Mach Cone Angle Calculator

About this calculator

When an object moves faster than the speed of sound, it outruns the pressure waves it generates, which pile up into a cone-shaped shockwave trailing behind it — the Mach cone, named after physicist Ernst Mach. The half-angle of that cone, called the Mach angle (μ), is given by μ = arcsin(1/M), where M is the object's Mach number (speed divided by the local speed of sound).

At exactly Mach 1 the angle is 90° (the cone degenerates into a flat wavefront), and it narrows as speed increases — at Mach 2 it's about 30°, at Mach 3 about 19.5°. Aerospace engineers use this relationship to predict shockwave geometry around supersonic aircraft and missiles, and it is also what determines the geometry of the audible sonic boom that sweeps across the ground beneath a supersonic flight path.