Barometric Formula Calculator

The barometric formula plays a crucial role in meteorology and aviation by estimating atmospheric pressure at different altitudes. Understanding how pressure changes with height allows pilots, scientists, and engineers to make informed decisions about flight safety, weather forecasting, and environmental monitoring.

Why Atmospheric Pressure Decreases with Altitude

Essential Background Knowledge

Atmospheric pressure decreases exponentially with altitude due to the weight of the air column above a given point. This phenomenon can be described mathematically using the barometric formula:

\[ P = P_0 \times \left( 1 + \frac{L \cdot h}{T_0} \right)^{\left(-\frac{g \cdot M}{R \cdot L}\right)} \]

Where:

• \( P \) is the pressure at altitude \( h \)
• \( P_0 \) is the pressure at sea level
• \( L \) is the temperature lapse rate (approximately 0.0065 K/m)
• \( h \) is the altitude in meters
• \( T_0 \) is the temperature at sea level in Kelvin
• \( g \) 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))

This formula accounts for the decrease in temperature as altitude increases, which affects the rate of pressure decline.

Practical Examples of Barometric Formula Calculations

Example 1: Standard Atmosphere Conditions

Scenario: Determine the atmospheric pressure at an altitude of 1,000 meters under standard conditions.

1. Inputs:
   • \( P_0 = 101325 \, \text{Pa} \)
   • \( T_0 = 288.15 \, \text{K} \)
   • \( h = 1000 \, \text{m} \)
2. Calculation:
   • Convert \( h \) to meters (already in meters).