The International Standard Atmosphere (ISA)

The International Standard Atmosphere (ISA) is an agreed, imaginary atmosphere. It fixes the temperature, pressure and density at mean sea level and lays down exactly how each changes with height, so that every altimeter, airspeed indicator and performance chart is built on the same reference. ICAO publishes it as the ICAO Standard Atmosphere, and the "standard atmosphere" of FAA material uses the same figures.

Real air almost never matches the model, and what matters to a pilot is the difference. An altimeter errs by an amount that depends on how far the temperature departs from ISA, and an airplane performs according to the actual density, not the standard one. Much of the arithmetic in EASA and FAA exams comes down to working out that difference. The layers of the real atmosphere are described in the atmosphere; this article looks at the model itself.

Why a standard atmosphere

Temperature and pressure at any level change from hour to hour and from place to place. An instrument cannot be calibrated, nor two airplanes compared, against something that moves, so aviation agreed on a fixed reference. The ISA serves the two purposes that exam questions name: the calibration of pressure instruments and the comparison of aircraft performance under identical conditions.

The model is defined in ICAO Doc 7488, the Manual of the ICAO Standard Atmosphere, and FAA material uses the same sea-level values, lapse rate and tropopause, so EASA and FAA exams work with the same numbers. Its assumptions are simple: the air is treated as an ideal gas, temperature follows a fixed profile with height, and pressure and density follow from the weight of the air above. The values represent average mid-latitude conditions; the ISA tropopause, at 11 km and −56.5 °C, matches the average tropopause near 50° latitude. Nothing in the model is measured on the day: +15 °C at sea level is the reference from which deviations are counted, not a prediction.

ISA sea-level values

These are the conditions in which the instruments read true. An airspeed indicator shows true airspeed only when the air density equals the ISA sea-level value, because it is calibrated for a density of 1.225 kg/m³. The standard pressure setting, usually rounded to 1013 hPa on the subscale and 29.92 inHg in the United States, is the ISA sea-level pressure. The absolute temperature, °C + 273, is the one used in the gas law and for the speed of sound.

Temperature lapse rate and the tropopause

In the ISA troposphere temperature falls uniformly at the standard lapse rate of 6.5 °C per km, which is 0.65 °C per 100 m or 1.98 °C per 1,000 ft. For mental arithmetic it is rounded to 2 °C per 1,000 ft; the FAA states it as about 2 °C, or 3.5 °F, per 1,000 ft. The fall continues to the tropopause at 11 km (36,090 ft; FAA material gives 36,089 ft), where the temperature has reached −56.5 °C.

Below the tropopause the ISA temperature follows a simple rule:

ISA temperature (°C) = 15 − 2 × pressure altitude in thousands of feet

At FL140 it is 15 − 28 = −13 °C; at 8,000 ft, −1 °C; at FL300, −45 °C. The rounded figure gives −57 °C at 36,000 ft against the exact −56.5 °C, a difference of rounding only. Above 36,090 ft the rule stops: at FL450 the ISA temperature is still −56.5 °C, not the −75 °C that carrying the lapse rate on would give.

The ISA lapse rate describes the model's air at rest, not a rising parcel: unsaturated air cools at the dry adiabatic lapse rate of about 3 °C per 1,000 ft, saturated air more slowly. The real profile on the day, the environmental lapse rate, comes from radiosonde ascents and may be steeper or shallower than ISA, or inverted (see lapse rates and atmospheric stability). The 2 °C figure remains the usual first estimate: an aerodrome at 1,000 ft reporting +6 °C suggests a freezing level near 4,000 ft.

The real tropopause varies far more: about 16 to 18 km and −75 to −80 °C over the equator, about 8 km and −40 to −50 °C over the poles, and higher in summer. A forecast or an upper-air chart therefore overrides the ISA tropopause. If the 300 hPa chart shows −54 °C and the tropopause is at FL330, the temperature at FL350 is about −60 °C: lapse 2 °C per 1,000 ft from FL300 to FL330, then hold it constant.

Pressure and density with height

Pressure at any level is the weight of the air above it. Air is compressible, so the lower layers are squeezed by those above and hold more mass per foot of depth. Pressure therefore falls quickly near the ground and ever more slowly higher up: in the ISA, 1 hPa corresponds to about 27 ft at sea level, about 50 ft at FL200 and about 100 ft at FL400. The FAA's working figure for the lower levels is 1 inHg per 1,000 ft.

The pressure has halved by about 18,000 ft and by FL400 is under a fifth of the sea-level value. The same figures give the approximate flight level of each standard pressure surface on upper-air charts.

Density follows from the gas law. Below the tropopause the falling temperature partly offsets the falling pressure, so density falls a little more slowly: at 20,000 ft the pressure is down to about 46 % and the density to about half. Above the tropopause the temperature is constant, the offset disappears and density falls in step with pressure, which is why a jet engine's thrust falls faster with height above the tropopause than below it.

