Mach Number Calculator
Enter an object's speed and the local speed of sound to get the Mach number — and find out whether the motion is subsonic, sonic, supersonic, or hypersonic.
One simple ratio
The Mach number is just the object's speed divided by the speed of sound (M = v ÷ a). It is dimensionless — the same number in any unit system.
Use matching units
Enter the object speed and the speed of sound in the same units (m/s here). Because both are speeds, the units cancel and the Mach number is unitless.
What is the Mach number?
Speed relative to sound
The Mach number is the ratio of an object's speed to the speed of sound in the surrounding medium. Named after physicist Ernst Mach, it tells you how fast something is moving compared with how fast sound travels around it. The Mach number calculator turns two speeds — the object's velocity and the local speed of sound, both in metres per second — into a single dimensionless figure. It is the number pilots, engineers, and physicists use to describe flight regimes, because the air behaves very differently below, at, and above the speed of sound.
Enter an object speed and the local speed of sound to get the Mach number instantly — and see which flight regime it falls into.
The Mach number is the object's speed divided by the speed of sound in the medium it moves through.
M = v ÷ aHere v is the object's speed and a is the local speed of sound. Both are measured in the same units, so they cancel and the Mach number carries no unit. At sea level in dry air at 20 °C the speed of sound is about 343 m/s, so an object moving at 343 m/s is at exactly Mach 1.
Suppose an aircraft flies at 686 m/s through air where the speed of sound is 343 m/s.
Note the two speeds
Object speed v = 686 m/s; local speed of sound a = 343 m/s.
Divide the speeds
686 ÷ 343 = 2 — the object's speed in units of the speed of sound.
Read the regime
M = 2, so the aircraft flies at Mach 2 — twice the speed of sound, firmly in the supersonic range.
The Mach number sorts motion into named regimes. Below Mach 1 (M < 1) the object is subsonic — it travels slower than sound, like a typical car or a passenger jet at cruise. At exactly Mach 1 (M = 1) it is sonic, moving at the speed of sound; this is where shock waves form and a sonic boom can be heard. Above Mach 1 (M > 1) the object is supersonic, outrunning the sound it produces, as a fighter jet or Concorde did. Beyond Mach 5 (M > 5) the motion is hypersonic, the realm of re-entry capsules and advanced missiles, where the air heats dramatically and its behaviour changes again. Because the speed of sound itself drops with altitude and temperature, the same true speed gives a higher Mach number high up than at ground level — which is why aircraft are rated by Mach number rather than by raw velocity.
The formula is exact, but a couple of practical points are worth keeping in mind for accuracy.
The speed of sound is not fixed
The Mach number depends entirely on the local speed of sound, which changes with the medium, its temperature, and altitude — about 343 m/s in air at 20 °C but only around 295 m/s in the cold thin air at cruising height. Use the correct speed of sound for your conditions, and keep both speeds in the same units, or the Mach number will be wrong. This calculator covers steady motion through a uniform medium and does not model the complex shock physics that occur right around Mach 1.