# How to Calculate the Radius From the Circumference

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The three primary characteristics of a circle are its circumference, diameter and radius. All circles share common properties that allow for formulas that relate these characteristics to one another. For example, the famous number pi (approximately 3.14, or a bit more precisely, 3.14156) is the ratio of a circle's circumference to its diameter, and this ratio holds true for all circles. It is also true that a circle's circumference has a specific relationship with its radius, and this means that there is a simple formula for calculating the radius of a circle if you know its circumference.

## Understanding Circumference

The circumference of a circle is the distance around a circle's edge. It is what you draw if you use a standard pin-and-pencil compass to draw a circle around a central point. The circumference of any circle is directly proportional to the diameter and the radius of the circle.

The radius of a circle is a line drawn from the direct center of the circle to its outer edge. A radius can be drawn in any direction from the central point. A circle's radius is exactly half the length of the same circle's diameter, which is a line that divides the circle into two equal halves.

## The Relationship of Circumference and Radius

The definition of pi reveals the equation for the circumference of a circle. Pi is equal to the circumference of a circle divided by its diameter. In mathematical terms this looks like the following:

pi = C / d

You get the equation for circumference by solving for C in the equation above.

C = pi x d

And since the diameter of a circle is twice as long as its radius, you can substitute 2r for d, with r standing for radius.

C = pi x 2r