Mach Number Calculator
Convert Mach number to true airspeed, or TAS to Mach, from outside air temperature. At FL350 on a standard day the speed of sound is about 576 kt, so M0.78 is about 450 kt TAS.
Dry-air formula, accurate for flight planning. Use the aircraft flight manual for speed limits (VMO/MMO).
Method
Speed of sound a (kt) = 38.967854 × √(OAT + 273.15). TAS = Mach × a, and Mach = TAS ÷ a. When you choose a flight level, the ISA temperature is 15 °C − 1.98 °C per 1,000 ft up to the tropopause (about 36,090 ft), then −56.5 °C, plus your ISA deviation.
Quick reference: speed of sound in ISA
| Level | ISA temp | Speed of sound |
|---|---|---|
| Sea level | 15.0 °C | 661 kt |
| FL200 | −24.6 °C | 614 kt |
| FL300 | −44.4 °C | 589 kt |
| FL350 | −54.3 °C | 576 kt |
| FL370+ | −56.5 °C | 574 kt |
Worked example
M0.78 at an OAT of −50 °C: a = 38.97 × √223.15 ≈ 582 kt, so TAS ≈ 454 kt, about 4 kt more than on a standard day at FL350.
Read the guide: Mach Number Explained: Speed of Sound, TAS and Crossover Altitude
ICAO Standard Atmosphere (Doc 7488) and FAA training material.
Last reviewed: November 2026
Frequently asked questions
Why does only temperature matter?
In an ideal gas the speed of sound depends on temperature alone. Altitude matters only because it is usually colder higher up.
Should I enter static or total air temperature?
Static (true outside) air temperature. Total air temperature at jet speeds reads several degrees warmer because of ram heating.
Scenario: the same Mach on a hot and a cold day
An airliner plans M0.80 at FL370. On a standard day the temperature there is −56.5 °C, the speed of sound is about 574 kt and the TAS is about 459 kt. On a day that is ISA+10 (−46.5 °C), the speed of sound rises to about 586 kt and the TAS to about 469 kt. Over a 6-hour flight, those 10 extra knots are worth about 60 NM, roughly 8 minutes of flying. This is one reason flight plans use forecast temperatures as well as winds.
Common mistakes
- Using the 661 kt sea-level speed of sound at cruise level.
- Entering total air temperature (TAT) instead of static air temperature.
- Treating Mach as an indicated airspeed. At constant Mach, IAS falls as you climb.