True Airspeed Calculator

Enter calibrated airspeed, pressure altitude, and outside air temperature to get true airspeed (TAS = CAS / √σ), density altitude, and the air density ratio.

Quick Facts

TAS formula
TAS = CAS / √σ
σ (sigma) is the air density ratio: actual density ÷ standard sea-level density (1.225 kg/m³).
Rule of thumb
≈ +2% per 1,000 ft
On a standard day, TAS runs about 2% above CAS for every 1,000 ft of pressure altitude.
ISA sea level
15°C, 1013.25 hPa (29.92 inHg)
The ICAO Standard Atmosphere lapses temperature about 1.98°C per 1,000 ft through the troposphere.

Your Results

Calculated
True Airspeed (TAS)
-
CAS corrected for air density
Density Altitude
-
Altitude with equivalent standard-day density
Density Ratio (σ)
-
Actual density ÷ standard sea-level density
TAS − CAS
-
Speed gained from the density correction

Ready

Enter CAS, pressure altitude, and OAT, then press Calculate.

How to Calculate True Airspeed (TAS)

An airspeed indicator measures dynamic pressure, not the aircraft's actual speed through the air — so calibrated airspeed (CAS), the corrected instrument reading, must be adjusted for the density of the air at altitude to get true airspeed (TAS). This calculator applies the standard aviation relationship TAS = CAS / √σ, where σ (sigma) is the density ratio: actual air density divided by the standard sea-level density (1.225 kg/m³, or 0.0023769 slug/ft³). It derives σ from your pressure altitude and outside air temperature (OAT) using the ICAO Standard Atmosphere (ISA) model and the ideal gas law, then also reports the equivalent density altitude.

From pressure altitude and OAT to air density

Pressure altitude is converted to a standard-atmosphere pressure using P = P₀ × (1 − 6.8756×10⁻⁶ × h)^5.2559, where h is pressure altitude in feet and P₀ = 1013.25 hPa (29.92 inHg) is standard sea-level pressure — the same barometric formula altimeters use internally. The OAT you enter (converted to Kelvin) is combined with that pressure through the ideal gas law, ρ = P / (R × T), using R = 287.05 J/(kg·K) for dry air, to get actual air density ρ. Dividing by the standard sea-level density ρ₀ gives the density ratio σ = ρ/ρ₀, which drives the TAS correction.

Density altitude and why it matters

Density altitude is the altitude in the standard atmosphere that has the same air density as your actual conditions — a single number summarizing how "thin" the air really is. On a hot day, density altitude climbs well above the field elevation, meaning engines, propellers, and wings all perform as if the aircraft were much higher, which lengthens takeoff rolls and reduces climb rate. This calculator finds density altitude by solving the ISA density-versus-altitude relationship for the altitude that matches your computed σ, so it stays consistent with the TAS result rather than relying on a separate rule-of-thumb approximation. The model applies to the troposphere (up to 36,089 ft / 11,000 m) and ignores compressibility, so it is best suited to typical piston and turboprop general-aviation speeds.

Frequently Asked Questions

What is the difference between true airspeed and calibrated airspeed?
Calibrated airspeed (CAS) is what the airspeed indicator shows after correcting for instrument and position error; it reflects dynamic pressure, not the aircraft's actual speed through the air. True airspeed (TAS) is the aircraft's actual speed relative to the surrounding air mass, found by correcting CAS for the lower air density found at altitude. Because air thins with altitude, TAS is almost always higher than CAS, and the gap grows with altitude and temperature.
How is density altitude calculated?
Density altitude is the altitude in the standard atmosphere (ISA) that has the same air density as your actual conditions. This calculator finds it by computing actual air density from pressure altitude and outside air temperature via the ideal gas law, then solving the ISA density-versus-altitude equation for the altitude that produces that same density. On a day warmer than standard, density altitude is higher than pressure altitude; on a colder day, it is lower.
Does this calculator account for compressibility (Mach) effects?
No. It uses the standard incompressible relationship TAS = CAS / √σ, which is accurate for typical general-aviation speeds and altitudes (roughly below 250 knots and Mach 0.3). At higher speeds or altitudes, compressibility effects become significant and the CAS-to-EAS correction should be applied before converting to TAS.
Why does true airspeed matter for flight planning?
Groundspeed, fuel burn, and time en route are calculated from true airspeed combined with forecast winds, not from calibrated or indicated airspeed. Pilots typically derive TAS from cruise CAS, pressure altitude, and OAT using an E6B or electronic flight computer, then add wind to get groundspeed and estimated time en route.

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