Calculate Atmospheric Pressure Based On Elevation

Barometric Formula:

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

Reference Pressure (P₀):

Molar Mass (M):

kg/mol

Gravity (g):

m/s²

Elevation (h):

Gas Constant (R):

J/mol·K

Temperature (T):

Atmospheric Pressure (P):

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1. What is the Barometric Formula?

The barometric formula calculates atmospheric pressure at a given elevation. It describes how atmospheric pressure decreases exponentially with increasing altitude, based on the ideal gas law and hydrostatic equilibrium.

2. How Does the Calculator Work?

The calculator uses the barometric formula:

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

Where:

\( P \) — Atmospheric pressure at elevation h (Pa)
\( P_0 \) — Reference pressure at sea level (Pa)
\( M \) — Molar mass of Earth's air (kg/mol)
\( g \) — Gravitational acceleration (m/s²)
\( h \) — Elevation above sea level (m)
\( R \) — Universal gas constant (J/mol·K)
\( T \) — Temperature (K)

Explanation: The formula assumes an isothermal atmosphere and ideal gas behavior, providing an exponential decrease in pressure with altitude.

3. Importance of Atmospheric Pressure Calculation

Details: Accurate atmospheric pressure calculation is crucial for meteorology, aviation, mountaineering, engineering applications, and understanding atmospheric phenomena.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for standard atmospheric conditions. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for the parameters?
A: Standard values: P₀ = 101325 Pa, M = 0.02896 kg/mol, g = 9.80665 m/s², R = 8.31446 J/mol·K, T = 288.15 K

Q2: How accurate is the barometric formula?
A: The formula provides good approximations for moderate altitudes but becomes less accurate at very high altitudes due to temperature variations and non-ideal gas effects.

Q3: Why does pressure decrease with altitude?
A: Pressure decreases because there's less atmospheric mass above higher elevations, and gravity pulls air molecules toward the Earth's surface.

Q4: Can this formula be used for other planets?
A: Yes, but with appropriate values for that planet's gravitational acceleration, atmospheric composition, and temperature.

Q5: How does temperature affect the result?
A: Higher temperatures result in less rapid pressure decrease with altitude, as warmer air is less dense and expands more.