What is my true airspeed?
Type your calibrated airspeed, pressure altitude and outside air temperature. The true airspeed calculator gives your speed through the air with the compressibility correction, the Mach number and the equivalent airspeed, from the standard atmosphere.
- True airspeed (TAS)
- 169.1 kn
At 8,000 ft and 0 °C, a CAS of 150 kn is a true airspeed of 169.1 kn (Mach 0.26254).
- True airspeed (mph)
- 194.6
- True airspeed (km/h)
- 313.1
- Mach number
- 0.26254
- Equivalent airspeed (EAS)
- 149.7 kn
- TAS without compressibility
- 169.5 kn
- Static pressure (hPa)
- 752.624
- ISA temperature (°C)
- −0.8496
- ISA deviation (°C)
- 0.8496
- Density ratio ρ ÷ ρ₀
- 0.78357
True airspeed (TAS): 169.1 kn. At 8,000 ft and 0 °C, a CAS of 150 kn is a true airspeed of 169.1 kn (Mach 0.26254).
How to calculate
True airspeed calculator: TAS from calibrated airspeed, pressure altitude and outside air temperature, with compressibility, the Mach number, the equivalent airspeed and the standard atmosphere values.
Example with the default inputs (Calibrated airspeed (CAS) 150 kn, Pressure altitude 8,000 ft, Outside air temperature (OAT) 0 °C): At 8,000 ft and 0 °C, a CAS of 150 kn is a true airspeed of 169.1 kn (Mach 0.26254).
Method: p = 101,325 × (1 − 0.0065h ÷ 288.15)^(34.1631947 ÷ 6.5) Pa; qc = p₀[(1 + 0.2(CAS ÷ a₀)²)^3.5 − 1]; M = √(5[(qc ÷ p + 1)^(2/7) − 1]); TAS = M × √(γRT), with γ = 1.4, R = 9.80665 ÷ 0.0341631947 J/(kg·K) and a₀ = √(γR × 288.15).
- Subsonic flight (Mach below 1), in the troposphere (pressure altitude up to 11,000 m, 36,089 ft).
- CAS already holds the instrument and position corrections; the temperature is the true outside air temperature.
Worked examples
Each example is checked against the calculator on every build.
- Calibrated airspeed (CAS) 100 kn, Pressure altitude 0 ft, Outside air temperature (OAT) 15 °C gives True airspeed (TAS) 100 kn, Equivalent airspeed (EAS) 100 kn, Density ratio ρ ÷ ρ₀ 1, Mach number 0.151176.Source: 14 CFR 1.1 General definitions (calibrated airspeed is equal to true airspeed in standard atmosphere at sea level; true airspeed is equivalent airspeed × (ρ₀ ÷ ρ)^½; Mach number is true airspeed ÷ the speed of sound), https://www.law.cornell.edu/cfr/text/14/1.1 (retrieved 2026-10-18): CAS equals TAS in the standard atmosphere at sea level; NASA Glenn Research Center, Isentropic Flow Equations (M = v ÷ a; a = √(γRT); p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1))), https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html (retrieved 2026-10-18)
- Calibrated airspeed (CAS) 150 kn, Pressure altitude 8,000 ft, Outside air temperature (OAT) 0 °C gives True airspeed (TAS) 169.1 kn, Mach number 0.262541, Static pressure (hPa) 752.623761, ISA temperature (°C) -0.8496.Source: 14 CFR 1.1 General definitions (calibrated airspeed is equal to true airspeed in standard atmosphere at sea level; true airspeed is equivalent airspeed × (ρ₀ ÷ ρ)^½; Mach number is true airspeed ÷ the speed of sound), https://www.law.cornell.edu/cfr/text/14/1.1 (retrieved 2026-10-18); NASA Glenn Research Center, Isentropic Flow Equations (M = v ÷ a; a = √(γRT); p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1))), https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html (retrieved 2026-10-18); U.S. Standard Atmosphere, 1976, as defined by Public Domain Aeronautical Software (101,325 Pa, 288.15 K, −6.5 K/km to 11 km, hydrostatic constant 34.1631947 K/km), https://www.pdas.com/atmosdef.html (retrieved 2026-10-18)
- Calibrated airspeed (CAS) 250 kn, Pressure altitude 30,000 ft, Outside air temperature (OAT) −45 °C gives True airspeed (TAS) 393.2 kn, Mach number 0.668107, Density ratio ρ ÷ ρ₀ 0.375057, TAS without compressibility 408.2 kn.Source: 14 CFR 1.1 General definitions (calibrated airspeed is equal to true airspeed in standard atmosphere at sea level; true airspeed is equivalent airspeed × (ρ₀ ÷ ρ)^½; Mach number is true airspeed ÷ the speed of sound), https://www.law.cornell.edu/cfr/text/14/1.1 (retrieved 2026-10-18); NASA Glenn Research Center, Isentropic Flow Equations (M = v ÷ a; a = √(γRT); p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1))), https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html (retrieved 2026-10-18); U.S. Standard Atmosphere, 1976, as defined by Public Domain Aeronautical Software (101,325 Pa, 288.15 K, −6.5 K/km to 11 km, hydrostatic constant 34.1631947 K/km), https://www.pdas.com/atmosdef.html (retrieved 2026-10-18)
How it works
Constants: p₀ = 101,325 Pa and T₀ = 288.15 K (sea level), lapse rate L = 0.0065 K/m, hydrostatic constant K = 34.1631947 K/km = 0.0341631947 K/m, g₀ = 9.80665 m/s², γ = 1.4. The gas constant of air is R = g₀ ÷ K = 287.0531 J/(kg·K), and the sea-level speed of sound is a₀ = √(γR × T₀) = 340.2941 m/s (661.4788 kt).
