True Airspeed (TAS) Calculator
Enter your calibrated (or indicated) airspeed, pressure altitude, and outside air temperature to get your true airspeed (TAS), equivalent airspeed (EAS), Mach number, local speed of sound, and density altitude. The calculator uses exact subsonic compressible-flow equations and the International Standard Atmosphere model. Switch between knots, km/h, mph, and m/s. Results update as you type.
Formula
Worked example
A Boeing 737 cruising at FL350 (35,000 ft / 10,668 m) with a CAS of 250 kts. ISA temperature: 288.15 - 0.0065 x 10668 = 218.8 K (-54.3 degC). Static pressure: 101325 x (218.8/288.15)^5.2561 = 23,842 Pa. Impact pressure from CAS: P0 x ((1 + 0.2 x (250 x 0.514/340.29)^2)^3.5 - 1) = 6,077 Pa. Mach = sqrt(5 x ((6077/23842 + 1)^(1/3.5) - 1)) = 0.797. Local speed of sound = 340.29 x sqrt(218.8/288.15) = 296.7 m/s (577 kts). TAS = 0.797 x 577 = 460 kts.
What is true airspeed and why does it differ from indicated airspeed?
Indicated airspeed (IAS) is what your cockpit instrument reads: a measure of dynamic pressure from the pitot-static system. At sea level on a standard day, IAS and true airspeed (TAS) are almost equal. But as you climb, the air becomes less dense. The pitot-static system still measures the same dynamic pressure for a given TAS, so it reads a lower IAS. TAS is the actual velocity of the aircraft through the surrounding air mass. A jet cruising at 250 kts indicated at 35,000 ft is actually traveling close to 460 kts through the air. The ratio grows with altitude: roughly 2% per 1,000 ft at low speeds in the troposphere. TAS is what you use for navigation and wind triangle calculations. It is also the speed that determines fuel burn per mile, not IAS.
CAS, EAS, and TAS: a step-by-step conversion
The conversion from cockpit reading to true airspeed has three stages. Indicated airspeed (IAS) is corrected for instrument and position error to get calibrated airspeed (CAS), using tables published in the aircraft flight manual. CAS is then corrected for the compressibility of air at high speed to get equivalent airspeed (EAS). The compressibility correction is small below 200 kts but grows significantly above Mach 0.3. Finally, EAS is divided by the square root of the density ratio (local density divided by sea-level density) to get TAS. This calculator uses the exact compressible-flow pitot equation rather than the simplified 2%-per-1000-ft rule, which improves accuracy at higher altitudes and Mach numbers. EAS is the speed relevant to aerodynamic loads and structural limits: aircraft design speeds (VA, VNE, VFE) are all expressed in EAS or CAS, not TAS, because dynamic pressure depends on air density.
The International Standard Atmosphere and how temperature affects TAS
The International Standard Atmosphere (ISA) defines a model of how temperature, pressure, and density vary with altitude. In the troposphere (below about 36,089 ft / 11,000 m), temperature decreases at 6.5 degC per 1,000 m. Above that, in the lower stratosphere, temperature holds constant at -56.5 degC up to about 65,617 ft. When your actual outside air temperature (OAT) differs from the ISA standard, your air density differs too. Warmer air is less dense, so density altitude exceeds pressure altitude and TAS is higher than the ISA calculation would suggest. Colder air is denser, density altitude is lower, and TAS is slightly reduced. This matters most for departure and landing performance in hot climates at high-elevation airports: a standard ISA +20 degC day at 5,000 ft elevation gives a density altitude close to 8,500 ft, dramatically increasing runway required.
Mach number and compressibility at high altitudes
Mach number is TAS divided by the local speed of sound, which depends on temperature only (not pressure or density). At ISA sea level, the speed of sound is 661.5 kts (340.3 m/s). At FL350 with ISA temperature (-54.3 degC), it falls to about 576 kts (296.5 m/s). This means that the same TAS represents a higher Mach number at altitude. Modern airliners are limited by Mach number in cruise (typically Mach 0.82 to 0.86) rather than by indicated or true airspeed, because shock wave formation on the wing depends on local Mach number. Below Mach 0.3, compressibility corrections to the pitot equation are less than 2% and the simple TAS = CAS / sqrt(density ratio) formula is adequate. Above Mach 0.3, the exact compressible equation used here is needed for accurate results.
