Mach Number Calculator Formula

Understand the math behind the mach number calculator. Each variable explained with a worked example.

Use the Mach Number Calculator

Formulas Used

Speed of Sound

sound_speed = 331.3 + 0.606 * temperature

Mach Number

mach_number = object_speed / (331.3 + 0.606 * temperature)

Variables

VariableDescriptionDefault
object_speedObject Speed(m/s)680
temperatureAir Temperature(°C)20

How It Works

Mach Number

The Mach number is a dimensionless ratio comparing an object's speed to the speed of sound in the surrounding medium.

Formula

M = v / v_sound

  • M < 1: subsonic
  • M = 1: sonic (speed of sound)
  • M > 1: supersonic
  • M > 5: hypersonic

    • Worked Example

    An aircraft flying at 680 m/s in air at 20 degrees C.

    object_speed = 680temperature = 20
    1. 01v_sound = 331.3 + 0.606 * 20 = 343.4 m/s
    2. 02M = 680 / 343.4
    3. 03M = 1.980
    4. 04The aircraft is supersonic (M > 1)

    Frequently Asked Questions

    What happens at Mach 1?

    At Mach 1, a shock wave forms around the object, producing a sonic boom. This is called the sound barrier.

    Does the speed of sound change with altitude?

    Yes. Temperature decreases with altitude, so the speed of sound also decreases, meaning the same airspeed gives a higher Mach number at altitude.

    What is the fastest manned aircraft?

    The SR-71 Blackbird reached about Mach 3.3. The X-15 experimental aircraft reached Mach 6.7.

    Ready to run the numbers?

    Open Mach Number Calculator