How do IAS, CAS, TAS and Mach relate?

How it works

The airspeed indicator measures how hard the air pushes into the pitot tube, and that push depends on the air's density as well as the speed. Calibrated to sea-level air, it shows the indicated airspeed (IAS); corrected for the aircraft's own instrument and position errors it becomes the calibrated airspeed (CAS). Higher up, the air is thinner, so the aircraft moves through it faster than the indicator shows: that real speed through the air is the true airspeed (TAS). The Mach number M = TAS / a compares it with the speed of sound a = √(γ · R · T), which depends only on the temperature T (γ = 1.4 and R the gas constant of air).

The calculator follows the standard method: it finds the air pressure at the pressure altitude in the ICAO standard atmosphere (Doc 7488), turns the CAS into the pressure the pitot tube feels with the compressible-flow formula, solves the Mach number at that altitude, and multiplies by the speed of sound at the outside air temperature. The equivalent airspeed (EAS) is the TAS scaled by the square root of the density ratio; above about Mach 0.3 it is noticeably lower than the CAS because the air compresses in the tube.

Example: 120 kt indicated at 8,000 ft on a standard day (−0.8 °C) is Mach 0.210 and about 135 kt true. The rule of thumb from the FAA Pilot’s Handbook of Aeronautical Knowledge, TAS ≈ IAS + 2% per 1,000 ft, gives 139 kt: handy in the cockpit, but it drifts higher with altitude and speed.

IAS is taken as CAS here, because the position error differs for every aircraft and is found in its flight manual. The answer holds below Mach 1 only. It is for learning and simulators, not for flight planning.