Mach Number Calculator

Mach number is the ratio of an object's speed to the local speed of sound in the surrounding medium. Named after Austrian physicist Ernst Mach, it is a dimensionless number: Mach 1 means the object is travelling at exactly the speed of sound, Mach 2 is twice the speed of sound, and so on. Because the speed of sound depends on air temperature (and to a lesser extent on pressure and humidity), the Mach number of an aircraft varies with altitude even if its ground speed is constant. At sea level and 20°C, the speed of sound is approximately 343 m/s (1,235 km/h).

A sonic boom is the loud noise produced when an object passes through the air faster than the speed of sound (Mach 1 or above). As the object exceeds Mach 1, it outruns the pressure waves it creates, and these pile up into a cone-shaped shockwave called a Mach cone. The sudden compression of air at the shockwave's edge creates a double boom heard on the ground. Sonic booms are not produced only at the moment of breaking the sound barrier; they are continuous as long as the object is travelling supersonically.

Subsonic means Mach below 0.8: standard commercial flight, most propeller aircraft. Transonic (Mach 0.8 to 1.2) is the regime where some parts of the aircraft (particularly the wing) exceed Mach 1 while others are still subsonic, causing complex mixed-flow shockwaves. Supersonic (Mach 1.2 to 5.0) is sustained faster-than-sound flight; the Concorde flew at about Mach 2. Hypersonic (above Mach 5) involves extreme aerodynamic heating; the Space Shuttle re-entered at approximately Mach 25.

The speed of sound in air increases with temperature because warmer air molecules have more kinetic energy and transmit pressure waves more quickly. The standard formula is c = 331.3 × sqrt(1 + T/273.15) m/s, where T is in °C. At 0°C the speed is 331.3 m/s; at 20°C it is approximately 343.2 m/s; at 100°C it is about 386 m/s. At high altitude (e.g., 11 km, the lower stratosphere), temperatures are around -56°C and the speed of sound drops to about 295 m/s, which is why Mach 1 at cruise altitude is a lower airspeed than at sea level.

Commercial airliners such as the Boeing 737 and Airbus A320 cruise at approximately Mach 0.78 to 0.82. The Concorde cruised at Mach 2.04. The SR-71 Blackbird reconnaissance aircraft held the air-breathing aircraft speed record at approximately Mach 3.3. The X-15 rocket plane reached Mach 6.7 in 1967. The Space Shuttle re-entered the atmosphere at approximately Mach 25, and the Apollo command modules re-entered at around Mach 36. Modern hypersonic test vehicles such as the Boeing X-51 Waverider have exceeded Mach 5.