Airspeed types: definitions and uses
| Airspeed | Symbol | Definition | Primary use |
|---|---|---|---|
| Indicated | IAS | Raw pitot-static instrument reading | Cockpit reference, stall/limit speeds |
| Calibrated | CAS | IAS corrected for position and instrument error | Structural design speeds, performance charts |
| Equivalent | EAS | CAS corrected for air compressibility | Structural load and flutter analysis |
| True | TAS | Actual speed relative to the air mass | Navigation, fuel planning, wind triangle |
Summary of the four airspeed measures used in aviation and how they relate to each other.
Frequently asked questions
What is the difference between IAS, CAS, EAS, and TAS?
Indicated airspeed (IAS) is the raw pitot-static instrument reading. Calibrated airspeed (CAS) corrects IAS for instrument and position error using tables in the aircraft manual. Equivalent airspeed (EAS) further corrects CAS for air compressibility, and is used for aerodynamic load calculations. True airspeed (TAS) is the actual speed of the aircraft through the air mass: EAS divided by the square root of the local-to-sea-level density ratio. For light aircraft below 200 kts, IAS and CAS are almost equal and compressibility corrections are tiny, so TAS is approximately IAS / sqrt(sigma).
Why does TAS increase with altitude even if IAS stays the same?
Because air density decreases with altitude. The pitot tube measures dynamic pressure (half the density times velocity squared). At high altitude the density is lower, so the aircraft must travel faster (higher TAS) to produce the same dynamic pressure reading. At FL350, air density is roughly 30% of sea-level density, so TAS is about 1/sqrt(0.30) or about 1.83 times the IAS for a given dynamic pressure - though in practice the relationship is modified by temperature and compressibility.
Can I use indicated airspeed instead of calibrated airspeed in this calculator?
For light general-aviation aircraft flying below 200 kts and at lower altitudes, IAS and CAS differ by only a few knots due to small position and instrument errors. Entering IAS directly will give a TAS result that is accurate to within 1-2%. For high-performance aircraft, particularly jets, use the CAS value from your aircraft performance manual for more accurate results.
What is density altitude and why does it matter for aircraft performance?
Density altitude is the altitude in the standard (ISA) atmosphere that has the same air density as your actual conditions. When OAT is higher than ISA standard, density altitude exceeds pressure altitude: the air is thinner than it would be on a standard day at the same pressure altitude. Aircraft engine power, propeller efficiency, and wing lift all depend on air density, so performance (takeoff roll, climb rate, engine output) is set by density altitude. A hot day at a high-elevation airport can create a density altitude thousands of feet above the field elevation, requiring significantly longer runways.
When does compressibility become important?
Compressibility of air becomes meaningful above roughly Mach 0.3. Below that speed, the simple rule TAS = CAS x sqrt(rho0/rho) is accurate to better than 1-2%. Above Mach 0.3, the pitot tube compresses the incoming air in a way that departs from Bernoulli's equation for incompressible flow, and you need the exact subsonic compressible-flow equation (used by this calculator) to get the right answer. For a typical airliner CAS of 250 kts at FL350, the compressibility correction increases the Mach number by several percent compared to the simple approximation.
What is the speed of sound at altitude and how is it calculated?
The speed of sound in air depends only on temperature, not altitude or pressure directly. The formula is a = sqrt(gamma x R x T), where gamma is 1.4 (ratio of specific heats for dry air), R is 287.058 J/(kg K), and T is the absolute temperature in Kelvin. At ISA sea level (288.15 K) this gives 340.3 m/s or 661.5 kts. At ISA FL350 (218.8 K) it is about 296.5 m/s or 576.7 kts. Mach number is TAS divided by this local speed of sound, so the same TAS represents a higher Mach number at higher altitude because the speed of sound is lower there.
How accurate is the 2% per 1,000 ft rule of thumb?
The "add 2% to IAS per 1,000 feet of altitude" rule is a quick mental estimate that works reasonably well below 10,000 ft for light aircraft at low speeds. At 10,000 ft it gives a TAS about 20% above IAS, which is close to the exact answer in mild conditions. At higher altitudes and speeds the approximation degrades: at FL350 with CAS of 250 kts, the exact compressible-flow calculation gives TAS around 460 kts (84% above CAS), while the linear rule would suggest only about 70% above CAS. Always use the exact method for jet operations above 20,000 ft.