- Static pressure at pressure altitude h (in metres): p = p₀ × (1 − L × h ÷ T₀)^(K ÷ L), with K ÷ L = 5.255876.
- Impact pressure from the calibrated airspeed: qc = p₀ × [(1 + 0.2 × (CAS ÷ a₀)²)^3.5 − 1]. This is the isentropic relation with γ = 1.4 at sea-level standard conditions, which is how an airspeed indicator is calibrated.
- Mach number: M = √(5 × [(qc ÷ p + 1)^(2/7) − 1]), the same relation solved at the static pressure p.
- True airspeed: TAS = M × √(γ × R × T), with T the outside air temperature in kelvins.
- Equivalent airspeed: EAS = a₀ × M × √(p ÷ p₀), so TAS = EAS × √(ρ₀ ÷ ρ).
- Density ratio σ = ρ ÷ ρ₀ = (p ÷ p₀) × (T₀ ÷ T); the TAS without compressibility is CAS ÷ √σ.
- ISA temperature = T₀ − L × h, and the ISA deviation is OAT − ISA temperature.
Rules
- CAS from 0.5 to 340 m/s (0.972 to 660.9 kt); pressure altitude from −1,000 m to 11,000 m (−3,280 ft to 36,089 ft, the troposphere); OAT from −90 °C to 60 °C.
- If the Mach number would be 1 or more there is no answer: the formulas are for subsonic flight.
Output format
The speeds show to 4 significant figures in knots (TAS also in mph and km/h; 1 kt = 1,852 ÷ 3,600 m/s), the Mach number and density ratio to 5, the pressure in hPa to 6, and the temperatures to 4. Every result is a 64-bit float.
Worked examples by hand
Sea level, standard day. CAS 100 kt, h = 0, 15 °C: p = p₀, so qc ÷ p gives back M = CAS ÷ a₀ = 51.4444 ÷ 340.2941 = 0.151176, and TAS = M × a₀ = 100 kt: CAS equals TAS at standard sea level.
150 kt at 8,000 ft and 0 °C. h = 2,438.4 m: p = 101,325 × (1 − 0.0065 × 2,438.4 ÷ 288.15)^5.255876 = 75,262.4 Pa. qc = 101,325 × [(1 + 0.2 × (77.1667 ÷ 340.2941)²)^3.5 − 1] = 3,694.4 Pa. M = √(5 × [(3,694.4 ÷ 75,262.4 + 1)^(2/7) − 1]) = 0.262541. a = √(1.4 × 287.0531 × 273.15) = 331.32 m/s, so TAS = 86.985 m/s = 169.1 kt. The ISA temperature is −0.85 °C.
250 kt at 30,000 ft and −45 °C. p = 30,089.6 Pa, qc = 10,498.2 Pa, M = 0.668107, a = √(1.4 × 287.0531 × 228.15) = 302.80 m/s, TAS = 202.30 m/s = 393.2 kt. The density ratio is 0.375057, so the density-only estimate is 250 ÷ √0.375057 = 408.2 kt.
Other questions people ask
How do you calculate true airspeed?
Turn the calibrated airspeed into the impact pressure it stands for at sea level, then find the Mach number that gives that impact pressure at your altitude and multiply by the speed of sound at the outside air temperature. 150 kt CAS at 8,000 ft and 0 °C is about 169 kt TAS.
Why is true airspeed higher than indicated airspeed at altitude?
The airspeed indicator senses the push of the air, which depends on its density. Thinner air pushes less at the same speed, so the aircraft must fly faster through it to show the same reading.
What is the difference between CAS, EAS and TAS?
Calibrated airspeed (CAS) is the indicated airspeed corrected for instrument and position error. Equivalent airspeed (EAS) is CAS corrected for compressibility at your altitude. True airspeed (TAS) is EAS × √(ρ₀ ÷ ρ), the speed through undisturbed air (14 CFR 1.1).
When does compressibility matter?
At low speed and altitude it is small: TAS from density alone, CAS ÷ √(ρ ÷ ρ₀), is within about 0.2% at 150 kt and 8,000 ft. At 250 kt and 30,000 ft the density-only figure reads about 15 kt too high.
What is pressure altitude?
The altitude your altimeter shows when set to 29.92 inHg (1013.25 hPa). It stands for the air pressure, which the true airspeed formula needs.
When are CAS and TAS the same?
In the standard atmosphere at sea level: 1013.25 hPa and 15 °C. Then 100 kt CAS is 100 kt TAS.