How to use it
- Choose Calculate: Mach to TAS to find the true airspeed, or TAS to Mach to find the Mach number.
- Choose Air temperature from: the Outside air temperature you read, or the ISA altitude when you have no temperature.
- Type the Mach number or the True airspeed, then read Result and Speed of sound.
- Use the table to see the true airspeed at each Mach number from 0.50 to 0.90.
How Mach number and true airspeed are linked
The Mach number is the ratio of the speed of the aircraft to the speed of sound in the air (NASA Glenn Research Center, Mach Number). The speed of sound depends on the temperature alone: a = √(γRT), where γ is 1.40 and R is 287.05 J/(kg K) for dry air (NASA Glenn, Speed of Sound).
The true airspeed is the Mach number times the speed of sound at the air temperature where the aircraft is, so the same Mach number gives a lower true airspeed in cold air. The page works the speed of sound from the outside air temperature, or from the ISA temperature at an altitude.
a = √(1.4 × 287.05 × T) (T in kelvin, a in m/s)
TAS = M × a
M = TAS ÷ a
1 kt = 0.514444 m/s; TAS in km/h = TAS in kt × 1.852- At sea level in the standard atmosphere, the speed of sound is 340.3 m/s, which is 661.5 kt.
- At −56.5 °C, the tropopause temperature of the standard, it is 295.1 m/s, which is 573.6 kt.
- The ISA altitude gives the standard temperature there. The real temperature may be higher or lower, so use the outside air temperature when you have it.
What this page does not cover
- The aircraft's Mach limit, its maximum operating speed and its buffet and compressibility limits. Those are in the aircraft's manual.
- Calibrated and indicated airspeed, which need the pressure and the compressibility correction.
- Total air temperature and the temperature rise at high speed, which the outside air temperature does not include.
- This page is for training and planning practice, not for real flight.
Worked example: Mach 0.78 at 35,000 ft in the ISA
At 35,000 ft the ISA temperature is −54.3 °C (218.81 K). The speed of sound is √(1.4 × 287.05 × 218.81) = 296.5 m/s, which is 576.4 kt.
TAS = 0.78 × 296.5 m/s = 231.3 m/s, which is 449.6 kt, or 832.7 km/h.
| Output | Value |
|---|---|
| Temperature | -54.3 °C (218.81 K) |
| Speed of sound | 576.4 kt (296.5 m/s) |
| Result | TAS 449.6 kt (832.7 km/h) |
Frequently asked questions
What is the difference between Mach number and true airspeed?
The Mach number is the speed as a fraction of the speed of sound at that temperature. True airspeed is the speed through the air in knots. The two are linked by the speed of sound, which changes with the air temperature.
Why does the same Mach number give a different TAS at another altitude?
The speed of sound falls as the air gets colder with height. At the same Mach number the TAS is therefore lower at high altitude in the standard atmosphere, where it is colder.
Should I use the outside air temperature or the ISA temperature?
Use the outside air temperature when you have a reliable reading, because it is the real air. The ISA temperature is the standard value at an altitude and is useful only when no temperature is known.
Why is the total air temperature not the right input?
The total air temperature includes the rise from the air stopped at the front of the aircraft, so it is higher than the static air temperature at speed. The speed of sound uses the static temperature of the air around the aircraft.
Can I use these numbers for a real flight?
No. The page is for training and planning practice. Use the aircraft's manual, its speed limits and the current weather for a real flight.
Sources
- NASA Glenn Research Center: Mach Number
- NASA Glenn Research Center: Speed of Sound (a = √(γRT))
- Wikipedia: International Standard Atmosphere (the ISA temperature at an altitude)
Figures and text last checked on Tuesday, November 10, 2026.