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Mach Number, Speed and Dry-Air Temperature Estimate

Relate positive object speed and sound speed to Mach number, with a retained approximate dry-air sound-speed and temperature inverse.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

At 0°C, the retained dry-air approximation gives sound speed 331.3 m/s; Mach 2 gives object speed 662.6 m/s.

M = v/c; c ≈ 331.3√(T_K/273.15)

Worked example

Enter these known values and leave the other values blank.

Temperature of air
0 °C
Mach number
2
Speed of object
662.6 m/s
Speed of sound
331.3 m/s

Assumptions and limitations

  • Object speed, sound speed and Mach number are positive magnitudes in this moving-flow workflow; zero and negative values are excluded. Temperature must be positive on the absolute Kelvin scale, with Celsius/Fahrenheit converted first.
  • Mach is the ratio of speed to the local sound speed. The retained air relation c≈331.3√(T_K/273.15) is an approximation for dry ideal air, not a universal sound-speed model or a humidity correction.
  • The equivalent initial temperatures are 20°C or 68°F by preference. Entering sound speed can infer the equivalent air temperature through this approximate relation; that inferred temperature is meaningful only under the stated air model. A sound speed for water or another gas does not establish an actual air temperature.
  • Use Mach and sound speed for object speed, two speeds for Mach, or object speed and Mach for sound speed. Temperature can supply sound speed; clear an unknown before solving backward. This does not supply aircraft performance, atmospheric altitude profiles, shock relations or a material property dataset.
  • The square-root relation has a mathematical positive-Kelvin domain. Real air can condense at low temperatures and its heat capacities vary; arithmetic precision does not establish physical accuracy in those regimes.

Common questions

Is Mach 1 a fixed speed in miles per hour?

No. Mach 1 equals the local sound speed, which depends on the medium and conditions. This retained dry-air model changes sound speed with absolute temperature.

Why can Celsius temperature be negative?

Negative Celsius is allowed above −273.15°C. The calculation converts to positive Kelvin before taking the square root.

What does the inferred temperature mean?

It is the temperature equivalent to the entered sound speed under the retained dry-air approximation. It is not a temperature measurement of an arbitrary medium.

References

Require positive absolute air temperature for the retained square-root dry-air sound-speed model; Celsius and Fahrenheit offsets are applied before this Kelvin-domain check.

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