How To Calculate Barometric Pressure By Altitude

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

Altitude (h):

Gas Constant (R):

J/mol·K

Temperature (T):

Barometric Pressure (P):

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1. What is the Barometric Formula?

The barometric formula calculates atmospheric pressure at a given altitude. It's based on the ideal gas law and assumes an isothermal atmosphere, providing the pressure decrease with increasing altitude.

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:

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

Explanation: The formula describes how atmospheric pressure decreases exponentially with altitude due to the decreasing weight of the air column above.

3. Importance of Barometric Pressure Calculation

Details: Accurate barometric pressure calculation is crucial for aviation, meteorology, altitude sickness prediction, and various scientific applications where pressure changes with altitude affect measurements and processes.

4. Using the Calculator

Tips: Enter reference pressure (typically 101325 Pa for sea level), molar mass of air (0.02896 kg/mol), gravitational acceleration (9.80665 m/s²), altitude in meters, gas constant (8.31446 J/mol·K), and temperature in Kelvin. 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 a given point at higher altitudes, resulting in lower weight of the air column.

Q2: What are typical reference values for the parameters?
A: Standard values are P₀=101325 Pa, M=0.02896 kg/mol, g=9.80665 m/s², R=8.31446 J/mol·K, T=288.15 K (15°C).

Q3: How accurate is the barometric formula?
A: The formula provides good approximations for moderate altitudes but becomes less accurate at very high altitudes where temperature variations and other atmospheric factors become significant.

Q4: Can this formula be used for other planets?
A: Yes, with appropriate values for gravitational acceleration, molar mass of the atmosphere, and temperature specific to that planet.

Q5: What's the relationship between pressure and altitude?
A: Pressure decreases exponentially with altitude - approximately halving every 5.5 km under standard atmospheric conditions.