True Airspeed Calculator: Convert IAS to TAS

Convert your Indicated Airspeed (IAS) into True Airspeed (TAS) by evaluating adiabatic compressible flow profiles and multi-regime supersonic shockwaves.

What is True Airspeed (TAS)

True Airspeed (TAS) is the actual physical velocity of an aircraft relative to the ambient air mass through which it flies. While Indicated Airspeed (IAS) is critical for monitoring cockpit structural limitations and aerodynamic safety margins (such as stall thresholds), it does not track real velocity across space. Correcting for shifting air density and high-speed compressibility is necessary to derive True Airspeed, which forms the baseline for precise cross-country navigation, fuel burn projection, and flight planning.

Aerodynamic Principles & Compressibility Factors

• Atmospheric Thinning Impact: Pitot-static systems measure dynamic pressure by catching rushing air molecules. As an aircraft climbs, ambient air density drops. Fewer air molecules enter the pitot tube, forcing raw indicated airspeed readings to sit lower than the aircraft’s true velocity through space.
• The Incompressible Flow Fallacy: Simple airspeed calculations utilize an uncorrected square-root density ratio shortcut. While acceptable below 200 knots and at low altitudes, this method assumes air is an un-squeezable fluid, introducing significant errors as flight profiles scale.
• Adiabatic Molecular Compression: At high cruise speeds, the rapid forward momentum of the aircraft physically compresses air molecules inside the entry neck of the pitot tube. This compression generates an artificial pressure build-up that requires thermodynamic compressible flow equations to resolve.
• Supersonic Bow Shockwaves: When flight velocities surpass Mach 1.0, a detached shockwave physical boundary forms directly in front of the pitot tube assembly. This alters total stagnation pressure parameters, requiring a mathematical transition from standard isentropic profiles to the Rayleigh Supersonic Pitot model.

How It’s Calculated

The tool processes fluid dynamics variables backward and forward across both subsonic and supersonic flight layers using these precise sequential steps:

1. Static Ambient Pressure Calculation

First, your input pressure altitude is mapped against the multi-layer ICAO Standard Atmosphere framework to calculate local static pressure (PressPa):

• Troposphere (Altitude <= 11,000 meters):PressPa = P0 * ((T0 – 0.0065 * altM) / T0)^5.25588326
• Lower Stratosphere (Altitude > 11,000 meters):PressPa = 22632.10 * e^(-g0 * (altM – 11000) / (R * 216.65))

2. Sea-Level Impact Pressure (qc) Generation

Your input airspeed value is treated as Calibrated Airspeed (CAS) and scaled against standard sea-level reference settings to calculate total pressure impact:

• Subsonic Flights (CAS / a0 <= 1.0):qc = P0 * ((1 + 0.2 * (CAS / a0)^2)^3.5 – 1)
• Supersonic Flights (CAS / a0 > 1.0):qc = P0 * ((166.92158 * (CAS / a0)^7) / (7 * (CAS / a0)^2 – 1)^2.5 – 1)

3. Flight Mach Number Derivation

The script evaluates the ratio of impact pressure to local static pressure (qc / PressPa). If this ratio breaches the transonic boundary threshold (0.89292916), the tool automatically executes a high-speed 10-step Newton-Raphson calculus convergence loop to invert the Rayleigh Supersonic Pitot equation:

f(M) = (166.92158 * M^7) / (7 * M^2 – 1)^2.5 – 1 – (qc / PressPa)

4. True Velocity Final Output

Once the exact Mach number is resolved, it is scaled against the local speed of sound (a), which is driven by your input temperature profile:

Speed of Sound (a) = 340.294 * Square Root((OAT + 273.15) / 288.15)

True Airspeed (TAS) = Mach * Speed of Sound (a)

Constants Applied:

• P0 (Standard Sea Level Pressure): 101,325 Pa
• T0 (Standard Sea Level Temperature Baseline): 288.15 K (15°C)
• a0 (Standard Sea Level Speed of Sound): 340.294 m/s
• g0 (Standard Acceleration of Gravity): 9.80665 m/s²
• R (Specific Gas Constant for Dry Air): 287.05287 J/(kg·K)

Scope and Limitations

• Rigid ISA Day Profile: Local static pressure and ambient temperature parameters are extracted assuming a static ICAO standard atmospheric profile. The system functions as a precise technical reference baseline and does not ingest active weather changes, local altimeter settings (QNH), or non-standard temperature deviations (ISA ± X).
• Zero Position Error Baseline: The core logic treats your raw indicated entry as Calibrated Airspeed (CAS). It does not maintain distinct correction tables to adjust for aircraft-specific pitot tube installation geometry errors or unique cockpit instrument position anomalies.
• Tropospheric Cap Boundary: The underlying atmospheric profile equations are strictly validated for geopotential altitudes ranging from -2,000 meters up to a ceiling of 20,000 meters (-6,561 feet to 65,617 feet). It does not model conditions extending past the lower stratosphere boundary layers.