The hypsometric equation, also known as the thickness equation, relates an atmospheric pressure ratio to the equivalent thickness of an atmospheric layer considering the layer mean of virtual temperature, gravity, and occasionally wind. It is derived from the hydrostatic equation and the ideal gas law.

The hypsometric equation is expressed as: $${\displaystyle h=z_{2}-z_{1}={\frac {R\cdot {\overline {T_{v}}}}{g}}\,\ln \left({\frac {p_{1}}{p_{2}}}\right),}$$ where:

In meteorology, ${\displaystyle p_{1}}$ and ${\displaystyle p_{2}}$ are isobaric surfaces. In radiosonde observation, the hypsometric equation can be used to compute the height of a pressure level given the height of a reference pressure level and the mean virtual temperature in between. Then, the newly computed height can be used as a new reference level to compute the height of the next level given the mean virtual temperature in between, and so on.

The hydrostatic equation:

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

This is combined with the ideal gas law:

to eliminate ${\displaystyle \rho }$:

This is integrated from ${\displaystyle z_{1}}$ to ${\displaystyle z_{2}}$: