Mach to TAS Calculator
True airspeed (TAS) is the actual speed of the aircraft through the air mass. At high altitudes and high speeds, aircraft instruments often display Mach number rather than airspeed in knots. To convert from Mach to TAS, you need to know the local speed of sound, which depends on the outside air temperature (OAT). This calculator uses the standard atmospheric physics formula for the speed of sound in air and multiplies by the Mach number to give TAS in knots. Enter your Mach number and the outside air temperature (SAT/OAT) in degrees Celsius. The calculator also shows the speed of sound at that temperature and the result in km/h and m/s.
Mach to TAS formula
T(K) = OAT(C) + 273.15
a (m/s) = sqrt(1.4 x 287.058 x T_K) = sqrt(401.87 x T_K)
TAS (m/s) = Mach x a
TAS (knots) = TAS (m/s) x 1.94384
The speed of sound formula uses gamma = 1.4 (ratio of specific heats for dry air) and R = 287.058 J/(kg K) (specific gas constant for dry air). These are ICAO standard atmosphere values. At -54 degrees C (219.15 K), the speed of sound is approximately 574 knots. At Mach 0.82, TAS is approximately 471 knots.
Mach number reference values
- Typical jet cruise: Mach 0.78 to 0.86.
- Concorde cruise: Mach 2.02 (retired).
- Speed of sound at ISA sea level (15 degrees C): 661.5 knots.
- Speed of sound at FL350 ISA (-54.3 degrees C): approximately 574 knots.
- Most modern jets have a maximum operating Mach (MMO) of 0.87 to 0.92.
Mach to TAS calculator: frequently asked questions
What is a Mach number?
A Mach number is the ratio of an object's speed to the local speed of sound in the surrounding medium. Mach 1.0 means the aircraft is traveling at exactly the speed of sound. Mach 0.80 means 80% of the local speed of sound.
How does temperature affect the Mach-to-TAS conversion?
The speed of sound in air depends on temperature: a = sqrt(gamma x R x T), where T is in Kelvin, gamma = 1.4 (ratio of specific heats for dry air), and R = 287.058 J/(kg K). Colder air has a lower speed of sound, so the same Mach number corresponds to a lower TAS at altitude versus sea level.
Why do high-altitude aircraft use Mach instead of knots?
Above a transition altitude (typically FL280 in the US), Mach number is more relevant to aerodynamic performance than calibrated or indicated airspeed. Compressibility effects become significant near Mach 1.0, so aircraft limiting speeds are specified in Mach (MMO) at high altitude.
What is the speed of sound at sea level ISA?
At ISA sea level (15 degrees C = 288.15 K), the speed of sound is approximately 661.5 knots (340.3 m/s). At cruise altitude (FL350, approximately -54.5 degrees C = 218.65 K), it drops to approximately 573.8 knots.
How do I find the outside air temperature at cruise altitude?
The outside air temperature (OAT or SAT) is shown on the aircraft's instruments or provided by datalink weather. For planning, use the ISA temperature: ISA(T) = 15 - 1.98 x (altitude in 1,000 ft), down to the tropopause at approximately -56.5 degrees C.
Official sources
- ICAO Standard Atmosphere (Doc 7488/3): icao.int.
- NIST Reference on Constants, Units, and Uncertainty: physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.