diameter

Diameter is a measure of distance used in geometry and related fields. In a circle, the diameter is a straight line segment that passes through the center and has its endpoints on the circle. It is the longest possible chord of the circle, and its length equals twice the circle’s radius. There are infinitely many diameters in a circle, all sharing the same midpoint—the center.

In three-dimensional contexts, the term extends similarly. For a sphere, the diameter is the greatest distance between any two points on the surface, and it also equals twice the radius. For ellipsoids and other solids, the maximum distance between two boundary points is not always along a single axis, but the diameter remains the supremum of distances between pairs of boundary points, often realized along a principal axis in symmetric shapes.

Beyond circles and spheres, diameter can refer to the diameter of a set in a metric space: the supremum of the distances d(x,y) for all x and y in the set. If the set is bounded, this supremum is finite and corresponds to the largest pairwise distance within the set. In graph theory, the diameter of a graph is the greatest distance between any pair of vertices, measured as the length of the shortest path between them. This quantity, together with the radius (the minimum eccentricity of a vertex), describes how spread out a graph is.

Formally, diameter has units of length and scales with the size of the object. For circles and spheres, the relation d = 2r holds, since the diameter equals twice the radius.