Calculate Barometric Pressure From Elevation

Barometric Pressure Equation:

\[ P = P_0 \times e^{-\frac{Mgh}{RT}} \]

Sea Level Pressure (P₀):

Elevation (h):

meters

Temperature (T):

Kelvin

Molar Mass of Air (M):

kg/mol

Calculated Pressure (P):

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1. What is the Barometric Pressure Equation?

The barometric formula calculates atmospheric pressure at a given elevation, assuming an isothermal atmosphere. It's derived from the ideal gas law and hydrostatic equilibrium.

2. How Does the Calculator Work?

The calculator uses the barometric pressure equation:

\[ P = P_0 \times e^{-\frac{Mgh}{RT}} \]

Where:

\( P \) — Pressure at elevation h (Pa)
\( P_0 \) — Sea level pressure (101325 Pa standard)
\( M \) — Molar mass of Earth's air (0.0289644 kg/mol)
\( g \) — Earth-surface gravitational acceleration (9.80665 m/s²)
\( h \) — Height above sea level (meters)
\( R \) — Universal gas constant (8.31447 J/(mol·K))
\( T \) — Temperature (Kelvin)

Explanation: The equation shows how atmospheric pressure decreases exponentially with altitude, with the rate of decrease depending on temperature and air composition.

3. Importance of Pressure Calculation

Details: Accurate pressure calculation is crucial for meteorology, aviation, mountaineering, and engineering applications where atmospheric conditions affect performance.

4. Using the Calculator

Tips: Enter sea level pressure (standard is 101325 Pa), elevation in meters, temperature in Kelvin, and molar mass of air (standard is 0.0289644 kg/mol). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why does pressure decrease with altitude?
A: Pressure decreases because there's less atmospheric mass above you as you go higher, resulting in lower hydrostatic pressure.

Q2: What are typical pressure values at different altitudes?
A: At sea level: ~1013 hPa; at 1000m: ~900 hPa; at 3000m: ~700 hPa; at 5500m (Mount Everest base camp): ~500 hPa.

Q3: How does temperature affect the calculation?
A: Higher temperatures result in slower pressure decrease with altitude because the atmosphere expands, becoming less dense at a given pressure.

Q4: What are limitations of this equation?
A: Assumes constant temperature and gravity with altitude, and doesn't account for weather systems or humidity. More complex models exist for precise applications.

Q5: Can this be used for other planets?
A: Yes, with appropriate values for P₀, M, g, and atmospheric composition for the specific planet.