Below about FL250 most aircraft fly to an indicated airspeed. Above it, jets switch to flying a Mach number: their speed as a fraction of the local speed of sound. Mach 0.78 does not mean the same speed in knots at every level, because the speed of sound depends only on air temperature. Convert between Mach and true airspeed for any level and temperature with the Mach Number Calculator.
Why Mach, and not knots?
As an aircraft approaches the speed of sound, air flowing over the wing speeds up locally and can reach Mach 1 even when the aircraft itself does not. That creates shock waves, buffet and a sharp rise in drag. These effects depend on Mach number, not on knots. So at high altitude the limit that matters is a maximum Mach number (MMO), and crews cruise at a planned Mach number, for example M0.78.
The speed of sound depends on temperature only
The speed of sound in air is:
a (kt) ≈ 38.97 × √T, where T is the outside air temperature in kelvin (°C + 273.15).
At 15 °C (ISA sea level) that gives 661.5 kt. Pressure and altitude do not appear in the formula: only temperature. A cold day at FL350 lowers the speed of sound, so the same Mach number gives a lower true airspeed.
True airspeed = Mach × a
Speed of sound and cruise TAS in the standard atmosphere
| Level | ISA temp | Speed of sound | TAS at M0.78 | TAS at M0.82 |
|---|---|---|---|---|
| Sea level | 15.0 °C | 661 kt | 516 kt | 542 kt |
| FL100 | −4.8 °C | 638 kt | 498 kt | 523 kt |
| FL200 | −24.6 °C | 614 kt | 479 kt | 504 kt |
| FL250 | −34.5 °C | 602 kt | 470 kt | 494 kt |
| FL300 | −44.4 °C | 589 kt | 460 kt | 483 kt |
| FL350 | −54.3 °C | 576 kt | 450 kt | 473 kt |
| FL370 and above | −56.5 °C | 574 kt | 447 kt | 470 kt |
Above the ISA tropopause, at about 36,090 ft, the standard temperature stays at −56.5 °C, so the speed of sound and the TAS for a given Mach stop changing with height.
Worked example
An airliner cruises at M0.78 at FL350. The actual outside air temperature is −50 °C, which is ISA+4.
- Temperature in kelvin: −50 + 273.15 = 223.15 K.
- Speed of sound: 38.97 × √223.15 = 38.97 × 14.94 ≈ 582 kt.
- TAS: 0.78 × 582 ≈ 454 kt.
On a standard day the same Mach would give 450 kt. The 4 °C warmer air adds about 4 kt of true airspeed. That small effect adds up over a long flight, which is why flight plans use forecast temperatures as well as winds.
Why the crossover altitude exists
During a climb at constant indicated airspeed, the true airspeed and Mach number both increase. At some level, the climb IAS and the climb Mach number give the same speed. That is the crossover altitude, often around FL270 to FL310 for typical jet climb speeds. Above it the crew holds Mach instead of IAS. In a descent the change happens the other way round. Holding IAS above the crossover would let the Mach number keep rising towards the limit.
Common mistakes
- Using a sea-level speed of sound. 661 kt is only right at 15 °C. At cruise levels it is roughly 13% lower.
- Forgetting to convert to kelvin. The square root must be taken of the absolute temperature.
- Using pressure altitude as if it set the speed of sound. Altitude matters only because it is usually colder up there. Use the actual outside air temperature when you know it.
- Mixing up Mach and IAS limits. VMO (an IAS limit) protects the structure at lower levels; MMO protects against compressibility effects higher up.
FAQ
Is Mach 1 the same speed everywhere?
No. It changes with temperature. It is about 661 kt at 15 °C and about 574 kt at −56.5 °C.
Why do jets fly slower in knots at high altitude?
They hold a fixed Mach number, and the speed of sound falls as the air gets colder. In true airspeed they are still faster than at low level, but the TAS for the same Mach is lower than it would be in warm air.
Does humidity matter?
Very slightly. At cruise levels the air holds almost no water vapour, so the dry-air formula is accurate enough for flight planning.
Sources and further reading
Speed-of-sound formula and ISA values from the ICAO Standard Atmosphere (Doc 7488) and the FAA Airplane Flying Handbook and Aircraft Dispatcher training material. Use the aircraft flight manual for speed limits and the operator’s flight plan for cruise Mach.
Last reviewed: November 2026.