Ringradius

Ringradius is a term that may be used in geometry and engineering to denote the radius associated with a ring, typically a planar annulus or a toroidal ring. In planar geometry, a ring (or annulus) consists of all points between two concentric circles with inner radius r and outer radius R, where R ≥ r ≥ 0. The ring radius is most often taken to refer to the outer radius R, though the inner radius r is also described as part of the ring’s size.

For a planar ring, the area is A = π(R^2 − r^2). The outer boundary has circumference 2πR and the inner boundary 2πr. The radial width w = R − r measures how thick the ring is. If the width is zero (r = R), the ring degenerates to a circle of radius R. If r = 0, the ring becomes a disk of radius R.

In three-dimensional applications, the term ring radius can refer to the major radius of a torus, the distance from the center of the hole to the centerline of the tube. For a torus with major radius R and minor radius r, the volume is V = 2π^2 R r^2 and the surface area is 4π^2 R r.

In engineering contexts, rings such as O-rings and seal rings are described by outer and inner radii and by cross-sectional radii, which influence fit and pressure containment.

See also: annulus, torus, major radius, minor radius, circumference, area.