Equivalent Airspeed from True Airspeed

An airspeed indicator is not a speedometer. It is a differential pressure gauge with a speed scale printed on the dial, and the only quantity it actually measures is dynamic pressure — $q = \tfrac{1}{2}\rho V^2$. To turn that into a speed it has to assume a density, and the density it assumes is 1.225 kg/m³, the standard sea-level value, because that is the number the dial was calibrated against on the bench.

Up high the air is thinner, so the same $q$ arrives from a much faster aeroplane, and the needle reads low. At 12,000 m, where the density is about a quarter of sea level, the needle reads roughly half the true airspeed. That is not an instrument fault to be corrected away. It is the instrument reporting the only thing the wing responds to, and the correction runs the other way: $V_E = V\sqrt{\rho/\rho_0}$ turns a true airspeed into the equivalent one, and the square root is there because $q$ depends on the square of speed.

The consequence is the single most useful fact in this shard. Lift, drag and stall all follow $q$, so all of them are fixed by the INDICATED speed and none of them care about altitude. The stall speed on the placard, the manoeuvring speed, the flap limit and the never-exceed line are all indicated speeds precisely because one number then serves at every height. Meanwhile the navigation problem — how long the fuel will last, when the aircraft will arrive — is entirely a true airspeed question. Two speeds, two jobs, and the confusion between them is the classic mistake this page exists to prevent.

Three refinements sit between the needle and the truth, and they are worth naming in order because the acronyms come up constantly. INDICATED airspeed is what the dial shows. CALIBRATED airspeed corrects it for the position and installation error of the static port, which is largest at high angles of attack — that is, on approach, where it matters most. EQUIVALENT airspeed removes the compressibility error that appears above roughly Mach 0.3, where the air being stopped at the pitot tube is squeezed rather than merely halted. TRUE airspeed applies the density ratio above. Below about 200 knots at low level the four are within a few knots of each other and the distinction is academic; in a jet at altitude they diverge enormously.

The mental arithmetic pilots use is that true airspeed runs about 2% above indicated per thousand feet of altitude, which is a linearisation of the square root above and holds well enough to about 20,000 ft. Past that it under-reads, and the exact relation is the one on this page.