Air pressure at altitude from the standard atmosphere, with temperature, air density and the boiling point of water, or the altitude for a given pressure.
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At 1,500 m (4,921 ft) the standard atmosphere gives 845.6 hPa (83.5% of sea-level pressure) and 5.3 °C. Water boils at 95.0 °C there.
This height is in the troposphere (−6.5 K/km).
g₀ = 9.80665 m/s², M = 0.0289644 kg/mol, R* = 8.31432 J/(mol·K) (1976 standard).
IAPWS-IF97 saturation-temperature equation (eq. 31); it reproduces the IAPWS check value Ts(0.1 MPa) = 372.755919 K.
Pressure at a height comes from the barometric formula of the U.S. Standard Atmosphere 1976: 1013.25 hPa and 15 °C at sea level, temperature falling 6.5 °C per kilometre up to 11 km, then steady at −56.5 °C to 20 km. The boiling point of water at that pressure comes from the IAPWS-IF97 saturation equation. Start from a pressure instead and the same formula runs backwards to the altitude.
Cooks, climbers, pilots and engineers use it to see how thin the air is. The default, 1,500 m, gives 845.6 hPa, 83.5% of sea-level pressure, and water boiling at 95.0 °C; on the summit of Everest (8,849 m) water boils at 70.2 °C.
The standard atmosphere is an average: real pressure moves with the weather, and the air temperature shown is the model's, not today's. Enter the day's sea-level pressure under More options for a weather-adjusted figure.
Up to 11 km, the U.S. Standard Atmosphere 1976 gives P = 1013.25 × (1 − 0.0065H ÷ 288.15)^5.25588 hPa, with H the geopotential height in meters. At 1,500 m that is 845.60 hPa, 83.5% of sea-level pressure, and water boils at 94.98 °C (203.0 °F).
These are average-day values. Real pressure rises and falls with the weather, and the boiling point moves with it.
The standard atmosphere starts from 1013.25 hPa and 15 °C (288.15 K) at sea level, with temperature falling 6.5 °C per kilometer. For 1,500 m:
The exponent is g₀M ÷ (RL), using the 1976 constants g₀ = 9.80665 m/s², M = 0.0289644 kg/mol, R = 8.31432 J/(mol·K) and lapse rate L = 0.0065 K/m.
Geopotential height corrects for gravity weakening with height. The correction is only 0.35 m at 1,500 m, but it puts the 11 km layer boundary at 11,019 m of real height.
From 11 to 20 km (geopotential) the temperature holds at −56.5 °C, so pressure falls exponentially from 226.32 hPa:
P = 226.32 × exp[−g₀M(H − 11,000) ÷ (R × 216.65)]*
At 20,000 m that leaves 55.29 hPa, 5.5% of sea-level pressure. Above 20 km the temperature rises 1 °C per kilometer, and the model ends at 32 km.
| Geometric altitude m | Pressure hPa | Sea-level share % | Water boils at °C |
|---|---|---|---|
| 0 | 1013.25 | 100.0 | 99.97 |
| 1000 | 898.76 | 88.7 | 96.65 |
| 1609 | 834.35 | 82.3 | 94.62 |
| 3640 | 646.05 | 63.8 | 87.83 |
| 8849 | 314.97 | 31.1 | 70.22 |
The rows are sea level, 1,000 m, Denver (1,609 m), La Paz (3,640 m) and the summit of Everest (8,849 m), all with standard sea-level conditions.
Pressure falls fastest near the ground, where the air is densest. The first kilometer above sea level takes away 114.5 hPa; the kilometer from 8,000 to 9,000 m takes away 48.5 hPa.
Water boils when its vapor pressure equals the pressure around it, so thinner air means a lower boiling point. The temperature comes from the IAPWS-IF97 saturation equation and depends on pressure alone.
Near sea level the boiling point falls about 1 °C for every 300 m, or 1.8 °F per 1,000 ft. The rate stays close to 3.3–3.4 °C per kilometer all the way to Everest's summit.
