# Barometric formula

The Barometric Formula,sometimes called the exponential atmosphere, is a formula used to model how the pressure (or density) of the air changes with altitude. It is based on the simplifying (not very realistic) assumption that the temperature does not depend on altitude. However, this formula agrees reasonably well with the actual pressure and density variations above the earth's surface up to a height of about 450,000 ft (140 km).

[itex] \rho = \rho_0 e^{- z / h} \,[itex]

or

[itex] P = P_0 e^{- M g_0 z / (RT)}[itex]

where h is the scale height, ρ (rho) is density, P is pressure, M = 0.029 kg mol-1 (the mass of 1 mole of air), R = 8.314 J K-1 mol-1 is the gas constant, T is temperature, [itex]g_0[itex] is gravity and z is the vertical height above the earth's surface.

As a rule of thumb, the pressure decreases by about 1% for every 80 metres increase in altitude.

An alternative rule of thumb, density drops in half every 20,000 feet below the tropopause, changing to every 15,000 feet above the tropopause to the stratopause.

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