Barometric Pressure at Altitude Calculator

Barometric Pressure Formula:

\[ P = P_0 \times e^{\left(\frac{-Mgh}{RT}\right)} \]

Sea Level Pressure (P₀):

Altitude (h):

meters

Temperature (T):

Kelvin

Molar Mass of Air (M):

kg/mol

Pressure at Altitude (P):

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1. What is the Barometric Pressure Formula?

The barometric formula calculates atmospheric pressure at a given altitude. It's derived from the ideal gas law and the hydrostatic equation, assuming an isothermal atmosphere (constant temperature with altitude).

2. How Does the Calculator Work?

The calculator uses the barometric formula:

\[ P = P_0 \times e^{\left(\frac{-Mgh}{RT}\right)} \]

Where:

\( P \) — Pressure at altitude (Pa)
\( P_0 \) — Sea level pressure (101325 Pa standard)
\( M \) — Molar mass of air (0.0289644 kg/mol standard)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Altitude (meters)
\( R \) — Universal gas constant (8.3144598 J/(mol·K))
\( T \) — Temperature (Kelvin)

Explanation: The equation shows how pressure decreases exponentially with altitude due to the decreasing weight of the overlying atmosphere.

3. Importance of Barometric Pressure Calculation

Details: Calculating barometric pressure at altitude is crucial for aviation, meteorology, mountaineering, and engineering applications where atmospheric conditions affect performance and safety.

4. Using the Calculator

Tips:

Standard sea level pressure is 101325 Pa (1 atm)
Standard molar mass of dry air is 0.0289644 kg/mol
Temperature must be in Kelvin (Celsius + 273.15)
For quick estimates, use standard values and just change altitude

5. Frequently Asked Questions (FAQ)

Q1: Why does pressure decrease with altitude?
A: Pressure decreases because there's less atmospheric mass above you exerting downward force.

Q2: How accurate is this formula?
A: It's accurate for moderate altitudes when temperature is constant. For greater accuracy at high altitudes, more complex models account for temperature variations.

Q3: What's the pressure at Mount Everest's summit?
A: About 32,000 Pa (vs 101,325 Pa at sea level) - roughly 30% of sea level pressure.

Q4: How does humidity affect the calculation?
A: Humid air has lower molar mass (water is lighter than N₂/O₂), so pressure decreases slightly slower with altitude in humid conditions.

Q5: What's the pressure at cruising altitude for jets?
A: At 10,000m (~33,000ft), pressure is about 26,000 Pa (25% of sea level).