# What is my true airspeed?

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.

- Page: https://www.acalculator.org/physics/true-airspeed-calculator
- JSON spec: https://www.acalculator.org/physics/true-airspeed-calculator.json
- Version: f4974546472c

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| cas | Calibrated airspeed (CAS) | The indicated airspeed corrected for instrument and position error. |
| pa | Pressure altitude | The altitude shown with the altimeter set to 29.92 inHg (1013.25 hPa). |
| oat | Outside air temperature (OAT) | The true temperature of the outside air. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| tas | True airspeed (TAS) | The speed of the aircraft through the air, in knots. |
| mph | True airspeed (mph) | TAS in miles per hour. |
| kmh | True airspeed (km/h) | TAS in kilometres per hour. |
| mach | Mach number | TAS ÷ the speed of sound at the outside air temperature. |
| eas | Equivalent airspeed (EAS) | CAS corrected for compressibility: TAS × √(ρ ÷ ρ₀). |
| simple | TAS without compressibility | CAS ÷ √(ρ ÷ ρ₀): the density-only estimate, which reads high at speed and altitude. |
| pressure | Static pressure (hPa) | The standard atmosphere pressure at this pressure altitude. |
| isa | ISA temperature (°C) | 15 °C − 6.5 °C per km of pressure altitude. |
| isaDev | ISA deviation (°C) | The outside air temperature minus the ISA temperature. |
| sigma | Density ratio ρ ÷ ρ₀ | (p ÷ p₀) × (T₀ ÷ T): the air density as a share of sea-level standard. |

## 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).

## Assumptions

- 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

1. cas = 51.444444, pa = 0, oat = 288.15 gives tas = 51.444444, eas = 51.444444, sigma = 1, mach = 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).
2. cas = 77.166667, pa = 2,438.4, oat = 273.15 gives tas = 86.984712, mach = 0.262541, pressure = 752.623761, isa = -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).
3. cas = 128.611111, pa = 9,144, oat = 228.15 gives tas = 202.302698, mach = 0.668107, sigma = 0.375057, simple = 210.004982. 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).

## FAQ

### 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.

## Sources

- 14 CFR 1.1 General definitions: calibrated, equivalent, indicated and true airspeed; true airspeed equals equivalent airspeed × (ρ₀ ÷ ρ)^½; calibrated airspeed equals true airspeed in standard atmosphere at sea level; Mach number, retrieved 2026-10-18. https://www.law.cornell.edu/cfr/text/14/1.1
- NASA Glenn Research Center, Beginner’s Guide to Aeronautics, Isentropic Flow Equations: M = v ÷ a, a = √(γRT), p ÷ pt = [1 + M²(γ − 1) ÷ 2]^(−γ ÷ (γ − 1)), retrieved 2026-10-18. https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html
- NASA Glenn Research Center, Specific Heats: γ = 1.4 for air on a standard day, retrieved 2026-10-18. https://www.grc.nasa.gov/www/k-12/airplane/specheat.html
- U.S. Standard Atmosphere, 1976 (COESA): sea-level pressure 101,325 Pa and temperature 288.15 K, lapse rate −6.5 K/km from 0 to 11 km, hydrostatic constant 34.1631947 K/km, as given by Public Domain Aeronautical Software, retrieved 2026-10-18. https://www.pdas.com/atmosdef.html (report: https://ntrs.nasa.gov/citations/19770009539)
- NIST, CODATA 2022: standard acceleration of gravity 9.80665 m/s² (exact), retrieved 2026-10-18. https://physics.nist.gov/cgi-bin/cuu/Value?gn
- NIST, CODATA 2022: standard atmosphere 101,325 Pa (exact), retrieved 2026-10-18. https://physics.nist.gov/cgi-bin/cuu/Value?stdatm
- NIST Special Publication 811 (2008), Appendix B.8: 1 knot = 1,852 ÷ 3,600 m/s, 1 ft = 0.3048 m, 1 mph = 0.44704 m/s, retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811