Calculate Altitude From Pressure

Altitude from Pressure Equation:

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

Pressure (P):

Reference Pressure (P₀):

Temperature (T):

Gas Constant (R):

J/mol·K

Gravity (g):

m/s²

Molar Mass (M):

kg/mol

Calculated Altitude (h):

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1. What is the Altitude from Pressure Equation?

The altitude from pressure equation, also known as the barometric formula, estimates altitude based on atmospheric pressure measurements. It's derived from the ideal gas law and the hydrostatic equation, assuming an isothermal atmosphere.

2. How Does the Calculator Work?

The calculator uses the barometric formula:

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

Where:

\( h \) — Altitude (meters)
\( R \) — Universal gas constant (8.3145 J/mol·K)
\( T \) — Temperature (Kelvin)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( M \) — Molar mass of Earth's air (0.0289644 kg/mol)
\( P \) — Measured pressure (Pa)
\( P_0 \) — Reference pressure at sea level (101325 Pa)

Explanation: The equation relates the decrease in atmospheric pressure with increasing altitude in an isothermal atmosphere.

3. Importance of Altitude Calculation

Details: Accurate altitude measurement is crucial for aviation, mountaineering, meteorology, and various scientific applications where pressure measurements are more readily available than direct altitude measurements.

4. Using the Calculator

Tips: Enter pressure in Pascals (Pa), reference pressure (typically sea level pressure), temperature in Kelvin, and other constants. Default values are provided for standard atmospheric conditions.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculation?
A: The calculation assumes an isothermal atmosphere and ideal gas behavior. For more precise results, more complex models accounting for temperature lapse rates should be used.

Q2: What is standard sea level pressure?
A: Standard sea level pressure is 101325 Pa (1013.25 hPa or 1 atm).

Q3: Why use Kelvin for temperature?
A: Kelvin is an absolute temperature scale required by the gas law equations. 0°C = 273.15K.

Q4: How does temperature affect the calculation?
A: Higher temperatures result in less dense air, causing the pressure to decrease more slowly with altitude.

Q5: Can this be used for very high altitudes?
A: The simple barometric formula becomes less accurate above about 10km where temperature variations become significant.