At standard sea-level pressure, water boils at 99.97 °C on today's ITS-90 temperature scale, not exactly 100 °C. At 1000 hPa it boils at 99.61 °C.
Food simmered in water cooks more slowly at altitude, because the water cannot get hotter than its boiling point. A pressure cooker raises the pressure inside the pot, and with it the boiling point.
Running the formula backward gives the height for a pressure. 500 hPa corresponds to 5,579.3 m of real height, or 5,574.4 m geopotential, the 5,574 m listed for that level in the ICAO standard atmosphere.
Use station pressure, the barometer's actual reading. Weather reports give pressure reduced to sea level (QNH or mean sea-level pressure), so a mountain town's report reads near 1013 hPa while Denver's actual station pressure is about 834 hPa.
At Denver's 1,609 m, a QNH of 1000 hPa gives 823.4 hPa and a boiling point of 94.26 °C. A QNH of 1030 hPa gives 848.1 hPa and 95.07 °C, so a 30 hPa swing moves the boiling point by 0.8 °C.
The air temperature at height is the standard atmosphere's average. Real profiles vary with season and weather, including inversions where the air warms with height.
Dry air is 20.9% oxygen at every height, but lower pressure packs fewer molecules into each breath. The oxygen partial pressure scales with the pressure ratio: 83.5% of the sea-level value at 1,500 m, 63.8% in La Paz and 31.1% on Everest's summit.
That ratio describes the air, not blood oxygen saturation, which depends on the body's response.
For wind chill, heat index and dew point from measured weather, use the wind chill and heat index calculator. To convert between hPa, inHg, psi and other units, use the pressure converter.
Checked against: U.S. Standard Atmosphere 1976 table (geometric altitude): 1000 m → 8.9876×10⁴ Pa, 281.651 K, 1.1117 kg/m³
Checked against: U.S. Standard Atmosphere 1976 table: 11 000 m geometric → 2.2700×10⁴ Pa
Checked against: U.S. Standard Atmosphere 1976 table: 20 000 m → 5.5293×10³ Pa, 216.65 K
Checked against: Inverse troposphere formula gives geopotential 5574.44 m (the ICAO 500 hPa level, 5574 m), converted to geometric height 5579.33 m
1013.25 hPa, the same as 101.325 kPa, 1 atm, 760 mmHg or 29.92 inHg, at an air temperature of 15 °C. These are the sea-level values of the U.S. Standard Atmosphere 1976 and of the ICAO standard atmosphere used in aviation. Actual sea-level pressure rises and falls with the weather around this value.
About 1 °C lower for every 300 m of height near sea level. At standard pressure water boils at 99.97 °C at sea level, 94.6 °C in Denver (1,609 m), 87.8 °C in La Paz (3,640 m) and 70.2 °C on Everest (8,849 m), by the IAPWS-IF97 saturation equation. Food simmered in water cooks more slowly at altitude because the water cannot get hotter than this.
Near sea level it falls by about 12 hPa per 100 m, or 36 hPa (1.07 inHg) over the first 1,000 ft, which is why pilots use a rule of 1 inHg per 1,000 ft. The drop slows with height: pressure halves at about 5.5 km (500 hPa at 5,579 m) and is under a quarter of sea level above 11 km.
The share of oxygen stays at 20.9% of dry air, but each breath holds fewer molecules because the total pressure is lower. The oxygen partial pressure, which drives how much reaches the blood, scales with the pressure ratio: 83.5% of the sea-level value at 1,500 m, 64% in La Paz at 3,640 m, and 31% on the summit of Everest in the standard atmosphere.
Weather reports give pressure reduced to sea level (QNH or mean sea-level pressure) so that maps compare like with like. The actual station pressure in Denver is near 834 hPa in the standard atmosphere. Enter the reported sea-level figure in the Sea-level pressure option to get the station pressure and boiling point for today's weather.
This calculator includes 6 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.