Mach Number Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The Mach number is calculated with M = speed ÷ speed of sound. An object moving at 686 m/s in air (speed of sound ≈ 343 m/s) reaches exactly Mach 2, or twice the speed of sound.
Explanation
The Mach number is a dimensionless number that expresses the speed of a moving object relative to the speed of sound in the medium it travels through, rather than as an absolute value (m/s or km/h). This way of measuring speed is especially relevant in aerodynamics, because the behavior of air around an object changes fundamentally depending on whether its speed is below, near, or above that of sound: below Mach 1 (subsonic regime), air flows relatively predictably around the object; around Mach 1 (transonic regime), complex compressibility phenomena appear; beyond Mach 1 (supersonic regime), the object outruns its own pressure waves, which generates the characteristic shock wave of the sonic boom — a phenomenon related to the acoustic Doppler effect (see our Doppler effect calculator), where the perceived frequency shift becomes extreme as the source's speed approaches that of sound. The speed of sound itself isn't a universal constant: it depends on the temperature and composition of the medium traveled through (about 343 m/s in air at 20°C at sea level, but noticeably lower at high altitude where the air is colder, which is why a plane can cross Mach 1 at a different absolute speed depending on its flight altitude). This number complements our Reynolds number calculator, another dimensionless number used in fluid mechanics, but based on the flow's viscosity rather than its compressibility — the two numbers characterize different, complementary aspects of the same flow.
Example: 686 m/s in air
Inputs
Speed: 686 m/s. Speed of sound: 343 m/s.
Calculation
M = 686 ÷ 343 = 2.
Result
This object is moving at exactly Mach 2, or twice the speed of sound.
Frequently asked questions
Why does the speed of sound vary with altitude?
The speed of sound in air mainly depends on temperature (not atmospheric pressure itself): air cools with altitude up to the tropopause, which slows the propagation of sound. That's why a plane can cross Mach 1 at a lower absolute speed (in km/h) at high altitude than at sea level, since the reference speed of sound is itself lower up there.
What physically happens when an object exceeds Mach 1?
Below Mach 1, a moving object in air "warns" the air ahead of it through the pressure waves it generates, which travel faster than it does. Beyond Mach 1, the object outruns its own pressure waves, which then pile up into a concentrated shock front (the shock wave), perceived on the ground as the characteristic sonic boom when breaking the sound barrier.
Does the Mach number also apply in media other than air?
Yes, the principle applies in any medium where sound propagates (water, other gases, solids), provided you use the speed of sound specific to that medium rather than air's: sound travels, for example, much faster in water (about 1,480 m/s) than in air, which completely changes the speeds corresponding to each Mach number.