True airspeed calculator
The airspeed indicator measures pressure, not speed. As air thins with altitude the same pressure means a higher real speed, so the number on the dial understates how fast you are actually moving through the air.
Calculator
This is an educational and planning aid. Use current official weather, your aircraft flight manual, and the rules that apply to your flight before you act on any figure here. See the aviation disclaimer.
What the result means
True airspeed is your speed relative to the air mass around you. It is what goes into the wind triangle and what, combined with wind, produces groundspeed.
Equivalent airspeed is shown as a middle step. It is calibrated airspeed with the compressibility error removed, and it matters above roughly 200 kt or 10,000 ft.
The Mach number is given because it is the honest way to know when this calculation is nearing the limits of the subsonic model it uses.
When this is useful
- Planning any leg where the wind triangle is needed, since that only works in true airspeed.
- Comparing your cruise performance against the aircraft flight manual, which normally quotes true airspeed.
- Understanding why an aircraft that indicates 120 kt at sea level indicates the same at 10,000 ft while actually going considerably faster.
How it is calculated
Calibrated airspeed is first converted into impact pressure using sea level standard conditions, because that is how the instrument is calibrated by definition. Pressure altitude then gives the actual static pressure surrounding the aircraft.
Those two pressures give the Mach number, and the outside air temperature gives the local speed of sound. Multiplying the two produces true airspeed.
This is the full compressible flow solution. The familiar cockpit rule of adding 2 percent per 1,000 ft is a rough approximation that reads a few knots high by 10,000 ft and drifts further above that.
true airspeed = Mach number x speed of sound, with Mach derived from impact and static pressure
Worked example
- Calibrated airspeed
- 150 kt
- Pressure altitude
- 10,000 ft
- Outside air temperature
- -5 C
True airspeed is about 174 kt, which is 24 kt more than the calibrated figure.
Check: Checked against the density ratio method independently: at 10,000 ft the standard density ratio is 0.7385, and dividing equivalent airspeed by the square root of that gives 173.7 kt. The two methods agree to within a knot. The 2 percent per 1,000 ft rule would have suggested 180 kt, about 6 kt high.
Limitations
- The static pressure comes from the standard atmosphere applied to your pressure altitude. On a day with an unusual pressure profile that introduces a small error.
- It assumes calibrated airspeed. If you enter indicated airspeed without applying your aircraft position error correction, the error carries straight through.
- The model is subsonic. Above roughly Mach 0.85 the calculator warns you, because transonic effects are outside what it describes.
Common mistakes
- Entering total air temperature instead of static air temperature. At speed the probe reads warm from ram rise, and using that figure inflates true airspeed.
- Using indicated altitude rather than pressure altitude, which is only the same thing when the subscale is set to standard.
- Assuming true airspeed always exceeds indicated. In very cold air at low level it can be lower.
Sources
- Pilot's Handbook of Aeronautical Knowledge, flight instruments chapter , US Federal Aviation Administration
- Mach Number and Speed of Sound , NASA Glenn Research Center
- Airspeed Measurement , SKYbrary, EUROCONTROL