Standard Atmosphere Calculator (ISA)
Look up the air at any height from 5 km below sea level to 86 km up. The US Standard Atmosphere 1976, which matches the ICAO International Standard Atmosphere to 32 km, gives temperature, pressure, density, speed of sound and viscosity, finds the pressure altitude for a pressure, and works out density altitude.
How to Use
- Pick what to find: the air at an altitude, the altitude for a pressure (pressure altitude), or the density altitude for a pressure altitude and temperature.
- Enter the altitude in metres, feet or kilometres and say whether it is geometric (height above sea level) or geopotential (the standard’s own scale, used for pressure altitude).
- For a hot or cold day, add an ISA deviation such as +15 °C; for density altitude, enter the outside air temperature.
- Read temperature, pressure, density and speed of sound, see the point on the temperature and pressure profile, and check the table for viscosity, gravity and other units.
- Press a preset for a ready-made example, and open Show Work for the layer and formula used.
Worked Example
The air at 35,000 ft. As a flight level this is a pressure altitude, so it is geopotential: 35,000 × 0.3048 = 10,668 m, inside the troposphere. T = 288.15 − 0.0065 × 10,668 = 218.81 K, −54.34 °C. p = 101,325 × (218.81 ÷ 288.15)^(0.0341632 ÷ 0.0065) = 23,842 Pa, 238.4 hPa. ρ = 23,842 × 0.0289644 ÷ (8.31432 × 218.81) = 0.3796 kg/m³, and a = √(1.4 × 8.31432 × 218.81 ÷ 0.0289644) = 296.54 m/s.
Density altitude on a hot day. At a pressure altitude of 5,000 ft (1,524 m) the standard pressure is 843.1 hPa and the standard temperature 5.09 °C. At 30 °C the air is 24.9 °C warmer, so ρ = 84,310 × 0.0289644 ÷ (8.31432 × 303.15) = 0.9688 kg/m³. The standard atmosphere has that density at 7,801 ft.
The common mistake: carrying the 6.5 K/km lapse rate above 11 km. Extending the troposphere formula to 20 km (geopotential) gives 288.15 − 130 = 158.15 K and 4,328 Pa. In the standard the temperature stops falling at the tropopause and stays at 216.65 K (−56.5 °C), so the right answer is 216.65 K and 5,474.9 Pa; the shortcut is 58.5 K too cold and 21% low on pressure.
Show Work
Formulas
Layers of the US Standard Atmosphere 1976 (defining values, geopotential heights; pressures follow from them):
| Base height Hb | Layer | Gradient L | Base temperature | Base pressure |
|---|---|---|---|---|
| 0 km | Troposphere | −6.5 K/km | 288.15 K | 101,325 Pa |
| 11 km | Tropopause | 0 | 216.65 K | 22,632.1 Pa |
| 20 km | Stratosphere | +1.0 K/km | 216.65 K | 5,474.89 Pa |
| 32 km | Stratosphere | +2.8 K/km | 228.65 K | 868.019 Pa |
| 47 km | Stratopause | 0 | 270.65 K | 110.906 Pa |
| 51 km | Mesosphere | −2.8 K/km | 270.65 K | 66.9389 Pa |
| 71 km | Mesosphere | −2.0 K/km | 214.65 K | 3.95642 Pa |
| 84.852 km | Top (86 km geometric) | — | 186.946 K | 0.373384 Pa |
Where the Standard Atmosphere Came From
Early aviators needed one agreed atmosphere to compare aircraft and calibrate altimeters, since the real air changes by the hour. National standards appeared in the 1920s, and the International Civil Aviation Organization adopted its Standard Atmosphere in 1952, with sea-level conditions of 15 °C and 1,013.25 hPa and a fall of 6.5 °C per kilometre up to the tropopause at 11 km.
