Mach Number & Speed of Sound Calculator (Standard Atmosphere)
The speed of sound depends only on air temperature, so it falls as you climb until about 11 km, then stays the same. The Mach number is your speed divided by the local speed of sound.
Standards:
- AP2 Unit 14
- CCSS HSN-Q.A.1
Our alignment; not reviewed by the standards bodies.
The equation
Worked example
- Given
- Altitude, standard atmosphere (m, 0–20 000): 11000 m
- True airspeed V (m/s): 250 m/s
- Answer
- Air temperature: 216.65 K
- Air temperature: -56.50 °C
- Speed of sound a: 295.07 m/s
- Speed of sound a: 1062.3 km/h
- Mach number M: 0.847
- Check
- The U.S. Standard Atmosphere 1976 tables give 340.29 m/s at sea level and 295.07 m/s at 11 km; the build checks both.
Assumptions
Dry air as an ideal gas, U.S. Standard Atmosphere 1976 (real days are warmer or colder).
Go deeper
Sources
- NOAA, NASA, USAF, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, 1976.
- J. D. Anderson Jr., Fundamentals of Aerodynamics, 6th ed., McGraw-Hill, 2017.
- NASA Glenn Research Center, Beginner’s Guide to Aeronautics.