True Airspeed Calculator

Your airspeed indicator measures the pressure of the air ramming into the pitot tube. It is marked for sea level on a standard day, so as you climb into thinner air it reads less than the speed you are really moving through the air. That real speed is the true airspeed (TAS), and it is what you use for navigation, fuel and flight planning.

• IAS (indicated): what the instrument shows.
• CAS (calibrated): IAS corrected for instrument and position error, from the table in your flight manual. Usually within a few knots of IAS.
• EAS (equivalent): CAS corrected for air compressibility. Matters above about 200 kt and 10,000 ft.
• TAS (true): your speed through the air mass.
• Mach: TAS divided by the local speed of sound, which depends only on temperature.

The formula

static pressure p (ISA, below 36,089 ft) = 1013.25 × (1 − 0.0019812 × PA ÷ 288.15)^5.2559 hPa
impact pressure qc = 1013.25 × ((1 + 0.2 × (CAS ÷ 661.48 kt)²)^3.5 − 1)
Mach M = √(5 × ((qc ÷ p + 1)^(2÷7) − 1))
speed of sound a = 661.48 kt × √(temperature in kelvin ÷ 288.15)
TAS = M × a
EAS = TAS × √σ, where σ = (p ÷ 1013.25) ÷ (kelvin ÷ 288.15)

Above 36,089 ft (11 km) the standard atmosphere stops cooling and stays at −56.5 °C, and pressure falls as p = 226.32 × e^(−(PA − 36,089) ÷ 20,806) hPa. The calculator switches formulas there and works up to 65,000 ft. Going the other way (from TAS, EAS or Mach to CAS) uses the same equations backwards.

Worked example

You are flying at 150 kt CAS at a pressure altitude of 10,000 ft and the outside air is −5 °C.

• The standard temperature at 10,000 ft is 15 − 1.9812 × 10 = −4.8 °C, so the air is 0.2 °C colder than standard. The static pressure is 696.8 hPa (20.58 inHg).
• Impact pressure: 150 ÷ 661.48 = 0.2268. qc = 1013.25 × ((1 + 0.2 × 0.2268²)^3.5 − 1) = 1013.25 × 0.03646 = 36.94 hPa.
• Mach: qc ÷ p = 36.94 ÷ 696.8 = 0.05302. M = √(5 × (1.05302^0.2857 − 1)) = √(5 × 0.014869) = 0.273.
• Speed of sound at −5 °C (268.15 K): 661.48 × √(268.15 ÷ 288.15) = 638.1 kt.
• TAS = 0.2727 × 638.1 = 174 kt, 16% faster than the 150 kt on the dial.
• σ = (696.8 ÷ 1013.25) ÷ (268.15 ÷ 288.15) = 0.6877 ÷ 0.9306 = 0.739, so EAS = 174.0 × √0.739 = 149.6 kt, and the density altitude is about 9,980 ft.

The 2% rule of thumb

A quick mental estimate is TAS ≈ IAS + 2% for every 1,000 ft. At 10,000 ft that is 150 × 1.20 = 180 kt, about 6 kt too high here. The rule works best in a light aircraft below about 10,000 ft on a standard day. It ignores temperature (each 10 °C warmer than standard adds roughly 2% more) and compressibility, so it drifts further off the higher and faster you go.

Temperature probes: OAT and TAT

At speed, air hitting a temperature probe heats up ("ram rise"). The total air temperature is TAT = OAT (in kelvin) × (1 + 0.2 × M²). A jet's TAT probe recovers all of this heating, so the recovery factor is 1.0. Choose "Probe reading (TAT)" in Advanced and the calculator works back to the real outside air temperature. At 150 kt the rise is only about 4 °C; at Mach 0.8 it is over 25 °C.

Wind

Add your true course and the wind (direction it blows from, true) to get the heading to fly and your ground speed: wind correction angle = arcsin(wind speed × sin(wind direction − course) ÷ TAS), ground speed = TAS × cos(correction angle) − wind speed × cos(wind direction − course).

Uses the ICAO Standard Atmosphere (sea level 15 °C, 1013.25 hPa, 1.225 kg/m³, lapse rate 6.5 °C per km to 11 km) and dry air, for speeds below Mach 1. For planning and training: use your aircraft's approved flight manual for operational figures.