Radius of a Circle or Sphere
High School
Definition
The line that connects the center of a circle to the circumference of the circle or sphere. Its plural form is radii. Two radii will give you the diameter of a circle, since the diameter is a line that touches two points on a circle's circumference that passes through the center.
Worked examples
\(r = 5\) cm\( \)→\( d = 2r = 10\) cm\(\)
The diameter is always twice the radius, since two radii placed end-to-end span the circle through the center.
\(d = 14\) m\( \)→\( r = \frac{d}{2} = 7\) m\(\)
If you know the diameter, divide by 2 to find the radius.
Common mistakes
- \(d = 10 \)→\( r = 10\) → \(d = 10 \)→\( r = 5\) The radius is half the diameter, not equal to it.
- using radius when the problem asks for diameter → double the radius to get the diameter Diameter = 2r. Always check whether the question asks for r or d.
- \(C = 2\pi d\) → \(C = 2\pi r\) or \(C = \pi d\) Circumference formulas use radius with the factor 2, or diameter without it—don't mix them.
Where you'll use it next
You'll use radius to calculate circumference, area of circles, surface area and volume of spheres and cylinders, and later in coordinate geometry when working with the equation of a circle.
Found in 1 StudyPug lesson
Mastering Circles and Circumference: Formulas, Examples, and Practice
10th Grade10thGeometry
Unlock the secrets of circles and circumference with our comprehensive guide. Learn easy-to-use formulas, work through practical examples, and sharpen your geometry skills with interactive practice problems.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026