Mach Number Calculator
Enter flow speed and the speed of sound to compute the Mach number M = v/a.
Input Data
Results
At a glance:The Mach number M = v/a is the ratio of a flow or object speed v to the local speed of sound a. It classifies flow regimes by compressibility: subsonic M<1 (density ~constant), transonic M≈1 (shocks begin), supersonic 1<M<5 (shock waves, Mach cone), hypersonic M>5 (strong heating, dissociation). a depends on the medium: in an ideal gas a = √(γRT/M_molar). The Mach number compares inertial to compressibility (acoustic) effects and determines whether density changes matter. This tool computes M = v/a from the two speeds.
Formula
Mach number: M = v/a
Sound speed (ideal gas): a = √(γ·R·T/M)
$$\mathrm{Ma} = \dfrac{v}{a}$$How to Use
- Enter the speed v (m/s).
- Enter the local speed of sound a (m/s).
- The calculator returns M.
Case Studies
Commercial airliner
v = 250 m/s, a = 340 m/s (cruise).
M ≈ 0.74.
Subsonic, efficient cruise below the drag rise near M=1.
FAQ
What does M = 2 mean?
The object moves at twice the speed of sound — supersonic, producing a Mach cone with half-angle μ = arcsin(1/2)=30°.
Why does the speed of sound matter?
It sets the threshold for compressibility effects; comparing v to a (i.e. M) tells whether density changes and shocks appear.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.