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Mach Number Calculator

Find the Mach number.

How it is calculated

The Mach number is the ratio of an object's speed to the local speed of sound: M = v / c. Enter the velocity v and the speed of sound c in the same unit; metres per second is typical. If the sound-speed field is left empty or set to zero or less, the tool uses 343 m/s, the usual value for air at about 20 °C at sea level. The result is rounded to two decimals and labelled Subsonic below 1 and Supersonic from 1 upward. Sound travels faster in warm air and slower in cold or thin air, so the speed of sound at altitude is lower than 343.

Worked example

An aircraft flies at v = 680 m/s where the speed of sound is c = 340 m/s. Mach = 680 / 340 = 2.00. The result is Mach 2.00, in the regime Supersonic, since the value is 1 or more. With the default 343 m/s the same speed would give 1.98, which shows how much the assumed speed of sound matters.

Try this example →

Common mistakes

  • Entering velocity in km/h while the speed of sound is in m/s; both must be in one unit.
  • Using 343 m/s at high altitude. In cold air at cruising height sound travels at roughly 295 m/s, so the same speed gives a higher Mach number.
  • Treating Mach 1.0 exactly as dangerous or special; the transition region around it, called transonic, is not shown by the two-way label.
  • Confusing Mach with a fixed speed. One Mach is different on every day and at every altitude.
  • Entering sound speed in air for an object moving through water or another medium.

About this calculator

This calculator finds the Mach number — the ratio of an object's speed to the local speed of sound — using M = v / a. Mach 1 is the speed of sound itself, so a Mach number above 1 means the object is traveling supersonically.

Aerospace engineering students use it to check homework on high-speed flight, and pilots and aviation enthusiasts use it to understand how fast an aircraft is really flying relative to the air around it, since the speed of sound itself changes with altitude and temperature. Enter the object's speed and the speed of sound to get the Mach number.

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