Barometric Formula Calculator

The Barometric Formula is used to calculate the atmospheric pressure at a given altitude based on the initial pressure, temperature, and altitude change. This is particularly important in fields such as meteorology, aviation, and environmental science.

Formula Background

The barometric formula can be expressed as:

\[ P(h) = P_0 \times \exp\left(\frac{-g \times M \times (h - h_0)}{R \times T}\right) \]

Where:

• \( P(h) \) is the pressure at height \( h \) (Pa).
• \( P_0 \) is the initial pressure (Pa).
• \( g \) is the gravitational acceleration (9.80665 m/s²).
• \( M \) is the molar mass of Earth's air (0.0289644 kg/mol).
• \( R \) is the universal gas constant (8.3144598 J/(mol·K)).
• \( T \) is the temperature in Kelvin (K).
• \( h - h_0 \) is the change in altitude (m).

Example Calculation

Given:

• Initial Pressure (\( P_0 \)) = 101325 Pa (standard atmospheric pressure).
• Temperature (\( T \)) = 288.15 K (standard temperature).
• Change in Altitude = 1000 m.

The pressure at 1000 meters can be calculated as:

\[ P(h) = 101325 \times \exp\left(\frac{-9.80665 \times 0.0289644 \times 1000}{8.3144598 \times 288.15}\right) \approx 89874 \text{ Pa} \]

This calculator helps in determining the pressure variations with altitude, crucial for altitude training, weather predictions, and more.