# Air Pressure at Altitude Calculator

Created by Krishna Nelaturu
Last updated: Jun 24, 2022

Welcome to our air pressure at altitude calculator, which can help you calculate the atmospheric pressure at any elevation on Earth and temperature. In this article, we aim to break down this confounding concept by addressing some fundamentals:

• Why the atmospheric pressure at an altitude is different from air pressure at sea level?
• What is the atmospheric pressure formula?
• How to calculate atmospheric pressure with height?

Similar to how air pressure changes with altitude, we know that the pressure in a liquid changes with depth. Find out why using our hydrostatic pressure calculator.

🔎 In our discussion, we use the terms "air pressure", "atmospheric pressure" and "barometric pressure" as synonyms of each other.

## Why atmospheric pressure varies with altitude?

Atmospheric pressure is the pressure exerted by the weight of the Earth's atmosphere. It varies with altitude because the weight of air present above the point of measurement changes. And since air is denser at sea level than at higher altitudes, you can understand that the air pressure decreases as the altitude increases.

Air pressure is also proportional to the temperature. At higher temperatures, the air particles move faster and bump into each other more frequently, increasing the air pressure. Humidity (not to be confused with ) is inversely proportional to the air pressure.

Ever wonder why air pressure at a higher elevation affects the boiling point? Learn more with our boiling point calculator.

## Atmospheric pressure formula to calculate barometric pressure

The following exponential equation gives the atmospheric pressure at altitude formula:

$p = p_0 \cdot \text{exp} \left( -\frac{gM(h-h_0)}{RT}\right)$

where:

• $p$ is the atmospheric pressure at altitude $h$;

• $p_0$ is the atmospheric pressure at reference altitude $h_0$;

• $g$ is the gravitational acceleration, equal to 9.81 m/s on Earth;

• $M$ is the molar mass of dry air, equal to 0.02896968 kg/mol;

• $R$ is the universal gas constant, equal to 8.31432 N·m/(mol·K); and

• $T$ is the temperature at the altitude $h$ in Kelvins.

If we choose sea level as the reference altitude, $h_0 = 0$, then $p_0$ is equal to the air pressure at sea level, 101.32 kPa. Rewriting our initial equation, we obtain the following atmospheric pressure formula:

$p = p_0 \cdot \text{exp} \left( -\frac{gMh}{RT}\right)$

It is vital to get the air temperature right here. You can use our temperature at altitude calculator if you need help.

## How do you calculate atmospheric pressure with height?

Using the pressure altitude formula we introduced in the previous section, let us calculate the air pressure for the cruising altitude of commercial flights, $35000 \text{ft}$ above sea level, and air temperature of $-51\degree \text{C}$.

\footnotesize \begin{align*} p &= 101.32 \cdot \text{exp} \left( -\frac{gM \cdot 35000\cdot 0.3048}{R\cdot (-51 + 273.15)}\right)\\ &= 101.32 \cdot \text{exp} \left( -\frac{gM \cdot 10668}{R\cdot 222.15}\right)\\ & = 19.6438 \text{ kPa} \end{align*}

The air pressure at this altitude is less than 20% of the air pressure at sea level. Understanding such drastic differences is what enables the safe design of aircraft!

## How to use this air pressure at altitude calculator?

This air pressure at altitude calculator is a powerful tool at your disposal to calculate the barometric pressure at any altitude:

1. Provide the value of air pressure at sea level.
2. Enter the altitude at which you want to calculate the air pressure.
3. Input the air temperature at this altitude, and this tool will calculate the air pressure at this altitude.

You can do more - this tool is versatile enough for you to enter any three of the four unknowns and thereby calculate the fourth.

Krishna Nelaturu
Pressure at sea level (P₀)
in Hg
Altitude (h)
m
Temperature (T)
°C
Pressure (P)
in Hg
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