 m/s. At -56°C (cruising altitude for jets): v_sound ≈ 295 m/s. The speed of sound in air decreases with altitude as temperature drops.
Mach number
M = v / v_sound
Flight regimes
Subsonic: M < 0.8. Normal aerodynamics applies. All commercial airliners cruise here (typically M 0.78-0.85).
Transonic: 0.8 < M < 1.2. Local regions of supersonic flow appear on the wings even though the aircraft is below M 1. Shock waves and wave drag appear. The “sound barrier” is actually this region of increasing wave drag.
Supersonic: 1.2 < M < 5. Shock waves are attached to the aircraft. The Concorde cruised at M 2.04; the SR-71 Blackbird at M 3.3.
Hypersonic: M > 5. Air begins to dissociate and ionize. Re-entry vehicles and ballistic missiles operate here; so does the Space Shuttle during re-entry (peak M ≈ 25). Aerodynamic heating becomes the dominant design challenge.
The boom
A sonic boom is not a one-time event at the moment of passing Mach 1. It is a continuous shock wave cone (Mach cone) that follows any supersonic object. The half-angle of the cone is arcsin(1/M). At M 2, the half-angle is 30°.