Barometric Formula Calculator

Formula

To calculate the atmospheric pressure at a given altitude:

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

Where:

\(P\) is the atmospheric pressure at altitude (Pascals)
\(P_0\) is the pressure at sea level (Pascals)
\(L\) is the temperature lapse rate (Kelvin/meter)
\(h\) is the altitude (meters)
\(T_0\) is the temperature at sea level (Kelvin)
\(g\) is the Earth-surface gravitational acceleration (approximately 9.80665 m/s²)
\(M\) is the molar mass of Earth's air (approximately 0.0289644 kg/mol)
\(R\) is the universal gas constant (approximately 8.314 J/(mol·K))

Barometric Formula Definition

The barometric formula describes the distribution of atmospheric pressure at various altitudes. It accounts for the temperature lapse rate, which is the rate at which temperature decreases with altitude. This formula is essential in meteorology and aviation for estimating atmospheric conditions based on altitude.

Example Calculation 1

Let's assume the following values:

Pressure at Sea Level (P0) = 101325 Pascals
Temperature Lapse Rate (L) = -0.0065 Kelvin/meter
Altitude (h) = 1500 meters
Temperature at Sea Level (T0) = 288.15 Kelvin

Using the formula:

\[ P = 101325 \times \left(1 + \frac{-0.0065 \times 1500}{288.15}\right)^{\left(\frac{-9.80665 \times 0.0289644}{8.314 \times -0.0065}\right)} \]

Calculating, the atmospheric pressure at 1500 meters altitude is approximately 85,088.74 Pascals.

Example Calculation 2

Let's assume the following values:

Pressure at Sea Level (P0) = 101325 Pascals
Temperature Lapse Rate (L) = -0.0065 Kelvin/meter
Altitude (h) = 3000 meters
Temperature at Sea Level (T0) = 288.15 Kelvin

Using the formula:

\[ P = 101325 \times \left(1 + \frac{-0.0065 \times 3000}{288.15}\right)^{\left(\frac{-9.80665 \times 0.0289644}{8.314 \times -0.0065}\right)} \]

Calculating, the atmospheric pressure at 3000 meters altitude is approximately 70,095.73 Pascals.