geoprimsField-grade geospatial math

Standard atmosphere

Temperature, pressure, density, speed of sound, and viscosity of the ICAO or US 1976 standard atmosphere at any altitude, on a standard or non-standard day.

Planning and education aid. Not for primary navigation. Full disclaimer

-4.812°C

At 10,000 ft in the standard atmosphere it is -4.812 °C with pressure 696.816 hPa and density 0.904637 kg/m³, in the troposphere.

Pressure
Density
Temperature ratio θ
Pressure ratio δ
Density ratio σ
Speed of sound
Provenance
Computed by
aviation.atmosphere.isa 1.0.0, core 0.1.0
Model
ICAO Standard Atmosphere (Doc 7488/3) layer equations on geopotential altitude; US 1976 optional
Accuracy
Exact evaluation of the standard's defining equations to double precision; matches the printed tables within their rounding
Notes
None
Cites
International Civil Aviation Organization, Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)); NOAA, NASA, and U.S. Air Force, U.S. Standard Atmosphere, 1976

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0 °CTropopause, 11 km-4.812 °C at 10,000 ftTemperature →Altitude ↑
How we got thisFormula, worked example, sources, and proof

Model: ICAO Standard Atmosphere (Doc 7488/3) layer equations on geopotential altitude; US 1976 optional

Accuracy: Exact evaluation of the standard's defining equations to double precision; matches the printed tables within their rounding

When to use this: Use this when you need the standard atmosphere's own numbers at an altitude: the temperature to compare a reported one against, the pressure or density a performance or instrument calculation assumes, or the speed of sound behind a Mach number. It is the reference the rest of the aviation tools are built on, and it takes a temperature deviation when the day is not standard.

Limitations: The standard atmosphere is a model, not a forecast: it describes a fixed average and says nothing about the air over your airport today. Above the tropopause the layers are isothermal by definition, and beyond the model's ceiling the tool stops rather than extrapolating. Use a real sounding, a METAR, or a forecast when the actual air matters.

Worked example: The standard atmosphere at 10,000 ft. Source: ICAO Doc 7488/3: 268.338 K, 696.82 hPa, 0.904637 kg/m³ at 3,048 m geopotential.

You enter

Altitude
10000 ft

You get

Temperature
-4.812 °C
Pressure
696.816 hPa
Density
0.904637 kg/m³
Temperature ratio θ
0.931244
Pressure ratio δ
0.687704
Density ratio σ
0.738479
Speed of sound
638.3 kt
Dynamic viscosity
0.000016922 Pa*s
Kinematic viscosity
0.000018705 m2/s
Gravity
9.79725 m/s²
Geopotential altitude
10,000 ft
Geometric altitude
10,005 ft
Layer
troposphere

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

Checked against: 22 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Constants this tool assumes

Values you do not enter, and where each comes from.

Sea-level pressure P0
101325 Pa — Manual of the ICAO Standard Atmosphere (Doc 7488)
Sea-level temperature T0
288.15 K — Manual of the ICAO Standard Atmosphere (Doc 7488)
Standard gravity g0
9.80665 m/s2 — Manual of the ICAO Standard Atmosphere (Doc 7488)
Gas constant for dry air R
287.05287 J/(kg K) — Manual of the ICAO Standard Atmosphere (Doc 7488)
Tropospheric lapse rate
-0.0065 K/m — Manual of the ICAO Standard Atmosphere (Doc 7488)
Earth radius for geopotential altitude
6356766 m — Manual of the ICAO Standard Atmosphere (Doc 7488)

Sources

Terms

ISA: International Standard Atmosphere
A reference atmosphere: 15 °C and 1013.25 hPa at sea level, cooling 6.5 °C per kilometer up to 11 km. Altimeters and performance charts are built on it. Source: Manual of the ICAO Standard Atmosphere (Doc 7488)