What is the Circumference Calculator?
The circumference of a circle is the total distance around its edge. This calculator finds that distance from either the radius or the diameter using the classic formula \(C = 2\pi r = \pi d\). As a bonus it also reports the matching radius, diameter, and enclosed area, so you get a full picture of the circle from a single measurement.
How to use it
Enter one number, then pick whether that number is the radius (the distance from the center to the edge) or the diameter (the distance straight across through the center). Press calculate and the tool returns the circumference along with the other circle properties. Keep your units consistent — if you enter centimeters, every result is in centimeters (and the area in square centimeters).
The formula explained
Pi (\(\pi \approx 3.14159\)) is the constant ratio of a circle's circumference to its diameter. Because the diameter is twice the radius (\(d = 2r\)), the formula can be written two equivalent ways: \(C = \pi d\) when you know the diameter, or \(C = 2\pi r\) when you know the radius. The area uses a related formula, \(A = \pi r^2\).
Worked example
Suppose a circle has a radius of 5 cm. Then $$C = 2 \times \pi \times 5 = 10\pi \approx 31.42 \text{ cm}.$$ Its diameter is 10 cm and its area is \(\pi \times 5^2 = 25\pi \approx 78.54 \text{ cm}^2\). If instead you only knew the diameter was 10 cm, \(C = \pi \times 10 = 31.42 \text{ cm}\) gives the same answer.
FAQ
What's the difference between circumference and perimeter? Circumference is simply the word for the perimeter of a circle — they mean the same thing.
Can I enter the diameter instead of the radius? Yes. Select "Diameter" and the calculator halves it internally to get the radius before computing.
What value of \(\pi\) is used? The calculator uses the full-precision value of \(\pi\) built into the math library, so results are accurate well beyond display precision.
