How this calculator works
Mach number uses local fluid conditions, so the same vehicle speed can correspond to different Mach numbers at different temperatures. For a calorically perfect gas, sound speed is the square root of specific heat ratio times specific gas constant times absolute static temperature. Dry-air defaults are rounded approximations near ordinary atmospheric conditions. Moisture, composition and high-temperature changes in heat capacity can require a more detailed sound-speed model.
Formula
M = v/a; a = sqrt(gamma R T). v = Ma; T = (v/M)^2/(gamma R). Use local static temperature, not stagnation temperature.
Worked example
At a local sound speed of 340 m/s, an object travelling 170 m/s has Mach 0.5. At 680 m/s it has Mach 2. With gamma = 1.4, R = 287.05 J/(kg K) and T = 288.15 K, a is about 340.2923 m/s.
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Frequently asked questions
Is Mach 1 a fixed speed?
No. It is the local sound speed, which varies with the medium and its state.
Should I use ground speed?
Use speed relative to the fluid. Aircraft ground speed differs from airspeed in wind.
Can Celsius be selected?
Yes. The temperature input converts to kelvin before the gas equation is evaluated.