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
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
Something look off?
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
- 2026-09-19, changed: Five more tools passed the stable verification bar: geodesic distance and destination (checked against GeographicLib's GeodTest), UTM forward and inverse (checked against exact transverse Mercator values), and the standard atmosphere (checked against a separately written implementation). Changelog
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
- Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)), International Civil Aviation Organization, 3rd edition, Doc 7488/3. Section 2 (defining constants and equations) and Table 1. Paid only.
- U.S. Standard Atmosphere, 1976, NOAA, NASA, and U.S. Air Force, NOAA-S/T 76-1562. Part 1, equations 23 and 33a, and Table I.
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)
Learn the concept: What is density altitude?