Main Content

Small Circles

In addition to rhumb lines and great circles, one other smooth curve is significant in geography, the small circle. Parallels of latitude are all small circles (which also happen to be rhumb lines). The general definition of a small circle is the intersection of a plane with the surface of a sphere. On ellipsoids, this only yields true small circles when the defining plane is parallel to the equator. Mapping Toolbox™ software extends this definition to include planes passing through the center of the planet, so the set of all small circles includes all great circles as limiting cases. This usage is not universal.

Small circles are most easily defined by distance from a point. All points 45 nm (nautical miles) distant from (45°N,60°E) would be the description of one small circle. If degrees of arc length are used as a distance measurement, then (on a sphere) a great circle is the set of all points 90° distant from a particular center point.

For true small circles, the distance must be defined in a great circle sense, the shortest distance between two points on the surface of a sphere. However, Mapping Toolbox functions also can calculate loxodromic small circles, for which distances are measured in a rhumb line sense (along lines of constant azimuth). Do not confuse such figures with true small circles.

To learn how to compute small circles, see Calculate Vector Data for Points Along a Small Circle.