Hypsometric equation

The hypsometric equation, also known as the thickness equation, relates an atmospheric pressure ratio to the equivalent thickness of an atmospheric layer under the assumptions of constant temperature and gravity. It is derived from the hydrostatic equation and the ideal gas law.

The hypsometric equation is expressed as:

where:

In meteorology, ${\displaystyle p_{1}}$ and ${\displaystyle p_{2}}$ are surfaces. In altimetry with the International Standard Atmosphere the hypsometric equation is used to compute pressure at a given height in isothermal layers in the upper and lower stratosphere.

The hydrostatic equation:

where ${\displaystyle \rho }$ is the density [kg/m³], is used to generate the equation for hydrostatic equilibrium, written in differential form:

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