Formula Barometric Formula Pressure Pressure at the bottom Scale height Height
$$\mathit{\Pi}(h) ~=~ \mathit{\Pi}_0 \, \mathrm{e}^{-h/H}$$ $$\mathit{\Pi}(h) ~=~ \mathit{\Pi}_0 \, \mathrm{e}^{-h/H}$$
Pressure
$$ \mathit{\Pi} $$ Unit $$ \mathrm{Pa} = \frac{ \mathrm{N} }{ \mathrm{m}^2 } $$ Air pressure (or the pressure of another fluid) at height \(h\) above the sea surface. According to this barometric formula, air pressure decreases exponentially with height.
Pressure at the bottom
$$ \mathit{\Pi}_0 $$ Unit $$ \mathrm{Pa} $$ Air pressure at sea level \(h = 0\).
Scale height
$$ H $$ Unit $$ \mathrm{m} $$ Scale height is a constant that depends, for example, on the temperature of the air and the gravitational acceleration. The scale height is approximately \(H=8\,\mathrm{km}\) on Earth.
Height
$$ h $$ Unit $$ \mathrm{m} $$ Height measured from the sea surface.