Circle Perimeter (Circumference) Calculator
Enter any one circle measurement - radius, diameter, area, or circumference - and this calculator finds all four properties instantly. The step-by-step panel shows the exact arithmetic, and you can switch between metric and imperial units at any time.
Formula
Worked example
A circle has a radius of 5 cm. Circumference: C = 2 x pi x 5 = 31.4159 cm. Diameter: d = 2 x 5 = 10 cm. Area: A = pi x 5^2 = 78.5398 cm^2. Semicircle perimeter: pi x 5 + 2 x 5 = 25.708 cm.
What is the perimeter of a circle?
The perimeter of a circle is its circumference - the total distance around its outer edge. While the word "perimeter" is used for polygons and "circumference" is more precise for circles, both refer to the same measurement. The formula is C = 2 pi r, where r is the radius, or equivalently C = pi d using the diameter. Because pi (approximately 3.14159) is irrational, the circumference of any circle with a rational radius is a non-terminating decimal. Every circle has the same ratio of circumference to diameter, exactly equal to pi.
How to use this calculator
Choose which measurement you already know from the "Solve from" menu: radius, diameter, circumference, or area. Enter the value, pick your unit system (metric in centimetres or imperial in inches), and all four circle properties update instantly. The "Show your work" panel traces the arithmetic step by step with your actual numbers. The chart below the results shows how circumference and area scale as radius increases, so you can see how your circle compares to larger and smaller ones.
Reverse-solving: from circumference or area back to radius
If you know the circumference and need the radius, rearrange C = 2 pi r to get r = C / (2 pi). For example, a wheel with a circumference of 200 cm has a radius of 200 / (2 x 3.14159) = 31.83 cm. If you know the area, solve A = pi r^2 for r to get r = square root of (A / pi). A circle of area 100 cm^2 has r = square root of (100 / 3.14159) = 5.642 cm. This calculator handles all four reverse cases automatically.
Semicircles and quarter-circles
A semicircle (half-circle) has a curved arc of length pi r, plus a straight diameter of 2r, giving a total perimeter of pi r + 2r. A quarter-circle (quadrant) has a curved arc of pi r / 2, plus two radii of length r each, giving pi r / 2 + 2r. These are useful for calculating fencing around half-circular paths, decorative arches, or quadrant-shaped garden beds. This calculator displays both values alongside the full circle results.
Common circle measurements by radius
| Radius (r) | Diameter (d) | Circumference (C) | Area (A) |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 3 | 6 | 18.8496 | 28.2743 |
| 4 | 8 | 25.1327 | 50.2655 |
| 5 | 10 | 31.4159 | 78.5398 |
| 6 | 12 | 37.6991 | 113.0973 |
| 7 | 14 | 43.9823 | 153.9380 |
| 8 | 16 | 50.2655 | 201.0619 |
| 9 | 18 | 56.5487 | 254.4690 |
| 10 | 20 | 62.8318 | 314.1593 |
Circumference and area for standard radii. All values are rounded to 4 decimal places using π = 3.14159265.
Frequently asked questions
What is the formula for the perimeter of a circle?
The circumference (perimeter) of a circle is C = 2 pi r, where r is the radius. An equivalent form using diameter is C = pi d. Pi is approximately 3.14159, so a circle with radius 5 cm has a circumference of 2 x 3.14159 x 5 = 31.416 cm.
How do I find the radius from the circumference?
Rearrange C = 2 pi r to get r = C / (2 pi). For example, if the circumference is 50 cm, the radius is 50 / (2 x 3.14159) = 7.9577 cm, and the diameter is twice that: 15.9155 cm.
Is circumference the same as perimeter for a circle?
Yes. "Circumference" is the technical term for the perimeter of a circle. Both describe the total distance around the outside of the shape. In everyday language and many textbooks the two words are used interchangeably when referring to circles.
How do I calculate the perimeter of a semicircle?
A semicircle perimeter includes the curved arc and the straight edge (diameter). The arc length is pi r, and the straight edge is 2r, so the total is pi r + 2r. For a semicircle with radius 5 cm: (3.14159 x 5) + (2 x 5) = 15.708 + 10 = 25.708 cm.
What units does this calculator use?
The calculator works in any consistent unit. In metric mode the reference unit is centimetres, and in imperial mode it is inches. You can enter measurements in any unit as long as you are consistent: if you enter a radius in metres the circumference will also be in metres, for example.
Why is the area of a circle proportional to the square of the radius?
The area formula A = pi r^2 contains r squared because area is a two-dimensional measurement. Scaling a circle's radius by a factor of k scales its area by k^2 and its circumference by k. So doubling the radius doubles the circumference but quadruples the area.