Parallellen

Parallellen, or parallels, are imaginary lines on the surface of the Earth (and other planets) that run east–west and remain parallel to the equator. They form circles of latitude, each defined by a constant latitude value measured in degrees north or south of the equator.

On a sphere, the length of a parallel at latitude φ is 2πR cos φ, where R is the planet's radius. The equator at 0° is the longest parallel; as φ approaches ±90°, the parallels shrink to points at the poles. Most parallels are small circles, not great circles, which only the equator is among the parallels.

Parallellen are used together with lines of longitude (meridians) to specify geographic coordinates. Latitudes can be defined on a reference ellipsoid (geodetic latitude) such as WGS84; apparent geocentric latitude differs slightly due to Earth's flattening.

Notable parallels include the equator (0°), the Tropics of Cancer (23.5°N) and Capricorn (23.5°S), and the Arctic and Antarctic Circles (approximately 66.5°N and 66.5°S). These lines relate to solar insolation patterns and climate zones.

In cartography, parallels are used as grid lines in many map projections. Depending on the projection, distances, areas, and shapes may be preserved or distorted differently along and between parallels.