True Airspeed Calculator

True airspeed (TAS) is the actual speed of the aircraft through the air mass — the speed at which the aircraft moves relative to the air surrounding it. Indicated airspeed (IAS) is the raw reading from the airspeed indicator, which measures dynamic pressure (the pressure difference between the pitot tube and the static port). At sea level in ISA conditions, IAS and TAS are approximately equal. At altitude, the air is less dense, so the same dynamic pressure corresponds to a higher true speed. TAS increases above IAS as altitude increases — at 10,000 ft in ISA conditions, TAS is approximately 20% higher than IAS. TAS is used for navigation calculations (wind triangle, groundspeed), fuel burn per nautical mile, and Mach number computation. IAS is used for all aircraft structural and performance limits because aerodynamic forces depend on dynamic pressure, not on TAS.

The standard formula is: TAS = CAS × √(T_actual / T_ISA), where temperatures are in Kelvin. T_actual is the outside air temperature (OAT) in Kelvin: OAT°C + 273.15. T_ISA is the ISA standard temperature at the pressure altitude: T_ISA = 288.15 − (0.0019812 × PA_feet) Kelvin. This formula assumes subsonic compressible flow and is accurate for most practical aviation use below Mach 0.7. At higher Mach numbers, compressibility corrections become significant and the relationship between CAS and TAS involves more complex equations. For quick mental calculation, use the rule of thumb: TAS ≈ IAS × (1 + 0.02 × altitude in thousands of feet). This is accurate to within 5% up to about 20,000 ft in ISA conditions.

Indicated Airspeed (IAS) is the raw reading from the airspeed indicator, uncorrected for instrument or position error. Calibrated Airspeed (CAS) is IAS corrected for position error — the error introduced by the location of the pitot-static ports in non-ideal airflow, particularly at high angles of attack or in sideslip. The correction is published in the POH as a position error correction table. At normal cruise speeds and configurations, the difference between IAS and CAS is typically less than 5 kt. Equivalent Airspeed (EAS) is CAS corrected for compressibility — at high speeds and high altitudes, the air in the pitot tube is compressed, causing the indicator to read higher than the equivalent speed at sea level. For most piston and turboprop aircraft below Mach 0.4, EAS ≈ CAS. True Airspeed (TAS) is EAS corrected for air density — the actual speed through the air. For practical navigation, pilots work with CAS (or IAS as an approximation of CAS) and convert directly to TAS using altitude and temperature.

The standard rule of thumb is: add approximately 2% of IAS per 1,000 feet of altitude for ISA conditions. For example, at 10,000 ft, TAS ≈ IAS × 1.20 (20% higher). At 5,000 ft, TAS ≈ IAS × 1.10. This approximation is accurate to within 2–3 kt for most speeds and altitudes encountered in general aviation. A more accurate version accounts for non-ISA temperature: if the temperature is above ISA, TAS will be slightly higher than the rule of thumb suggests; if below ISA, slightly lower. Some pilots use a slightly higher factor of 2.2% per 1,000 ft for greater accuracy at typical cruise altitudes.

Temperature affects TAS because air density depends on temperature as well as pressure. Hot air is less dense than cold air at the same pressure — so the same dynamic pressure corresponds to a higher true speed. Conversely, cold air is denser, so TAS is lower for the same indicated airspeed. The effect is captured in the temperature ratio in the TAS formula: TAS = CAS × √(T_actual / T_ISA). If OAT is higher than ISA (positive ISA deviation), T_actual > T_ISA, so TAS > CAS. The ISA temperature lapse rate is 1.98°C per 1,000 ft, so on a hot day with ISA+20°C deviation, TAS will be approximately 3–4% higher than in ISA conditions at the same pressure altitude. This matters for flight planning: the same indicated cruise speed produces a higher TAS and therefore a higher groundspeed on a hot day.

Mach number is the ratio of TAS to the local speed of sound. Speed of sound depends only on temperature: a = 661.47 × √(T/288.15) knots, where T is the ambient temperature in Kelvin. Mach number = TAS ÷ a. For piston and turboprop pilots, Mach number becomes relevant at higher altitudes and speeds. A turboprop flying at 250 KIAS at FL200 might be at Mach 0.5 or higher — approaching the region where compressibility effects begin to matter. For most GA piston aircraft below 10,000 ft at less than 200 KIAS, Mach is well below 0.4 and compressibility is negligible. However, understanding Mach number is part of the ATPL knowledge base and is essential for pilots operating into airspace with Mach number speed restrictions.

TAS is the aircraft speed used in all wind triangle calculations because the wind triangle represents the relationship between the aircraft's motion through the air (TAS at the true heading) and the wind vector to produce the ground track and groundspeed. Using IAS instead of TAS in the wind triangle would introduce a systematic error proportional to the IAS/TAS ratio — approximately 20% at 10,000 ft ISA. This error would produce a wrong wind correction angle and groundspeed, leading to an off-track aircraft and a wrong ETE. The E6B always uses TAS. To get TAS for the wind triangle, use this calculator with your cruise CAS, planned pressure altitude, and forecast temperature.

Density altitude is the pressure altitude corrected for temperature — it represents the altitude at which the current air density equals the ISA standard density. DA = PA + (ISA deviation × 120). Density altitude and true airspeed are related because both depend on air density. At a given TAS, the aircraft generates the same lift as it would at the equivalent ISA altitude (the density altitude). This is why performance charts use density altitude — all aerodynamic forces (lift, drag, thrust, propeller efficiency) depend on density, which the density altitude captures in a single number. In the TAS calculator, density altitude is computed as a by-product of the temperature and pressure altitude inputs.

Yes. The reverse formula is simply: CAS = TAS × √(T_ISA / T_actual). The same temperature ratio is used, but inverted. This is useful when planning at a specific TAS — for example, if you need to fly at exactly 200 kt TAS for a formation flight, you can compute what CAS to maintain at your planned altitude and temperature, then set that CAS on your airspeed indicator. The reverse calculation is also used when comparing airspeed readings from different altitudes — converting to TAS allows comparison of true speeds.

Below 3,000 ft, the TAS/IAS difference is typically less than 6% and is often within the accuracy of the wind forecast itself — so using IAS in the wind triangle introduces less error than the uncertainty in the wind. Above 5,000 ft, the divergence becomes 10% or more and begins to meaningfully affect ETE and fuel calculations. Above 10,000 ft, the difference is typically 20% or more and must always be corrected. For instrument flight above 10,000 ft, failing to use TAS for the wind triangle can produce ETEs that are 10–15 minutes wrong on a 1-hour leg — enough to create concerns about fuel and arrival sequencing. As a general rule, always use TAS for any navigation leg where the cruise altitude will be above 5,000 ft.