# Air Pressure at Altitude Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jan 19, 2023

This air pressure at altitude calculator is a tool that helps you to calculate the atmospheric pressure at any level and by any temperature.

## What is atmospheric pressure

Air pressure is the force exerted by the atmospheric air on the surface of the planet. It changes with altitude and temperature. The higher the elevation, the smaller is the mass of the air overlying the ground. Also, atmospheric pressure increases with the increase in temperature.

The units of pressure are Pascals (symbol: Pa). You can convert it to other units in this calculator or use the pressure conversion tool.

## How to calculate air pressure at altitude

It is necessary to use the barometric formula:

$P = P_0 \text{e}^{\frac{-gM(h-h_0)}{\text{R}T}}$

Where:

• $h$ is the altitude at which we want to calculate the pressure, expressed in meters.
• $P$ is the air pressure at altitude $h$.
• $P_0$ is the pressure at the reference level $h_0$. In our pressure calculator, it is assumed that the reference level is located as sea level, so $h_0 = 0$.
• $T$ is the temperature at altitude $h$, expressed in Kelvins. The temperature at altitude calculator may help you find it.
• $g$ is the acceleration due to the gravitational force. For Earth, $g = 9.80665 \mathrm{\frac{m}{s^2}}$.
• $M$ is the molar mass of air. For Earthly air, $M = 0.0289644 \ \mathrm{\frac{kg}{mol}}$.
• $\text{R}$ is the universal gas constant. Its value is equal to $R = 8.31432 \ \mathrm{\frac{N\cdot m}{(mol·K)}}$.

The procedure of calculating air pressure at altitude is as follows:

1. Choose the altitude at which you want to calculate the atmospheric pressure - for example, $4,000 \ \text{m}$.
2. Choose the reference pressure $P_0$. A typical value for Earth is $1 \ \text{atm}$, or $101,325 \ \text{Pa}$.
3. Determine the air temperature - for instance, $30 \mathrm{\degree C}$.
4. Type the data into the calculator (remember about correct units).
5. You have just obtained the result - in our example, the air pressure at altitude $4,000 \ \text{m}$ is equal to $64,557.76 \ \text{Pa}$.

🙋 If you are keen on atmospheric studies, have a look at our dew point calculator and the density altitude calculator!

## FAQ

### Why does water boild eariler at a higher altitude?

Water boils earlier (and your pasta gets ruined as a consequence) at high altitudes thanks to the decreased air pressure. Since boiling is defined as the moment where the vapor pressure on the surface of a liquid equals the ambient pressure, a lower ambient pressure means a lower temperature is needed to reach the ebullition point. The effect is noticeable: at 4000 ft, water boils at 204 °F (95.5 °C)!

### How do I calculate the air pressure at a certain altitude?

To calculate the air pressure at a certain altitude, use this simple formula:
P = P0 × exp(-g × M × (h - h0)/(R × T)
where:

• P0 and h0 — The pressure and altitude of the reference point. Often, these values correspond to the ones at sea level.
• P — The pressure at altitude h.
• T — The temperature at altitude h.
• M — The molar mass of air (M = 0.0289644 kg/mol).
• R — The universal gas constant (R = 8.31432 N · m/(mol · K)).
• g — The acceleration due to gravity.

### At which altitude is an airplane cabin pressurized?

The pressure in an airplane cabin usually lies between 0.75 atm and 0.81 atm, values corresponding to altitudes between 2400 m (8000 ft) and 1800 m (5900 ft). This is a compromise between the need for sturdier airframes able to withstand a higher pressure differential and the comfort of the passengers. The pressurization happens gradually from the moment of the takeoff. Try to close a bottle of water when still at cruising altitude, and see it getting crushed during the descent!

### What is the air pressure on the summit of Mount Everest?

The pressure on the summit of Mount Everest is about 0.3 atm. Calculate it with the air pressure at altitude formula:

1. Choose the parameters: h = 8949 m, and T = -30 °C.
2. Fix the reference values at h0 = 0 m and P0 = 1 atm.
3. Use the air pressure at altitude formula:
P = P0 × exp(-g × M × (h - h0)/(R × T)=
=1 × exp(-9.81 × 0.0289644 × 8949/(8.31432 × (273.15 - 30)=
=0.28 atm

At less than a third of the pressure at sea level, the summit lies in the so-called "death zone".

Bogna Szyk
Pressure at sea level (P₀)
inHg
Altitude (h)
m
Temperature (T)
°C
Pressure (P)
inHg
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