How to Find the Radius

By Allan Robinson; Updated April 24, 2017

The radius of a circle is the distance from its center to any point on the circle. The value pi (?) establishes the relationship between a circle’s circumference and its radius, and is the same for all circles. You can therefore find the radius of a circle from its circumference with your accuracy being limited to the accuracy of the value of pi that you use.

Select the value of pi that you’ll use. Many math problems involving pi simply use the variable “pi” in the answer. The value 3.141593 is usually a more than an adequate estimation for high school math problems where a specific value of pi is required.

Learn the definition of pi. Pi is defined as Pi = c/d, where c is the circumference of a circle and d is its diameter. The diameter is the length of a line segment that contains the center of the circle and has points on the circle as its end points. A circle’s circumference is always twice that of its radius.

Substitute radius for diameter in the equation Pi = c/d. Since d = 2r for all circles, you can say that Pi = c/2r.

Solve for r. The equation Pi = c/2r means that Pi (r) = c/2, so r = c / (2 Pi). The radius of a circle is therefore equal to c / (2 Pi) where c is the circumference of the circle.

About the Author

Allan Robinson has written numerous articles for various health and fitness sites. Robinson also has 15 years of experience as a software engineer and has extensive accreditation in software engineering. He holds a bachelor's degree with majors in biology and mathematics.