The speed of sound depends only on absolute temperature, about 38.95 × √T knots with T in kelvin: 661 kt at sea level, about 588 kt at FL300 and 573 kt at and above the tropopause. Climbing at constant CAS, true airspeed rises as density falls and Mach number rises faster still: from sea level to FL360 at 330 kt CAS in ISA, TAS goes from 330 to about 555 kt and Mach number from 0.50 to about 0.97 (see airspeed indicator and Machmeter).

ISA deviation calculations

ISA deviation is the actual temperature minus the ISA temperature at the same pressure altitude, written ISA +10 or ISA −5. It is the temperature input to most performance tables, fuel predictions and density calculations. The temperature used is the static or outside air temperature (SAT, OAT), not the total air temperature, which includes ram heating (see air data computer and air temperature).

The method has three steps:

1. Find the pressure altitude: the flight level in cruise or, for an aerodrome, the elevation corrected for QNH.
2. Work out the ISA temperature there: 15 °C minus 2 °C per 1,000 ft below 36,090 ft, −56.5 °C above.
3. Subtract, actual minus ISA. A positive result is warmer than standard, a negative one colder.

The last two rows show why the pressure altitude comes first. With a low altimeter setting the aerodrome's pressure altitude lies above its elevation, its ISA temperature is lower, and the deviation is larger than a calculation from elevation would give.

View full schematic

ISA in altimetry

A pressure altimeter measures static pressure and displays the height at which that pressure occurs in the ISA, counted from the pressure set on its subscale. With the standard setting it shows pressure altitude, the ISA height corresponding to the pressure around the aircraft. Pressure altitude underlies:

• flight levels, pressure altitudes in hundreds of feet: flight level zero is the 1013.2 hPa surface (see transition altitude and transition level);
• the altitude a transponder reports, whatever the subscale shows;
• cabin altitude, the pressure altitude of the air inside a pressurized cabin;
• performance charts, which are entered with pressure altitude, not elevation.

On the ground, pressure altitude comes from the elevation and the altimeter setting; QNH is itself the aerodrome pressure reduced to sea level through the ISA (see atmospheric pressure). Each hectopascal below 1013 puts it about 27 to 30 ft above the elevation: an aerodrome at 1,200 ft with QNH 998 hPa has a pressure altitude of about 1,650 ft at 30 ft per hPa. With the FAA's 1,000 ft per inch, an airport at 3,500 ft with 30.42 inHg is at about 3,000 ft. A low setting gives a higher pressure altitude, a high setting a lower one.

Because the scale assumes ISA temperatures, every departure from them becomes altimeter temperature error. In air colder than ISA the pressure levels lie closer together, the altimeter over-reads and the aircraft is lower than indicated; in warmer air it under-reads. PANS-OPS gives a rule of thumb of 4 % of the height above the altimeter setting source for every 10 °C below ISA, about 4 ft per 1,000 ft per degree. The rule is safe only for aerodrome temperatures above about −15 °C; colder than that, the ICAO correction table is used:

• Cruising at 6,000 ft on the QNH of a station at 2,000 ft, in air 15 °C below ISA, the aircraft is about 4 × 4 × 15 = 240 ft lower than indicated.
• At an aerodrome 2,000 ft high reporting −14 °C, ISA −25, a final approach fix published at 5,000 ft needs about 4 × 3 × 25 = 300 ft added.

An ILS glide path, a radio signal, is unaffected; every altitude read from the barometric altimeter is (see pressure altimeter and cold-weather altimetry).

ISA in performance

Performance charts are entered with pressure altitude and temperature or ISA deviation. What the wing and engines respond to is density, usually expressed as density altitude: pressure altitude corrected for non-standard temperature, the ISA height at which the density would equal the actual density. In ISA conditions the two are equal. Each degree above ISA adds roughly 120 ft, so at a pressure altitude of 5,500 ft and ISA +30 the density altitude is about 9,100 ft, and the airplane accelerates, lifts off and climbs as if it were there (see density altitude and factors affecting takeoff and landing performance). Humid air is a little less dense again, and performance charts assume dry air.

The airspeed indicator, calibrated for ISA sea-level density, under-reads true airspeed whenever the air is thinner. The rule of thumb of about 2 % per 1,000 ft makes 100 kt CAS about 114 kt TAS at 7,000 ft; at FL350 in ISA, 250 kt IAS is about 430 kt TAS.

Jet engines are flat-rated: they deliver full rated thrust up to a flat-rating temperature, often quoted as an ISA deviation, and less above it; on the A320 the assumed temperature for a flexible takeoff may not exceed ISA +53 °C. Cruise and integrated range tables are indexed by ISA deviation as well as weight and level. A warm deviation lowers the maximum altitude and raises fuel burn, and a large gap between the forecast and actual temperatures changes the FMS predictions of fuel and optimum altitude (see cost index and cruise economics).

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.