By Allan Robinson | Updated Aug 30, 2022

The radius of a circle is the straight‑line distance from its center to any point on its circumference. The constant π (pi) links the circumference and diameter of every circle, making it possible to derive the radius from a known circumference.

Step 1: Choose a Value for π

For most educational purposes, the approximation 3.141593 is sufficiently accurate. If a problem specifies a different precision, use that value. In many proofs and formulas, π is left as the symbol π.

Step 2: Recall the Definition of π

π is defined as the ratio of a circle’s circumference (c) to its diameter (d):

π = c / d

The diameter is the straight‑line segment passing through the center and touching the circle at two points.

Step 3: Express the Diameter in Terms of the Radius

Since the diameter equals twice the radius (d = 2r) for any circle, substitute this into the formula:

π = c / (2r)

This expresses the relationship directly in terms of the radius.

Step 4: Solve for the Radius

Rearrange the equation to isolate r:

r = c / (2π)

Thus, the radius can be found by dividing the known circumference by twice the value of π.

These steps provide a reliable method for calculating a circle’s radius from its circumference, applicable to any size and context.