What does radius mean?
A radius is a measurement extending from the centre of a circle to its circumference. The term is also used more broadly for the distance from the central point of a region, system, or object, and for the extent or range within which something operates. For example, a service area may have a radius of twenty kilometres, while a circle's radius determines its size and the relationship between its diameter, circumference, and area. In medicine, radius names the larger of the two bones in the forearm. In engineering, it can describe the thickness of a pipe or cylinder by referring to the distance from its central axis to its outer surface. The word comes from Latin, where radius originally meant a spoke or ray, a meaning still reflected in related words such as radial, radiate, and radiation.
nounThe radius is the distance from the centre of a circle to its circumference, or the length of a line segment joining the centre of a circle to a point on it. By extension, it means the extent, range, or boundary of something.
- In geometry, the distance from the centre of a circle to its circumference, or the length of a line segment from the centre to a point on the circle.
- The distance from the centre or middle point of an object, region, or system.
- A specified area or range within which something operates or occurs.
- The outer bone of the forearm, between the elbow and the wrist.
- The distance from the centre of a cylinder to one of its curved surfaces, especially when describing a pipe or tube.
"The earthquake's effects were felt within a radius of fifty kilometres."
"The station serves communities within a ten-mile radius."
"Each circle has a radius of four centimetres."
"The doctor examined the patient's wrist and radius for signs of a fracture."
Radii is the standard plural in mathematics. “Radiuses” is also accepted, but it is less common and may sound informal in technical writing.
"The radii of the three circles were calculated before the diagram was drawn."
The word radius originally described a wagon wheel's spoke, before mathematics turned it into a measurement of distance from a centre.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does radius come from?
The English word comes from Latin radius, meaning “ray” or “spoke,” especially the spoke of a wheel. It was adopted into English in the 16th century for the geometric sense of a line from a circle's centre to its circumference. The Latin word is related to radere, “to scrape,” and radix, “root,” from which words including radiate, radical, and radish also developed.
Related word forms
How radius is actually used
In general usage, radius often means the boundary or scope of an area, especially in phrases such as “within a radius of”. In technical contexts, it can refer to a geometric measurement, a bone, or the thickness of a cylindrical object.
Easily confused with radius
A radius runs from the centre of a circle to its edge, whereas a diameter runs across the circle through its centre and is twice as long.