Radius (geometry)

A 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, making this measurement fundamental to understanding circular and spherical geometry. The radius is exactly half the diameter.

Beyond these basic shapes, radius appears across mathematics and science. It describes the size of atoms, the orbits of satellites, and the reach of particle accelerators. In data clustering, a radius defines neighborhoods around central points. Tectonic models use radii to describe planetary structure. Architects and engineers apply radius measurements in 3D design, while astronomers measure the radii of exoplanets and stars.

The concept dates to ancient geometry, where circles held mystical and practical significance. Today, radius remains one of the most universal constants in mathematics and nature—a simple line that unlocks understanding of everything from subatomic particles to cosmic structures.

The symbol r or R typically denotes radius in equations.

Related

Circle, Sphere, Arc (geometry), Circumference, Volume, Geometry