International Standard Atmosphere

Comparison of a graph of International Standard Atmosphere temperature and pressure and approximate altitudes of various objects and successful stratospheric jumps

The International Standard Atmosphere (ISA) is a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations. It has been established to provide a common reference for temperature and pressure and consists of tables of values at various altitudes, plus some formulas by which those values were derived. The International Organization for Standardization (ISO) publishes the ISA as an international standard, ISO 2533:1975.[1] Other standards organizations, such as the International Civil Aviation Organization (ICAO) and the United States Government, publish extensions or subsets of the same atmospheric model under their own standards-making authority.


The ISA mathematical model divides the atmosphere into layers with an assumed linear distribution of absolute temperature T against geopotential altitude h.[2] The other two values (pressure P and density ρ) are computed by simultaneously solving the equations resulting from:

  • the vertical pressure gradient resulting from hydrostatic balance, which relates the rate of change of pressure with geopotential altitude:
, and

at each geopotential altitude, where g is the standard acceleration of gravity, and Rspecific is the specific gas constant for dry air.

Air density must be calculated in order to solve for the pressure, and is used in calculating dynamic pressure for moving vehicles. Dynamic viscosity is an empirical function of temperature, and kinematic viscosity is calculated by dividing dynamic viscosity by the density.

Thus the standard consists of a tabulation of values at various altitudes, plus some formulas by which those values were derived. To accommodate the lowest points on Earth, the model starts at a base geopotential altitude of 610 meters (2,000 ft) below sea level, with standard temperature set at 19 °C. With a temperature lapse rate of −6.5 °C (-11.7 °F) per km (roughly −2 °C (-3.6 °F) per 1,000 ft), the table interpolates to the standard mean sea level values of 15 °C (59 °F) temperature, 101,325 pascals (14.6959 psi) (1 atm) pressure, and a density of 1.2250 kilograms per cubic meter (0.07647 lb/cu ft). The tropospheric tabulation continues to 11,000 meters (36,089 ft), where the temperature has fallen to −56.5 °C (−69.7 °F), the pressure to 22,632 pascals (3.2825 psi), and the density to 0.3639 kilograms per cubic meter (0.02272 lb/cu ft). Between 11 km and 20 km, the temperature remains constant.[3][4]

Layers in the ISA Standard Atmosphere 1976
Layer Level
Altitude above MSL[5]
h (m)
Altitude above MSL[5]
z (m)

( °C/km)[a]

T (°C)
p (Pa)
ρ (kg/m3)
0 Troposphere -610 -611 +6.5 +19.0 108,900 (1.075 bar) 1.2985
1 Tropopause 11,000 11,019 0.0 −56.5 22,632 0.3639
2 Stratosphere 20,000 20,063 -1.0 −56.5 5474.9 0.0880
3 Stratosphere 32,000 32,162 -2.8 −44.5 868.02 0.0132
4 Stratopause 47,000 47,350 0.0 −2.5 110.91 0.0020
5 Mesosphere 51,000 51,413 +2.8 −2.5 66.939
6 Mesosphere 71,000 71,802 +2.0 −58.5 3.9564
7 Mesopause 84,852 86,000 −86.28 0.3734
a lapse rate given per kilometer of geopotential altitude

In the above table, geopotential altitude is calculated from a mathematical model that adjusts the altitude to include the variation of gravity with height, while geometric altitude is the standard direct vertical distance above mean sea level (MSL).[2] Note that the Lapse Rates cited in the table are given as °C per kilometer of geopotential altitude, not geometric altitude.

The ISA model is based on average conditions at mid latitudes, as determined by the ISO's TC 20/SC 6 technical committee. It has been revised from time to time since the middle of the 20th century.

Use at non-standard day conditions

The ISA models a hypothetical standard day to allow a reproducible engineering reference for calculation and testing of engine and vehicle performance at various altitudes. It does not provide a rigorous meteorological model of actual atmospheric conditions (for example, changes in barometric pressure due to wind conditions). Neither does it account for humidity effects; air is assumed to be dry and clean and of constant composition. Humidity effects are accounted for in vehicle or engine analysis by adding water vapor to the thermodynamic state of the air after obtaining the pressure and density from the standard atmosphere model.

Non-standard (hot or cold) days are modeled by adding a specified temperature delta to the standard temperature at altitude, but pressure, density, and viscosity are not recalculated at the resultant non-standard temperature. (Thus the temperature effects on them are considered to be much less important than the effect of altitude.) Hot day, Cold day, Tropical, and Polar temperature profiles with altitude have been defined for use as performance references, such as United States Department of Defense MIL-STD-210C, and its successor MIL-HDBK-310.[6]

Other Languages