In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.
More generally — in geometry, science, engineering, and many other contexts — the radius of something (e.g., a cylinder, a polygon, a mechanical part, a hole, or a galaxy) usually refers to the distance from its center or axis of symmetry to a point in the periphery: usually the point farthest from the center or axis (the outermost or maximum radius), or, sometimes, the closest point (the short or minimum radius). If the object does not have an obvious center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter (which is usually defined as the maximum distance between any two points of the figure)
The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity.
The radius of a circle with area A is
To compute the radius of a circle going through three points P1, P2, P3, the following formula can be used:
where θ is the angle
These formulas assume a regular polygon with n sides.
The radius can be computed from the side s by:
The radius of a d-dimensional hypercube with side s is
RADIUS, properly a straight rod, bar or staff, the original meaning of the Latin word, to which also many of the various meanings seen in English were attached; it was thus applied to the spokes of a wheel, to the semi-diameter of a circle or sphere and to a ray or beam of light, "ray" itself coming through the Fr. raie from radius. From this last sense comes "radiant," "radiation," and allied words. In mathematics, a radius is a straight line drawn from the centre to the circumference of a circle or to the surface of a sphere; in anatomy the name is applied to the outer one of the two bones of the fore-arm in man or to the corresponding bone in the fore-leg of animals. It is also used in various other anatomical senses in botany, ichthyology, entomology, &c. A further application of the term is to an area the extent of which is marked by the length of the radius from the point which is taken as the centre; thus, in London, for the purpose of reckoning the fare of hackneycarriages, the radius is taken as extending four miles in any direction from Charing Cross.
r= d ÷ 2
d= 2 x r = d= r + r
r= Radius d= Diameter
The relationship between the radius and the circumference of a circle is
The area of a circle of radius is