In mathematics, the radius is the distance from the point of intersection of the axes of symmetry of a closed curve. More specifically, the distance from the center of a circle to its circumference, from the center of a sphere to its surface, or from the center of a regular polygon to any one of its vertices. All radii of a circle or sphere are equal; and it is generally profitable to consider only the longest and shortest radii (semi-major and semi-minor axes) of an ellipse. The radius of curvature, r, at any point of a curve is r = 1/κ, where κ is the curvature.
In astronomy, a radius is an old instrument for measuring the angular distance between two celestial objects.