Mach Number Calculator

The Mach number, M, is the dimensionless ratio of an object's speed to the local speed of sound in the surrounding medium. It is the standard way aerospace engineers and pilots describe how fast something is moving relative to the speed limit set by sound itself.

M = v/c, where v is the object's velocity and c is the local speed of sound in the surrounding air (or other fluid) at that specific location and temperature.

Because the speed of sound depends on air temperature (and therefore altitude), an aircraft flying at a fixed true airspeed has a different Mach number at different altitudes. Using the local speed of sound as the reference makes Mach number a physically meaningful measure of how close a vehicle is to compressibility and shock-wave effects, regardless of altitude.

The standard aerodynamics convention is: subsonic below Mach 0.8, transonic from 0.8 to 1.2 (where both subsonic and supersonic flow regions can coexist around an aircraft), supersonic from 1.2 to 5, and hypersonic above Mach 5.

Mach 1 means traveling at exactly the local speed of sound (M=1). It is not a single fixed speed worldwide, it depends on the local air temperature, so Mach 1 is about 340 m/s at sea level but only about 295 m/s at high-altitude cruise, where the air is much colder.

As an aircraft approaches Mach 1, air can no longer smoothly flow out of the way fast enough, causing shock waves to form and dramatically increasing drag (the so-called 'sound barrier'). Aircraft designed to fly supersonically use special shapes to manage these shock waves efficiently.

Mach number matters anywhere compressible flow effects are significant: rocket and missile aerodynamics, high-speed wind tunnel testing, high-velocity projectile ballistics (a rifle bullet can exceed Mach 2-3), and even astrophysical shock waves in supernova remnants, which are often described using Mach number relative to the local interstellar medium.

No, Mach number depends only on the object's velocity relative to the local speed of sound, not on its size, shape, or mass. However, the practical effects of a given Mach number (like when shock waves form) do depend on the object's shape and size.

Commercial airliners typically cruise around Mach 0.78 to 0.85, comfortably subsonic. The Concorde, a supersonic passenger jet retired in 2003, cruised at about Mach 2.0, twice the local speed of sound.

Yes, the same definition (velocity divided by local speed of sound in that medium) applies to any fluid, though it is most commonly used for air in aerospace contexts. The speed of sound differs enormously between fluids (much faster in water and solids than in air), so the same object speed corresponds to a very different Mach number in each.