How to use the true airspeed calculator
- Enter the calibrated airspeed in knots, the pressure altitude in feet, and the outside air temperature in Celsius.
- Read the true airspeed and Mach number in the results.
- Check the equivalent airspeed, density ratio and density altitude to see how thin the air is.
- Use the steps to follow the calculation from pressure to Mach to speed.
Formula
Static pressure p = 1013.25 (1 - 6.8755856e-6 h)^5.2558797 hPa
Impact pressure qc = 1013.25 [ (1 + 0.2 (CAS / 661.4786)^2)^3.5 - 1 ]
Mach M = sqrt( 5 [ (qc / p + 1)^(2/7) - 1 ] )
Speed of sound a = sqrt(1.4 x 287.05287 x T) with T in kelvin; TAS = M x a
Density ratio sigma = (p / 1013.25) / (T / 288.15); EAS = TAS sqrt(sigma)
The first formula is the pressure in the standard atmosphere up to 36,089 feet. 661.4786 knots is the speed of sound at sea level at 15 C.
Two flight levels
At 10,000 feet pressure altitude the static pressure is 696.82 hPa. With a calibrated airspeed of 150 knots and an outside air temperature of -4.8 C, the Mach number is 0.2727, the speed of sound is 638.3 knots and the true airspeed is 174.1 knots. The equivalent airspeed is 149.6 knots and the density ratio is 0.7384.
At 20,000 feet and -24.6 C, 250 knots calibrated gives Mach 0.5469 and a true airspeed of 336.0 knots, with static pressure 465.63 hPa and density ratio 0.5328. At sea level in standard air the true and calibrated speeds are equal.
Why the speeds differ
The airspeed indicator measures the pressure of the air pushed against the aircraft, which depends on how many air molecules hit per second, not on how fast the aircraft really moves over the ground in air. In thin air at altitude, an aircraft must move faster to get the same pressure, so true airspeed is higher than the indicated value. A rule of thumb adds about 2% per 1,000 feet, which this page replaces by the full calculation.
Calibrated airspeed is the indicated speed corrected for instrument and position errors. Equivalent airspeed also removes the compressibility of air, and true airspeed removes the effect of density. The Mach number compares the true speed with the speed of sound at the same temperature.
Limits and neighbors
The formulas assume subsonic flow in the standard atmosphere pressure model up to 36,000 feet, and they take the temperature you enter as the true outside temperature, not the temperature measured with ram heating. For a related figure, the density altitude calculator works from the altimeter setting and field elevation, and the speed of sound calculator shows the temperature dependence on its own.
The wind triangle calculator turns true airspeed into ground speed and heading, and the flight arrival time calculator plans the trip. This page is for learning and checking; it does not replace approved flight planning or the aircraft manual.
Assumptions and limits
- Flight is below Mach 1, in the standard-atmosphere pressure model between -1,000 and 36,000 feet of pressure altitude.
- The temperature entered is the true static air temperature, without ram rise.
- Calibrated airspeed already includes the corrections for instrument and position error.
- Density altitude and standard temperature use the standard lapse rate of 6.5 C per kilometer.
Frequently asked questions
What is the difference between indicated, calibrated and true airspeed?
Indicated is the raw reading, calibrated corrects it for instrument and installation errors, and true is the actual speed through the air. True is the one used for navigation and flight time.
Why does the page limit the altitude to 36,000 feet?
Above about 36,089 feet the standard temperature stops falling and the pressure formula changes. This page uses only the lower-atmosphere formula so every output stays correct.
What is pressure altitude?
It is the altitude shown when the altimeter is set to the standard pressure of 1013.25 hPa (29.92 inHg). It describes the pressure of the air at your level, which is what the airspeed formulas need.
Does wind change true airspeed?
No. True airspeed is the speed through the air mass. Wind affects the ground speed, which is the true airspeed combined with the wind vector.