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The radius of a circle is the length of a line segment from its center to its outer edge. The same definition also applies to the radius of a sphere. Alternatively, a shape's radius can be defined as half of its diameter. The diameter is the length of a straight line segment passing through a circle or sphere's center.

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The radius is commonly used in many areas of geometry. For example, the radius is required to calculate the area of a circle or sphere, as well as the volume. For shapes that do not have an obvious center, the word "radius" can refer to its circumradius, meaning the radius of a circle that passes through all vertices. In circles and spheres, the radius equals the diameter when multiplied by two. Measurements relating to diameter and radii are in linear units, such as inches and centimeters.

The word originates from Latin "radius," meaning the spoke of a chariot wheel. The plural form of "radius" can be either the Latin "radii" or the conventional English "radiuses." The typical mathematical variable name and abbreviation for radius is "r." Occasionally, the word "radius" is used to refer to the line segment itself rather than the length.

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