Pressure Altitude Calculator

Pressure altitude is the altitude at which a given pressure occurs in the International Standard Atmosphere. It is not a measurement of where you are but a translation of measured pressure into a standard-atmosphere equivalent, obtained by inverting the barometric formula for a constant lapse rate troposphere: PA = 44330 (1 - (P/1013.25)^0.1903) in meters. The exponent 0.1903 is the reciprocal of g divided by the product of the standard lapse rate 0.0065 K per m and the gas constant 287.05, and the coefficient 44330 is the standard sea level temperature of 288.15 K divided by that lapse rate. Near sea level the relation works out to about 8.3 m, or 27 ft, per hPa. Because engine power and wing lift depend on air density rather than pressure alone, aviation practice adds a temperature correction to obtain density altitude, approximately 120 ft per degree C of deviation from the ISA temperature at that pressure altitude. A mountain airport sitting at 1500 m pressure altitude on a 35 degrees C afternoon can easily show a density altitude above 3000 m. Takeoff roll grows roughly 10 percent per 1000 ft of density altitude, and a normally aspirated piston engine loses about 3 percent of rated power per 1000 ft. The corrections have limits: the 120 ft per degree rule is a linearization valid in the lower troposphere, humidity is ignored even though moist air is slightly less dense, and the constant lapse rate assumption fails above the 11 km tropopause of the standard model.

The chain begins with Evangelista Torricelli, who demonstrated the mercury barometer in 1643, and with Blaise Pascal, whose 1648 experiment on the Puy de Dome showed that pressure falls with elevation. Pierre-Simon Laplace put the relation on an analytical footing around 1800 with the hypsometric formula, which allowed barometers to serve as altimeters for surveying long before aircraft existed. Aviation forced standardization. Early aircraft altimeters were simply aneroid barometers with an altitude scale, and Paul Kollsman's sensitive altimeter of 1928 added the adjustable setting window that let pilots dial in local pressure, a feature still called the Kollsman window. Competing national standard atmospheres proliferated in the 1920s, and the International Civil Aviation Organization adopted a unified Standard Atmosphere in 1952, published as Doc 7488, fixing sea level values of 1013.25 hPa, 15 degrees C and 1.225 kg per cubic meter with a 6.5 degrees C per km tropospheric lapse rate; the US Standard Atmosphere of 1976 extended the same lower-atmosphere profile to much greater heights. That shared reference is what makes the flight level system workable: above the transition altitude, 18000 ft in the United States, every aircraft sets 29.92 inHg so vertical separation rests on a common pressure altitude rather than on true height.