Calculate true airspeed (TAS) from indicated airspeed, altitude, and temperature. Find Mach number, density altitude, and ISA deviation.
The true airspeed (TAS) calculator converts indicated airspeed (IAS) to the actual speed of an aircraft through the air mass, correcting for the effects of altitude, temperature, and barometric pressure. Pilots, flight planners, and aviation students use TAS to calculate ground speed, fuel burn, and flight time, since indicated airspeed underestimates the true speed at higher altitudes where air density decreases.
At sea level on a standard day, IAS and TAS are essentially equal. But at 35,000 feet, where air density is roughly one-quarter of the sea-level value, a jet indicating 280 knots IAS is actually traveling at approximately 460 knots TAS through the air. This difference grows with altitude and with temperatures above ISA standard, making TAS calculation essential for accurate flight planning.
This calculator accounts for non-standard pressure (via altimeter setting) and non-standard temperature (via OAT), computes pressure altitude, density altitude, the density ratio (σ), Mach number, and ISA deviation. The altitude comparison table shows how TAS varies across flight levels at the same indicated airspeed, a critical reference for performance planning.
Accurate TAS calculation is fundamental to flight planning. Ground speed — the basis for estimating arrival time and fuel burn — is TAS corrected for wind. An error of 10 knots in TAS can translate to several minutes of arrival time difference and significant fuel planning errors on long flights.
This calculator is especially useful for flight students learning the relationship between IAS, TAS, and Mach; for GA pilots planning cross-country flights; and for anyone studying atmospheric physics or aircraft performance.
Pressure altitude: PA = Alt + (29.92 − QNH) × 1000 ft. Air pressure (troposphere): P = P₀(1 − Lh/T₀)^(g/RL) where L = 0.0065 K/m, T₀ = 288.15 K. Air density: ρ = P/(RT). Density ratio: σ = ρ/ρ₀. TAS = EAS / √σ ≈ IAS / √σ. Mach number: M = TAS / √(γRT) where γ = 1.4, R = 287.058 J/(kg·K).
Result: TAS ≈ 462 kts, Mach 0.79, density altitude 36,200 ft
At FL350, pressure ≈ 23,842 Pa and ISA temp = -54.5°C. With OAT = -54°C (ISA+0.5), density ≈ 0.380 kg/m³, σ = 0.310. TAS = 280/√0.310 ≈ 503 kts... (simplified). Actual result varies with compressibility correction.
An aircraft's pitot-static system measures the difference between total (ram) pressure and static pressure. This dynamic pressure (q = ½ρv²) is proportional to both air density and the square of velocity. The airspeed indicator is calibrated to read correctly at sea-level standard density (ρ₀ = 1.225 kg/m³), so it directly indicates Equivalent Airspeed (EAS). In practice, IAS ≈ EAS for most GA aircraft after accounting for small instrument and position errors.
True Airspeed is the actual velocity of the aircraft through the air mass. At altitude, where density is reduced, the aircraft must fly faster to generate the same dynamic pressure. The correction factor is 1/√σ, where σ = ρ/ρ₀ is the density ratio. At FL350, σ ≈ 0.31, so TAS is about 1.8× IAS.
This calculator uses the International Standard Atmosphere (ISA) model. In the troposphere (0-11,000 m), temperature decreases at a lapse rate of 6.5°C per kilometer from 15°C at sea level. Above the tropopause (11,000 m / 36,089 ft), temperature remains constant at -56.5°C in the lower stratosphere. Pressure and density are calculated using the barometric formula derived from the hydrostatic equation and ideal gas law.
Non-standard conditions are handled through the altimeter setting (which adjusts pressure altitude) and the OAT input (which provides actual temperature). The ISA deviation — the difference between actual and standard temperature — is a key performance planning parameter used in aircraft operating manuals.
For cross-country flight planning, the pilot determines TAS from the aircraft's performance charts, applies wind corrections to obtain ground speed, and uses ground speed to calculate leg times and fuel requirements. Modern GPS provides ground speed directly, but TAS remains essential for performance calculations, fuel planning at altitude, and understanding the aircraft's operating envelope. Jet aircraft typically plan in Mach number at cruise altitude, converting to TAS for wind correction.
The airspeed indicator measures dynamic pressure, which depends on air density. At altitude, air is thinner, so the aircraft must move faster through the air to generate the same dynamic pressure. TAS corrects for this density effect.
Pressure altitude is altitude corrected for non-standard barometric pressure. Density altitude further corrects for non-standard temperature. Density altitude determines aircraft performance (takeoff distance, climb rate, engine power).
At sea level (0 ft) on a standard day (15°C, 29.92 inHg), IAS equals TAS (assuming no instrument or position errors). Any increase in altitude or temperature above this standard makes TAS greater than IAS.
ISA deviation is the difference between actual OAT and the standard atmosphere temperature at that altitude. Positive ISA deviation means warmer-than-standard air, which reduces density and increases TAS for a given IAS. It directly affects engine performance and TAS calculations.
This calculator uses the simple density-ratio method (TAS = IAS/√σ) which is accurate for subsonic speeds below Mach 0.3. Above Mach 0.3, compressibility effects become significant and a full compressible-flow correction should be applied.
The transonic regime typically spans Mach 0.8 to 1.2. In this range, some airflow over the aircraft exceeds the speed of sound even though the aircraft itself is subsonic. This creates shock waves and changes in drag characteristics.