What is the Circumference-to-Radius Calculator?
This calculator finds the radius of a circle when you know its circumference. The circumference is the distance around the circle's edge, and the radius is the straight-line distance from the center to that edge. Because every circle's circumference is exactly 2π times its radius, you can reverse the relationship to recover the radius from any measured circumference.
How to use it
Enter the circumference of your circle in any unit (centimeters, inches, meters — the result will be in the same unit). Click calculate and the tool returns the radius, along with the diameter (twice the radius) and the area for convenience.
The formula explained
The circumference of a circle is \(C = 2\pi r\). Solving for \(r\) gives $$r = \frac{C}{2\pi}$$, where \(\pi \approx 3.14159\). Dividing the circumference by roughly \(6.2832\) yields the radius. From there, the diameter is \(d = 2r\) and the area is \(A = \pi r^2\).
Worked example
Suppose a circle has a circumference of 31.4159 units. Then $$r = \frac{31.4159}{2 \times 3.14159} \approx \frac{31.4159}{6.28318} \approx 5.$$ So the radius is about 5 units, the diameter is 10 units, and the area is \(\pi \times 5^2 \approx 78.54\) square units.
FAQ
What units does it use? Any consistent unit. If you enter centimeters, the radius is in centimeters.
Can I use this for a sphere? Yes — the great-circle circumference of a sphere relates to its radius the same way, \(r = \frac{C}{2\pi}\).
What value of π is used? The calculator uses the full-precision value of π built into the math library, so results are highly accurate.
