How to Find the Radius

The radius of a circle is the distance from its center to any point on the circle. The value pi (π) 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.

Things You'll Need

• Calculator

Instructions

1. 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.

2. 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.

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

4. 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.

References

• Mrs. Glosser's Math Goodies