Radius

Radius is the distance from the center of a circle or sphere to any point on its boundary. In a circle, all radii are equal, and the radius is half the circle’s diameter. The radius is usually denoted by r and relates to other circle measurements by the formulas C = 2πr for circumference and A = πr^2 for area.

In three-dimensional geometry, the radius of a sphere is the distance from its center to any point on its surface. For a sphere of radius r, the surface area is 4πr^2 and the volume is (4/3)πr^3. The concept also appears in broader contexts, such as polar coordinates, where the radius describes the radial distance from the origin to a point in the plane.

Beyond circles and spheres, the term radius is used in various disciplines to indicate a size scale around a central point, such as regions defined by a circular boundary or measurements relative to a center.