True Airspeed Calculator (CAS/IAS to TAS & Mach)

Understanding the true airspeed calculator — concept and principle

An aircraft's airspeed indicator reads correctly only in sea-level standard air. Higher up, where the air is thinner, the aircraft actually moves through the air faster than the indicator shows. This calculator converts calibrated airspeed (CAS) into true airspeed (TAS) and Mach number from pressure altitude and outside air temperature, including compressibility, and also gives equivalent airspeed and the density ratio.

At 8,000 ft the air is thinner, so 120 kt indicated is 136.6 kt through the air.

How it is calculated

Impact pressure: qc/p₀ = (1 + 0.2 (CAS ÷ a₀)²)^3.5 − 1, with a₀ = 661.48 kt

Static pressure ratio δ from the ISA at your pressure altitude

Mach number: M = √(5 × [(qc/p + 1)^(2/7) − 1])

TAS = M × 661.48 × √(T ÷ 288.15 K)

Density ratio σ = δ × 288.15 ÷ T; EAS = TAS × √σ

T is the outside air temperature in kelvin; above 11 km the ISA temperature is constant at 216.65 K.

The principle

The pitot tube measures impact pressure, the extra pressure created by ramming into the air. That pressure depends on both speed and air density. The indicator is calibrated assuming sea-level density, so in thinner air the same reading means a higher true speed. The calculation first recovers the impact pressure from CAS, then uses the actual static pressure at altitude to find the Mach number with the compressible-flow relation, and finally multiplies by the local speed of sound, which depends on temperature. Because it includes compressibility, it remains accurate at jet speeds while subsonic.

Worked example

Default inputs: CAS 120 kt, pressure altitude 8,000 ft, OAT 5 °C.

qc/p₀ = (1 + 0.2 × (120 ÷ 661.48)²)^3.5 − 1 = 0.02323.
At 8,000 ft, δ = 0.7428 (about 752.6 hPa).
M = √(5 × [(0.02323 ÷ 0.7428 + 1)^(2/7) − 1]) = 0.21.
TAS = 0.2102 × 661.48 × √(278.15 ÷ 288.15) = 136.6 kt = 253 km/h = 157 mph, which is 13.8% above CAS.
σ = 0.7428 × 288.15 ÷ 278.15 = 0.769; EAS = 136.6 × √0.769 = 119.8 kt.

Each point is the calculator re-run with only “Calibrated airspeed (kt)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Calibrated airspeed (kt)	True airspeed (kt)
30	34.2
60	68.4
90	102.5
120	136.6
150	170.6
180	204.6
240	272.1

How to read the result

A common rule of thumb is that TAS rises about 2% per 1,000 ft above CAS at low altitudes, which matches this example roughly. TAS is the speed used for navigation and fuel planning; ground speed then follows from TAS and wind. EAS is slightly below CAS at higher speeds and altitudes because of compressibility. Warmer than standard air raises TAS for the same CAS.

Common mistakes

Using indicated airspeed without correcting for position and instrument error.
Entering true altitude instead of pressure altitude.

Keep in mind: This tool is for planning and study. Use the aircraft's approved flight manual and certified avionics for operational decisions.

Frequently asked questions

What is the difference between CAS and TAS?

CAS is the indicator reading corrected for instrument and position error; TAS is the actual speed through the air.

Why is TAS higher at altitude?

Thinner air produces less pitot pressure at the same speed, so the indicator under-reads.

What is equivalent airspeed?

The sea-level speed that would give the same dynamic pressure; it is close to CAS at low speeds.

Sources: NACA Technical Note 1120 (1946), "Standard Nomenclature for Airspeeds with Tables and Charts for Use in Calculation of Airspeed" · NASA Glenn Research Center, "Isentropic Flow"; ICAO Doc 7488/3 (standard atmosphere)

Checked 9 Nov 2026. NACA Technical Note 1120 (1946), “Standard Nomenclature for Airspeeds with Tables and Charts for Use in Calculation of Airspeed” (adiabatic impact-pressure relation; V = M·a); NASA Glenn Research Center, “Isentropic Flow” (p/pₜ = (1 + (γ−1)/2·M²)^(−γ/(γ−1)), γ = 1.4); ICAO Doc 7488/3 standard atmosphere.

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