Geopotential height, also known as geopotential altitude or geopotential elevation, is a vertical coordinate (with dimension of length) representing the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. Geopotential heights are referenced to Earth's mean sea level, taking its best-fitting equigeopotential as a reference surface or vertical datum. In SI units, a geopotential height difference of one meter implies the vertical transport of a parcel of one kilogram; adopting the standard gravity value (9.80665 m/s²), it corresponds to a constant work or potential energy difference of 9.80665 joules.

Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same amount of work is to be performed". It is a useful concept in meteorology, climatology, and oceanography; it also remains a historical convention in aeronautics as the altitude used for calibration of aircraft barometric altimeters.

Geopotential is the gravitational potential energy per unit mass at elevation ${\displaystyle Z}$:

where ${\displaystyle g(\phi ,Z)}$ is the acceleration due to gravity, ${\displaystyle \phi }$ is latitude, and ${\displaystyle Z}$ is the geometric elevation.

Geopotential height may be obtained from normalizing geopotential by the acceleration of gravity:

where ${\displaystyle g_{0}}$ = 9.80665 m/s², the standard gravity at mean sea level. Expressed in differential form,

Geopotential height plays an important role in atmospheric and oceanographic studies. The differential form above may be substituted into the hydrostatic equation and ideal gas law in order to relate pressure to ambient temperature and geopotential height for measurement by barometric altimeters regardless of latitude or geometric elevation:

where ${\displaystyle P}$ and ${\displaystyle T}$ are ambient pressure and temperature, respectively, as functions of geopotential height, and ${\displaystyle R}$ is the specific gas constant. For the subsequent definite integral, the simplification obtained by assuming a constant value of gravitational acceleration is the sole reason for defining the geopotential altitude.