Mach Number Calculator

Calculate the Mach number from object speed and speed of sound, with temperature corrections for accurate aerodynamic analysis.

MACH NUMBER
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Mach Number
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Speed of Sound
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Flow Regime
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Object Speed
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What Is Mach Number?

The Mach number is the ratio of an object's speed to the local speed of sound. Named after Austrian physicist Ernst Mach, it is the key dimensionless parameter in compressible fluid dynamics. At Mach 1, an object travels at exactly the speed of sound, creating a shock wave known as a sonic boom. The Mach number determines the nature of the airflow around an object and is critical for aircraft design, rocket engineering, and ballistics.

The speed of sound depends on the air temperature (and composition), not on pressure or altitude directly. At sea level and 15 degrees C, the speed of sound is about 340 m/s (1,225 km/h). At cruise altitude (11 km, -57 C), it drops to about 295 m/s, so an aircraft at the same airspeed has a higher Mach number at altitude.

Mach Number Formula

M = v / a
a = 331.3 √(1 + T/273.15) m/s

Where M is the Mach number, v is the object's velocity, a is the speed of sound, and T is temperature in °C.

Flow Regimes

RegimeMach RangeCharacteristics
SubsonicM < 0.8Smooth flow, no shock waves
Transonic0.8 - 1.2Mixed sub/supersonic regions, shocks
Supersonic1.2 - 5.0Full shock wave system, sonic boom
HypersonicM > 5.0Extreme heating, chemical reactions

Frequently Asked Questions

Why does the speed of sound change with temperature?

Sound is a pressure wave that propagates through molecular collisions. At higher temperatures, gas molecules move faster and transmit the pressure disturbance more quickly. The speed of sound is proportional to the square root of absolute temperature: a = 20.05 sqrt(T in Kelvin) m/s for air.

What happens at Mach 1?

At Mach 1, pressure disturbances cannot travel ahead of the object, causing them to pile up into a shock wave (sonic boom). The transonic regime (Mach 0.8-1.2) is particularly challenging for aircraft design because different parts of the airframe may simultaneously experience subsonic and supersonic flow, creating complex shock-boundary layer interactions.

What is the fastest aircraft ever?

The SR-71 Blackbird holds the official air-breathing speed record at Mach 3.3 (3,530 km/h). The X-15 rocket plane reached Mach 6.7. The Space Shuttle reentered at about Mach 25. Current hypersonic research focuses on scramjet-powered vehicles targeting Mach 5-10+ for future aircraft and weapons.