Convert aircraft Mach numbers to true airspeed in knots, km/h, and mph based on flight altitude and atmospheric temperature.
How This Calculator Works
The Mach number (named after Austrian physicist Ernst Mach) is a dimensionless ratio comparing the speed of an object to the local speed of sound in the surrounding gas:
Mach = True Airspeed ÷ Local Speed of Sound
Crucially, the speed of sound depends solely on ambient air temperature, not on air pressure or density. In warmer air near sea level (15°C / 59°F), sound travels at approximately 661.5 knots (1,225 km/h / 761 mph). High in the stratosphere at 35,000 feet, where the standard temperature drops to -56.5°C, sound slows down to only 573.8 knots (1,062 km/h / 660 mph).
Therefore, cruising at Mach 0.82 at sea level produces a vastly different true airspeed than flying at Mach 0.82 at FL390. Modern commercial jets cruise in the high subsonic regime between Mach 0.78 and 0.86 to optimize fuel efficiency and avoid aerodynamic wave drag.
Mathematical Formula
Worked Examples
Example 1: Boeing 787 Cruising at Mach 0.85 at FL390
At FL390 (39,000 ft), temperature is -56.5°C (216.65 K). Speed of sound is 573.6 knots.
TAS = 0.85 × 573.6 = 487.6 knots (903.0 km/h / 561.1 mph)
Example 2: Concorde Supersonic Cruise at Mach 2.0 at FL550
Concorde cruised at Mach 2.04 in the stratosphere.
TAS = 2.0 × 573.6 = 1,147.2 knots (2,124.6 km/h / 1,320.2 mph)
Frequently Asked Questions
Does air pressure affect the speed of sound?
No. In an ideal gas, the speed of sound depends exclusively on absolute temperature, regardless of atmospheric pressure.
What is the transonic flight regime?
The transonic regime occurs between roughly Mach 0.80 and 1.20, where airflow over curved wing surfaces accelerates to supersonic speeds even while the airplane as a whole is flying subsonic.
What is MMO on an airliner?
MMO stands for Maximum Operating Mach Number. It is the structural limit that flight crews must not exceed to prevent Mach tuck and aerodynamic shock stall.
Why do airliners switch from knots to Mach at high altitude?
At high altitudes, aerodynamic compressibility becomes the dominant limit on aircraft controllability, making Mach number the primary airspeed reference.
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