Barometric Pressure Formula Calculator

Barometric Pressure Formula:

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

Initial Pressure (P₀):

Molar Mass (M):

kg/mol

Gravity (g):

m/s²

Height (h):

Gas Constant (R):

J/mol·K

Temperature (T):

Barometric Pressure (P):

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1. What is the Barometric Pressure Formula?

The barometric formula calculates atmospheric pressure at different altitudes. It describes how pressure decreases exponentially with height in an isothermal atmosphere, 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:

\( P \) — Barometric pressure at height h (Pa)
\( P_0 \) — Initial pressure at reference level (Pa)
\( M \) — Molar mass of air (kg/mol)
\( g \) — Gravitational acceleration (m/s²)
\( h \) — Height above reference level (m)
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)

Explanation: The formula assumes constant temperature and gravitational acceleration with height, and dry air composition.

3. Importance of Barometric Pressure Calculation

Details: Accurate barometric pressure calculation is crucial for meteorology, aviation, mountaineering, and engineering applications where pressure variations with altitude affect performance and safety.

4. Using the Calculator

Tips: Enter all values in appropriate units. For Earth's atmosphere, typical values are: M = 0.029 kg/mol, g = 9.8 m/s², R = 8.314 J/mol·K. Sea level pressure P₀ is approximately 101325 Pa.

5. Frequently Asked Questions (FAQ)

Q1: Why does pressure decrease with altitude?
A: Pressure decreases because there's less atmospheric mass above higher elevations, resulting in lower weight of air column.

Q2: What are typical values for molar mass of air?
A: For dry air, M ≈ 0.02897 kg/mol. The value varies slightly with humidity and composition.

Q3: How accurate is this formula?
A: It provides reasonable estimates for moderate altitude changes but becomes less accurate for large altitude differences due to temperature variations.

Q4: Can this be used for other planets?
A: Yes, with appropriate values for planetary gravity, atmospheric composition, and temperature.

Q5: What's the difference between barometric and atmospheric pressure?
A: Barometric pressure specifically refers to pressure measured by a barometer, while atmospheric pressure is the general term for air pressure.