Atmospheric Pressure Calculator

Formula

To calculate the atmospheric pressure at a certain altitude:

\[ P = P_0 \cdot \exp\left(-\frac{g \cdot M \cdot H}{R \cdot T}\right) \]

Where:

\(P\) is the atmospheric pressure
\(P_0\) is the base level pressure at no height (101325 Pa)
\(H\) is the height (meters)
\(T\) is the temperature (K)
\(g\) is the acceleration due to gravity (9.8 m/s²)
\(M\) is the molar mass of dry air (0.028969 kg/mol)
\(R\) is the universal gas constant (8.3144626 J/(mol*K))

Atmospheric Pressure Definition

Atmospheric pressure refers to the force exerted by the Earth's atmosphere on objects within it. It is the weight of the air above a specific point, pushing down on the surface below. This pressure results from the gravitational pull on the air molecules, causing them to be more tightly packed closer to the Earth's surface.

Example Calculation 1

Let's assume the following values:

Height (\(H\)) = 1000 meters
Temperature (\(T\)) = 288 K

Using the formula:

Step 1: Calculate the exponent:

\[ \frac{g \cdot M \cdot H}{R \cdot T} = \frac{9.8 \cdot 0.028969 \cdot 1000}{8.3144626 \cdot 288} \approx 0.119 \]

Step 2: Calculate the atmospheric pressure:

\[ P = 101325 \cdot \exp(-0.119) \approx 89957.125 \, \text{Pa} \]

Example Calculation 2

Let's assume the following values:

Height (\(H\)) = 5000 meters
Temperature (\(T\)) = 255 K

Using the formula:

Step 1: Calculate the exponent:

\[ \frac{g \cdot M \cdot H}{R \cdot T} = \frac{9.8 \cdot 0.028969 \cdot 5000}{8.3144626 \cdot 255} \approx 0.663 \]

Step 2: Calculate the atmospheric pressure:

\[ P = 101325 \cdot \exp(-0.681) \approx 51874.43 \, \text{Pa} \]