Mach Number Calculator

What is Mach Number?

The Mach number (M) is a dimensionless quantity that represents the ratio of an object's speed to the local speed of sound in the surrounding medium. Named after Austrian physicist Ernst Mach, this number is fundamental in aerodynamics, aerospace engineering, and fluid dynamics for classifying flow regimes and predicting aerodynamic behavior.

Mach Number Formula

The Mach number is calculated using the following formula:

M = v / a

Where M is the Mach number, v is the velocity of the object relative to the medium, and a is the local speed of sound in the medium. Since the speed of sound varies with temperature and the medium, the same velocity can correspond to different Mach numbers at different altitudes or in different gases.

Flow Regime Classifications

The Mach number classifies aerodynamic flow into four main regimes:

• Subsonic (M < 0.8): Flow behaves like an incompressible fluid with smooth streamlines. Most commercial aircraft cruise in this regime.
• Transonic (0.8 ≤ M < 1.2): Mixed regime where pockets of supersonic flow create local shock waves and drag increases sharply.
• Supersonic (1.2 ≤ M < 5): Well-defined oblique shock waves form, requiring specialized aerodynamic designs like swept wings and area-ruled fuselages.
• Hypersonic (M ≥ 5): Extreme aerodynamic heating dominates, requiring advanced thermal protection systems. Re-entry spacecraft and advanced missiles operate in this regime.

Using the Three Calculation Modes

Our Mach number calculator offers three calculation modes:

• Mach Number: Calculate the Mach number when you know the velocity and local speed of sound.
• Velocity: Find the actual speed when you know the Mach number and speed of sound.
• Speed of Sound: Determine the local speed of sound from velocity and Mach number.