What Is the Mach Number?
The Mach number (M) is a dimensionless quantity that expresses the speed of an object relative to the speed of sound in the surrounding medium. Named after physicist Ernst Mach, it is fundamental in aerodynamics and fluid dynamics for describing how compressibility effects influence airflow around aircraft, rockets, and projectiles.
How to Use This Calculator
Enter the object's speed and the local speed of sound, both in metres per second (m/s). The speed of sound at sea level in dry air at 15 °C is about 340–343 m/s, but it decreases with altitude and temperature, so use the value appropriate to your conditions. The calculator returns the Mach number and classifies the flow regime.
The Formula Explained
The Mach number is simply the ratio \(M = v / a\), where v is the object's velocity and a is the speed of sound in the same medium. Because both are speeds, the units cancel and M has no dimension. \(M < 1\) is subsonic, \(M \approx 1\) is transonic, \(M > 1\) is supersonic, and \(M > 5\) is hypersonic.
$$M = \frac{\text{Object Speed (m/s)}}{\text{Speed of Sound (m/s)}}$$
Worked Example
An aircraft flies at 600 m/s where the local speed of sound is 300 m/s. Then $$M = 600 / 300 = 2.0.$$ The aircraft is travelling at Mach 2, which is in the supersonic regime.
FAQ
Does the speed of sound change? Yes. It depends mainly on temperature (and thus altitude). At high altitude the speed of sound is lower, so the same true airspeed yields a higher Mach number.
What is the sound barrier? It refers to the sharp rise in drag near Mach 1 (the transonic region). Breaking the sound barrier means accelerating past \(M = 1\).
Can I use other units? Yes, as long as the speed and the speed of sound use the same unit, the Mach number is identical since the units cancel.
