Calculate Atmospheric Pressure From Elevation

Barometric Formula:

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

Sea Level Pressure (P₀):

Elevation (h):

meters

Temperature (T):

Kelvin

Molar Mass (M):

kg/mol

Atmospheric Pressure (P):

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1. What is the Barometric Formula?

The barometric formula describes how atmospheric pressure decreases with altitude in 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 formula:

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

Where:

\( P \) — Pressure at elevation (Pa)
\( P_0 \) — Sea level pressure (101325 Pa by default)
\( M \) — Molar mass of air (0.02896 kg/mol by default)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Elevation above sea level (meters)
\( R \) — Universal gas constant (8.314 J/(mol·K))
\( T \) — Temperature (Kelvin)

Explanation: The formula shows how pressure decreases exponentially with altitude, with the rate of decrease depending on temperature and the molar mass of air.

3. Importance of Pressure Calculation

Details: Understanding pressure changes with elevation is crucial for aviation, meteorology, engineering, and scientific research. It affects weather patterns, aircraft performance, and even human physiology at high altitudes.

4. Using the Calculator

Tips:

Standard sea level pressure is 101325 Pa (1 atm)
Standard molar mass of dry air is 0.02896 kg/mol
Temperature must be in Kelvin (273.15 + Celsius)
For Earth's atmosphere, temperature typically decreases with altitude (lapse rate)

5. Frequently Asked Questions (FAQ)

Q1: Why does pressure decrease with altitude?
A: Pressure decreases because there's less atmospheric mass above pushing down at higher elevations.

Q2: How accurate is this formula?
A: It's accurate for an isothermal atmosphere. Real atmospheres have temperature variations, so this is an approximation.

Q3: What's the pressure at Mount Everest's summit?
A: About 32,000 Pa (vs 101,325 Pa at sea level) for standard conditions (8848m, T=229K).

Q4: Does humidity affect the calculation?
A: Yes, humid air has slightly lower molar mass (water is lighter than N₂/O₂), but this calculator uses dry air values.

Q5: Can this be used for other planets?
A: Yes, with appropriate values for P₀, M, g, and T for that planet's atmosphere.