Mach Angle Calculator
Enter flow speed and sound speed to compute the Mach number and the Mach angle μ = arcsin(1/M) of a supersonic cone.
Input Data
Results
At a glance:The Mach angle μ is the half-angle of the cone of disturbances (Mach cone) formed by an object moving faster than sound. It satisfies sin μ = 1/M, where M = v/a is the Mach number (v object speed, a local sound speed). For M ≤ 1 the angle is undefined (no shock cone; disturbances propagate ahead). As M increases, μ shrinks: at M=2, μ=30°; at M=√2, μ=45°. The Mach cone surface marks the shock wave. This tool computes M = v/a and μ = arcsin(1/M) for supersonic cases (returns undefined/0 for subsonic).
Formula
Mach number: M = v/a
Mach angle: sin μ = 1/M → μ = arcsin(1/M)
$$\mu = \arcsin\left(\frac{1}{M}\right), \quad M = \frac{v}{c}, \quad \text{supersonic when } M > 1$$How to Use
- Enter the flow speed v (m/s).
- Enter the local sound speed a (m/s).
- The calculator returns M and the Mach angle μ.
Case Studies
Supersonic jet
v = 680 m/s, a = 340 m/s.
M = 2, μ = arcsin(0.5) = 30°.
Shock cone half-angle 30°.
FAQ
Why is there no Mach angle below M=1?
Subsonic disturbances outrun the object and spread spherically ahead, so no cone forms. The Mach cone only exists for supersonic (M>1) motion.
How does μ change with speed?
μ = arcsin(1/M) decreases as M grows — faster objects have a narrower, sharper Mach cone.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.