Mach number calculator
Mach number is your true airspeed divided by the speed of sound where you are. The speed of sound depends only on temperature, which is why the same true airspeed gives a higher Mach number in cold air.
Calculator
This is an educational and planning aid. Use current official weather, your aircraft flight manual, and the rules that apply to your flight before you act on any figure here. See the aviation disclaimer.
What the result means
Mach 0.80 means you are moving at 80 percent of the local speed of sound. It is the number that matters at high level, because compressibility effects depend on it rather than on airspeed.
The local speed of sound is shown alongside. At 15 C it is 661 kt, and at a typical cruise temperature of -56 C it has fallen to about 573 kt.
Above roughly Mach 0.75 airflow over parts of the wing is already supersonic even though the aircraft is not. That is the transonic range, and it is why airliners have a maximum operating Mach number as well as a maximum speed.
When this is useful
- At high altitude, where aircraft limits are expressed in Mach rather than airspeed.
- Understanding why an airliner climbs at a constant indicated airspeed and then switches to a constant Mach number partway up.
- Converting between a Mach figure from a flight manual and a true airspeed for flight planning.
How it is calculated
The speed of sound in a gas depends on the square root of its absolute temperature. In air it works out at 661.48 kt multiplied by the square root of the temperature in kelvin divided by 288.15.
Dividing true airspeed by that figure gives the Mach number. Pressure and altitude do not appear at all, which surprises people, but it is correct: they affect the speed of sound only through their effect on temperature.
speed of sound (kt) = 661.48 x sqrt(temperature in kelvin / 288.15), Mach = TAS / speed of sound
Worked example
- True airspeed
- 400 kt
- Outside air temperature
- -30 C
The speed of sound at -30 C is about 608 kt, so 400 kt true is Mach 0.66.
Check: At the standard sea level temperature of 15 C the formula must return exactly 661.48 kt, and it does. At -30 C, which is 243.15 K, the square root of 243.15 divided by 288.15 is 0.9186, and 661.48 multiplied by that is 607.6 kt.
Limitations
- This gives the speed of sound in dry air. Humidity changes it very slightly, far below the precision anyone needs in the cockpit.
- The altitude shown at the bottom of the results is context only. It tells you where that temperature would be standard, which on a real day it usually is not.
- Above Mach 1 the subsonic assumptions behind most airspeed instrumentation no longer hold, and this page stops being useful for anything other than the ratio itself.
Common mistakes
- Assuming the speed of sound falls with altitude directly. It falls because temperature falls, and in the stratosphere where temperature holds constant, so does the speed of sound.
- Using total air temperature from the probe rather than static air temperature.
- Entering calibrated or indicated airspeed. Mach number is defined against true airspeed.
Sources
- Mach Number and Speed of Sound , NASA Glenn Research Center