Mach number and the local speed of sound
Mach number is the ratio of an object or flow speed to the local speed of sound. It is dimensionless, so the two speeds must use identical units.
The speed of sound is not universal. It depends on the medium and thermodynamic conditions; 343 m/s is only an approximate example for dry air near 20 °C.
How to use the Mach number calculator
- Choose the unknown: Select Mach number, object speed, or local speed of sound.
- Match speed units: Enter object speed and sound speed in m/s for this calculator.
- Use local conditions: Supply sound speed for the actual gas, temperature, and state.
- Calculate: Review the ratio without treating the example sound speed as universal.
Formula and variables
Divide object speed v by local sound speed a, using the same speed unit for both.
M = v/a- M — Mach number
- Ratio of object or flow speed to local sound speed (dimensionless)
- v — Object speed
- Speed relative to the surrounding medium (m/s)
- a — Local speed of sound
- Sound speed in the medium at local conditions (m/s)
Sonic speed in the example air condition
An object travels at 343 m/s where the local speed of sound is 343 m/s.
- Object speed
- 343 m/s
- Sound speed
- 343 m/s
- M = 343/343 = 1
Result: The Mach number is 1.
The object speed equals the local speed of sound for the stated condition.
Understanding your results
Mach number is condition-dependent
The same object speed can produce a different Mach number when temperature, gas composition, or other local conditions change.
- M < 1 is subsonic.
- M = 1 is sonic.
- M > 1 is supersonic.
- Near Mach 1, local flow around an object can contain both subsonic and supersonic regions.
Assumptions
- Object speed is measured relative to the surrounding medium.
- A single representative local sound speed is appropriate.
- Both speeds use the same units.
Limitations
- Does not calculate sound speed from temperature, gas composition, humidity, or altitude.
- Does not model compressible flow, shocks, drag, or local velocity variations.
- Flight-regime labels alone do not predict aerodynamic performance.
Common mistakes
- Using ground speed instead of speed relative to the air.
- Assuming 343 m/s at every altitude and temperature.
- Mixing mph with m/s in the ratio.
- Treating Mach number as a speed unit rather than a ratio.
Practical use cases
Aerodynamics education
Relate flow speed to acoustic propagation speed.
Condition-specific conversion
Convert Mach to m/s after establishing local sound speed.
Frequently asked questions
Is Mach 1 always 343 m/s?
No. Mach 1 equals the local speed of sound, which varies with medium and conditions.
Does altitude affect Mach number?
It can, mainly because atmospheric temperature changes the local speed of sound.
Is Mach number dimensionless?
Yes. It is a ratio of two speeds expressed in the same unit.
Sources and review
- Mach Number — NASA Glenn Research Center. Accessed 2026-07-13.
- Mass Flow Rate Equations — NASA Glenn Research Center. Accessed 2026-07-13.
Reviewed 2026-07-13.