Mach number calculator
The speed of sound falls with temperature, so the same true airspeed is a higher Mach number at altitude.
kt
ft
Mach number
0.7730
- Speed of sound
- 582.12 kt
- Speed of sound
- 299.47
- Speed of sound
- 1078.1 km/h
- True airspeed at your target Mach
- 454.05 kt
- Speed of sound at ISA for that altitude
- 576.48 kt
- Temperature deviation from ISA
- 4.3 degrees C
Show the working
- True airspeed = 450
- Static air temperature = -50
- Altitude = 35 000
- Target Mach number = 0.78
- temp_k = -50 + 273.15 = 223.15
- Speed of sound = sqrt(1.4 * 287.058 * 223.15) = 299.466
- Speed of sound = 299.466 / 0.5144444444444445 = 582.115
- Mach number = 582.115 > 0 ? 450 / 582.115 : 0 = 0.773 043
- True airspeed at your target Mach = 0.78 * 582.115 = 454.05
- isa_temp = 35 000 < 36089 ? 15 - 1.98 * 35 000/1000 : -56.5 = -54.3
- Speed of sound at ISA for that altitude = sqrt(1.4 * 287.058 * (-54.3 + 273.15)) / 0.5144444444444445 = 576.479
- Temperature deviation from ISA = -50 - -54.3 = 4.3
- Speed of sound = 299.466 * 3.6 = 1078.08
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- speed of sound = sqrt(gamma R T), which depends only on temperature
- Mach = TAS / speed of sound
Above the tropopause at about 36 089 feet the standard atmosphere is isothermal at -56.5 degrees Celsius, so the speed of sound stops falling.
This is a planning and study tool. Use certified charts, an approved flight manual and official publications for anything operational.