Mapping Toolbox

Great Circles and Rhumb Lines

In plane geometry, lines have two important characteristics. A line represents the shortest path between two points, and the slope of such a line is constant. When describing lines on the surface of a spheroid, however, only one of these characteristics may be guaranteed at a time.

In geography, a great circle is the shortest path between two points along the surface of a sphere. The precise definition of a great circle is the intersection of the surface with a plane passing through the center of the planet. In general, great circles do not have a constant azimuth, the spherical analog of slope; they cross successive meridians at different angles. When the Earth is taken as a sphere, the Equator and all meridians are great circles. Great circles always bisect the sphere.

A rhumb line is a complex curve, the special property of which is that it crosses each meridian at the same angle. This curve is also referred to as a loxodrome. In general, a rhumb line is not the shortest path between two points on the rhumb line. All parallels, including the Equator, are rhumb lines, since they cross all meridians at 90°. Additionally, all meridians are rhumb lines. Rhumb lines always terminate at the poles, unless the azimuth is true east or west, in which case the rhumb line closes on itself to form a parallel of latitude.

A description of how to calculate points along great circles and rhumb lines appears later in this document.

Geographic Measurement

Measuring Distance