True Airspeed Formula (TAS)
Convert Calibrated Airspeed (CAS) to True Airspeed (TAS) using altitude and outside air temperature.
Essential for accurate flight planning.
The Formula
T_actual = OAT(°C) + 273.15 [Kelvin]
TAS ≈ CAS × √(T_actual / T_ISA) × Altitude correction factor
True Airspeed (TAS) is the actual speed of the aircraft relative to undisturbed air. As altitude increases, air becomes less dense — the same number of air molecules passes over the wings and pitot tube more slowly, causing indicated and calibrated airspeed to read lower than the aircraft's actual speed. TAS corrects for this by accounting for both altitude (pressure) and temperature.
Simplified Rule of Thumb
At standard ISA temperature, TAS increases roughly 2% above CAS for every 1,000 feet of altitude. A temperature deviation from ISA adds approximately an additional 1% TAS per 5°C warmer than standard. This rule of thumb is accurate to within 2–3% at altitudes below 25,000 ft and is widely used in general aviation for mental calculations.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| CAS | Calibrated Airspeed (IAS corrected for instrument error) | knots |
| TAS | True Airspeed — actual speed through air | knots |
| OAT | Outside Air Temperature | °C |
| T_ISA | ISA standard temperature at altitude (K) | Kelvin |
| T_actual | Actual temperature at altitude (K) | Kelvin |
| Altitude | Pressure altitude | feet |
Example 1
CAS = 120 knots. Altitude = 8,000 ft. OAT = −5°C. Find TAS.
Using rule of thumb: +2% per 1,000 ft = +16% at 8,000 ft
ISA temp at 8,000 ft = 15 − (8 × 2) = −1°C. OAT is −5°C — 4°C below ISA → −0.8% correction
TAS ≈ 120 × 1.16 × 0.992 ≈ 120 × 1.151
TAS ≈ 138 knots
Example 2
CAS = 95 knots. Altitude = 4,000 ft. OAT = 20°C (ISA +13°C). Find TAS.
Altitude correction: +2% × 4 = +8%
Temperature deviation: +13°C → +2.6% extra
TAS ≈ 95 × (1.08 + 0.026) = 95 × 1.106
TAS ≈ 105 knots
When to Use It
- Flight planning: TAS combined with wind gives ground speed and actual flight time
- Fuel planning: burn rates are based on TAS and engine power setting
- Filing flight plans: TAS is the speed entered in official flight plan documents
- Calculating wind correction angles and ground speed accurately
- Performance comparisons between aircraft at different altitudes