Rockets and satellites pushed the need higher. The US Standard Atmosphere of 1962 and its 1976 revision, published jointly by NOAA, NASA and the US Air Force, extend the model to 1,000 km. Below 32 km the 1976 standard is identical to the ICAO one; up to 86 km it is built from the seven straight-line temperature layers in the table, and above that the air is no longer well mixed, so molecular weight and temperature are given by separate formulas this calculator does not cover. The constants used here, including the 1976 gas constant 8.31432 J/(mol·K), are the defining values of that standard (US Standard Atmosphere 1976, NOAA/NASA/USAF).
About This Tool
This calculator evaluates the US Standard Atmosphere 1976 from −5 km to 86 km. It converts geometric to geopotential height, finds the layer, and gives the temperature, pressure, density, speed of sound, dynamic and kinematic viscosity and gravity, with an optional ISA deviation for hot and cold days. It also runs backwards from a pressure to the pressure altitude, and finds the density altitude from a pressure altitude and the outside air temperature, with the pilot’s rule of thumb alongside. The standard is an average: real air on a given day can differ by tens of degrees and tens of hectopascals.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Density Altitude Calculator, Speed of Sound Calculator, and Terminal Velocity Calculator.
Frequently Asked Questions
What is the International Standard Atmosphere?
It is an agreed model of average mid-latitude air: 15 °C (288.15 K) and 101,325 Pa at sea level, cooling at 6.5 K per km up to 11 km, then constant at −56.5 °C to 20 km. Sea-level density works out at 1.225 kg/m³ and the speed of sound at 340.29 m/s (661.48 kn). Aircraft instruments, engine ratings and performance charts are all calibrated to it.
What is the air like at cruising altitude?
At 35,000 ft (FL350) the standard gives −54.34 °C, 238.4 hPa, under a quarter of sea-level pressure, and 0.3796 kg/m³, 31% of sea-level density. The speed of sound there is 296.54 m/s, 576.4 kn, so Mach 0.85 is about 490 kn true airspeed.
What is pressure altitude?
It is the height in the standard atmosphere that has a given pressure, which is what an altimeter set to 1,013.25 hPa (29.92 inHg) shows. 500 hPa, the level weather charts use for the middle of the atmosphere, is at a pressure altitude of 5,574 m geopotential, 5,579 m geometric: half the air is below that.
What is density altitude?
It is the standard altitude with the same air density as the real air. At an airfield with a pressure altitude of 5,000 ft on a 30 °C day (24.9 °C above standard there) the air is 0.9688 kg/m³, the standard density at 7,801 ft, so the aeroplane performs as if it were 2,800 ft higher. The pilot’s rule PA + 120 ft per °C gives 7,989 ft.
What is the difference between geometric and geopotential altitude?
Geometric altitude is the real height. Geopotential altitude allows for gravity weakening with height, so that the pressure formulas can use a constant g₀ = 9.80665 m/s². They differ little low down but grow apart: 30 km geometric is 29,859 m geopotential, and the standard’s top, 86 km geometric, is 84,852 m geopotential.
How do I use the Standard Atmosphere Calculator (ISA)?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Aircraft performance
A hot day at a 5,000 ft airfield gives a density altitude of 7,801 ft and only 79.09% of sea-level air density for the wings and engine.
Mountaineering
On the summit of Everest (8,849 m) the standard air is 314.97 hPa, 31% of sea-level pressure, at −42.44 °C; real pressure there runs a little higher.
Weather balloons and high-altitude flight
At 30 km the standard air is 11.97 hPa and 0.01841 kg/m³, 1.5% of sea-level density, at −46.64 °C.
Engineering design
An ISA+20 day at sea level (35 °C) cuts air density from 1.225 to 1.1455 kg/m³, which lowers engine power and fan output by about 6.5%.
Aerodynamics homework
The 1976 standard gives the speed of sound, viscosity and kinematic viscosity at any height, for Mach and Reynolds numbers: 295.07 m/s and 1.4216 × 10⁻⁵ Pa·s at 11 km.
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