Altitude to Air Pressure Calculator: Standard Atmosphere Pressure, Temperature, Density and Oxygen
Air pressure at any altitude from −1,000 m to 86 km (U.S. Standard Atmosphere 1976 / ISA), or the altitude from a pressure reading, in hPa, kPa, inHg, mmHg, psi or atm, with temperature, air density, speed of sound, equivalent oxygen, inspired oxygen pressure and the boiling point of water. Set a non-standard sea-level pressure or a hot/cold day offset.
How it works
Geopotential height H = 6,356,766 × z ÷ (6,356,766 + z) · Troposphere (H ≤ 11 km): T = 288.15 − 0.0065 × H, P = 1013.25 × (T ÷ 288.15)^5.25588 · Isothermal layers: P = Pb × e^(−0.0341632 × (H − Hb) ÷ Tb) · Other layers: P = Pb × (T ÷ Tb)^(−0.0341632 ÷ L) · Density ρ = P ÷ (287.053 × T) · Effective O₂ = 20.95% × P ÷ 1013.25 · PiO₂ = 0.2095 × (P − 47 mmHg)
The calculator uses the U.S. Standard Atmosphere 1976, which is the same as the ICAO International Standard Atmosphere up to 32 km. It starts at 1013.25 hPa and 15 °C at sea level. Temperature falls 6.5 °C per kilometre up to 11 km, stays at −56.5 °C to 20 km, then rises slowly through the stratosphere. Each layer has its own exact pressure formula, which comes from the hydrostatic equation and the ideal gas law, so the result matches the published tables at every height up to 86 km. Heights are converted to geopotential metres first, which is how the standard is defined. Pressure → altitude solves the same equations backwards, layer by layer. Oxygen stays 20.95% of dry air at every altitude; what falls is the pressure, so each breath carries fewer oxygen molecules. The effective oxygen figure is the oxygen percentage at sea level that gives the same oxygen pressure, which is how altitude-tent and hypoxic-training charts quote it. Inspired oxygen pressure (PiO₂) also subtracts the 47 mmHg of water vapour in warm, humidified air in the airways, the figure physiologists use. The boiling point comes from the Antoine vapour-pressure equation for water. Under More options you can enter the day’s sea-level pressure and a temperature offset (for example ISA +20 °C on a hot day). The model then shifts every layer by that offset and recomputes the pressures, which is close to what happens in a real warm or cold air mass. The standard atmosphere is a yearly mid-latitude average: weather moves real pressure a few percent and temperature by tens of degrees.
Worked example
At 3,500 m (11,483 ft) the geopotential height is 3,498 m. The temperature is 288.15 − 0.0065 × 3,498 = 265.41 K (−7.7 °C), and the pressure is 1013.25 × (265.41 ÷ 288.15)^5.25588 = 657.8 hPa, which is 64.9% of sea level, 19.42 inHg or 493.4 mmHg. Air density is 65,780 Pa ÷ (287.053 × 265.41) = 0.863 kg/m³. Effective oxygen is 20.95% × 657.8 ÷ 1013.25 = 13.6%, inspired oxygen pressure is 0.2095 × (493.4 − 47) = 94 mmHg, and water boils at 88.4 °C. In the other direction, a station reading of 700 hPa corresponds to about 3,014 m (9,887 ft).
Sources: NOAA/NASA/USAF: U.S. Standard Atmosphere, 1976 (NASA-TM-X-74335) · Engineering ToolBox: U.S. Standard Atmosphere table (SI) · Mide: Air pressure at altitude calculator and table · Omni Calculator: Air pressure at altitude (barometric formula)
Frequently asked questions
What is the air pressure at sea level?
The standard value is 1013.25 hPa, which is 101.325 kPa, 29.92 inHg, 760 mmHg or 14.696 psi. On real days it usually ranges from about 980 to 1,040 hPa, and below 950 hPa only in deep storms.
How much does air pressure drop per 1,000 feet?
Near sea level it drops about 1 inHg (about 34 hPa) per 1,000 ft, roughly 12 hPa per 100 m. The drop shrinks with height because the air above is thinner: at 10,000 ft it is about 0.8 inHg per 1,000 ft.
Why does my barometer read 1,010 hPa in the mountains?
Weather barometers and phone apps usually show pressure reduced to sea level so forecasts can be compared. The real (station) pressure at 2,000 m is nearer 795 hPa. Use station pressure for altitude calculations.
What is the air pressure on top of Mount Everest?
The standard atmosphere gives about 315 hPa at 8,849 m, 31% of sea level. Measured summit pressure is higher, about 333–337 hPa, because the atmosphere is thicker over the tropics; that difference is part of why Everest can be climbed without bottled oxygen.
Is the oxygen percentage lower at altitude?
No. Air is 20.95% oxygen up to about 80 km. The pressure is lower, so each breath carries fewer oxygen molecules. At 3,500 m a breath holds about the same oxygen as a breath of 13.6% oxygen air at sea level.
At what temperature does water boil at altitude?
About 1 °C lower for every 300 m: 95 °C at 1,600 m (Denver), 90 °C at about 3,000 m and about 70 °C on Everest. Food cooks more slowly, so recipes add time or use a pressure cooker.
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