What is the perimeter of a circle?
The perimeter of a circle, more commonly called its circumference, is the total distance around the edge of the circle. Unlike polygons, a circle has no straight sides, so its perimeter is found using the constant pi (\(\pi \approx 3.14159\)). This calculator computes the circumference instantly from the radius, and also reports the diameter and area for convenience.
How to use this calculator
Enter the radius (the distance from the centre to the edge) of your circle and the calculator returns the perimeter using the formula \(P = 2\pi r\). The radius can be in any unit (cm, m, inches) — the result is in the same unit. If you only know the diameter, simply halve it to get the radius before entering it.
The formula explained
The perimeter is given by $$P = 2 \times \pi \times r,$$ where \(r\) is the radius. Because the diameter \(d = 2r\), this is identical to \(P = \pi \times d\). Pi is the ratio of any circle's circumference to its diameter, which is why it appears in every circle measurement.
Worked example
Suppose a circle has a radius of 5 units. Then $$P = 2 \times 3.14159 \times 5 = 31.4159 \text{ units}.$$ Its diameter is \(2 \times 5 = 10\) units and its area is \(\pi \times 5^2 = 78.54\) square units.
FAQ
Is perimeter the same as circumference? Yes — for a circle the perimeter is specifically called the circumference, and both terms refer to the distance around the outside.
What if I only have the diameter? Divide the diameter by 2 to get the radius, then enter that value. Or use \(P = \pi d\) directly.
What units does the answer use? The perimeter is in the same unit as the radius you enter; the area is in those units squared.
