# Air pressure at altitude and boiling point calculator

> 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.

Interactive version: https://www.calcopenly.com/earth/altitude-air-pressure-boiling-point
Subject: Weather, earth and fun calculators

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.

## Inputs

- **Start from** (options: Altitude, Air pressure)
- **Altitude above sea level**
- **Air pressure**
- **Sea-level pressure**: 1013.25 hPa is the standard atmosphere; use today's QNH for a weather-adjusted figure.
- **Sea-level temperature**

## Results

- Air pressure (hPa) — main result
- Altitude (m)
- Altitude (ft)
- Share of sea-level pressure
- Air temperature (standard atmosphere) (°C)
- Air density (kg/m³)
- Water boils at (°C)
- Water boils at (°F)

## Formula

$$
P = P_b\left(\frac{T_b}{T_b + L(H - H_b)}\right)^{\frac{g_0 M}{R^* L}},\qquad H = \frac{r_0 h}{r_0 + h}
$$

## Worked examples

### 1,000 m

- Start from: Altitude
- Altitude above sea level: 1000 m
- **Air pressure: 898.76 hPa**
- **Air temperature (standard atmosphere): 8.50 °C**
- **Air density: 1.1117 kg/m³**
- Checked against: U.S. Standard Atmosphere 1976 table (geometric altitude): 1000 m → 8.9876×10⁴ Pa, 281.651 K, 1.1117 kg/m³

### 11,000 m (top of the troposphere)

- Start from: Altitude
- Altitude above sea level: 11 km
- **Air pressure: 227.00 hPa**
- Checked against: U.S. Standard Atmosphere 1976 table: 11 000 m geometric → 2.2700×10⁴ Pa

### 20,000 m (isothermal layer)

- Start from: Altitude
- Altitude above sea level: 20,000 m
- **Air pressure: 55.29 hPa**
- **Air temperature (standard atmosphere): -56.50 °C**
- Checked against: U.S. Standard Atmosphere 1976 table: 20 000 m → 5.5293×10³ Pa, 216.65 K

### Altitude of the 500 hPa level

- Start from: Air pressure
- Air pressure: 500 hPa
- **Altitude: 5,579.3 m**
- Checked against: Python decimal: inverse troposphere formula gives geopotential 5574.44 m (the ICAO 500 hPa level, 5574 m), converted to geometric height 5579.33 m

### Boiling point at 1000 hPa

- Start from: Air pressure
- Air pressure: 1000 hPa
- **Water boils at: 99.61 °C**
- Checked against: IAPWS-IF97 verification table: Ts(0.1 MPa) = 372.755919 K = 99.6059 °C

### Boiling point at sea level

- Start from: Altitude
- Altitude above sea level: 0 m
- **Water boils at: 99.97 °C**
- **Air pressure: 1,013.25 hPa**
- Checked against: IAPWS-IF97 saturation temperature at 101 325 Pa = 373.1243 K (99.974 °C, the ITS-90 boiling point)

## Questions

### What is standard air pressure at sea level?

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.

### At what temperature does water boil at altitude?

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.

### How much does air pressure drop with altitude?

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.

### Is there less oxygen at high altitude?

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.

### Why does my weather app show about 1013 hPa in a mountain town?

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.

### How accurate is the air pressure at altitude and boiling point calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “1,000 m” is checked against U.S. Standard Atmosphere 1976 table (geometric altitude): 1000 m → 8.9876×10⁴ Pa, 281.651 K, 1.1117 kg/m³.

### Where does the method come from?

U.S. Standard Atmosphere, 1976 (NOAA/NASA/USAF), NASA-TM-X-74335; IAPWS R7-97(2012) — IAPWS-IF97, region 4 saturation-temperature equation.

## Sources

- [U.S. Standard Atmosphere, 1976 (NOAA/NASA/USAF), NASA-TM-X-74335](https://ntrs.nasa.gov/citations/19770009539)
- [IAPWS R7-97(2012) — IAPWS-IF97, region 4 saturation-temperature equation](http://www.iapws.org/relguide/IF97-Rev.html)