True Airspeed Calculator
True airspeed (TAS) is the speed of the aircraft relative to the air mass surrounding it, accounting for the actual air density at altitude rather than the standard sea-level density assumed by the airspeed indicator. TAS is essential for accurate navigation, wind triangle calculations, and fuel planning. This calculator uses the ICAO standard atmosphere density ratio: it computes actual air density from pressure altitude and temperature, then scales calibrated airspeed by the square root of the density ratio to produce TAS.
True airspeed formula
T(K) = OAT(°C) + 273.15
P = P0 x (1 - 6.87535e-6 x PA)^5.2561 (pressure in Pa)
rho = P / (287.058 x T)
sigma = rho / 1.225
TAS = CAS / sqrt(sigma)
Where P0 is sea-level standard pressure (101,325 Pa), PA is pressure altitude in feet, T is temperature in Kelvin, rho is actual air density in kg/m3, 1.225 kg/m3 is ISA sea-level density, and sigma is the density ratio. This is the standard ICAO method. For subsonic flight below about 300 knots CAS, compressibility correction to EAS is minor and is omitted here.
Practical notes for pilots
- A quick in-flight approximation: add 2% of CAS per 1,000 ft of altitude. For example, 120 kt CAS at 8,000 ft gives approximately 120 + (8 x 2.4) = 139 kt TAS.
- TAS is used to compute ground speed: ground speed = TAS +/- headwind/tailwind component.
- Flight plans filed with ATC use TAS. Do not file CAS.
- High altitude jets routinely cruise at 250+ kt IAS but 480+ kt TAS due to low air density at altitude.
True airspeed calculator: frequently asked questions
What is true airspeed?
True airspeed (TAS) is the actual speed of the aircraft relative to the surrounding air mass, uncorrected for instrument or positional error. It differs from indicated airspeed (IAS) and calibrated airspeed (CAS) because those are measured at standard sea-level air density. As altitude increases and air density decreases, TAS is always higher than CAS for the same aircraft speed.
How is true airspeed calculated from calibrated airspeed?
TAS = CAS x sqrt(rho_0 / rho), where rho_0 is the standard sea-level density (1.225 kg/m3) and rho is the actual air density at altitude. In practice the simplified formula TAS = CAS x (1 + 0.02 x PA / 1000) is used as a pilot approximation, where PA is pressure altitude in thousands of feet. The more accurate method uses ISA density ratio from pressure altitude and temperature.
Why does TAS matter for navigation?
Wind correction calculations and ground speed calculations use TAS. If you use IAS or CAS instead of TAS, your estimated position, fuel burn and ETA will be incorrect, especially at high altitudes where the difference between CAS and TAS can exceed 100 knots.
What is the difference between IAS, CAS, EAS, and TAS?
Indicated airspeed (IAS) is raw airspeed indicator reading. Calibrated airspeed (CAS) corrects IAS for instrument and position error. Equivalent airspeed (EAS) corrects CAS for compressibility effects at high speed. True airspeed (TAS) corrects EAS for actual air density. At low altitudes and speeds below about 200 knots, CAS and TAS are the only practically relevant values.
What units does this calculator use?
Calibrated airspeed is entered in knots. Pressure altitude in feet. Outside air temperature in degrees Celsius. The output true airspeed is in knots. These are the standard units used in ICAO documentation and general aviation flight planning.
Official sources
- ICAO: Manual of the ICAO Standard Atmosphere, Doc 7488.
- FAA: Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25), Chapter 7: Flight Instruments.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.