Circle Perimeter Calculator

This circumference calculator lets you find the perimeter of a circle, which is the distance around it. But there are also other options to calculate: if you know one value like radius, diameter, circumference or area, you can calculate the remaining three.

After entering a value and selecting its unit, the rest will be calculated automatically with the circumference as the main result. Also under "Sector" you can find the length of an arc segment and the perimeter of a sector.

What is the circumference of the circle?

The circumference of a circle is the total length around its edge, or the distance you would travel if you walked all the way around it. Because a circle has no straight sides, this boundary has its own name: the circumference. So circumference and perimeter are synonyms for the same value. It can be measured in any standard unit of length, such as centimeters or inches. A circle is the set of points that are all the same distance from a given center point; this distance is called the radius. To calculate the circumference, you only need to know the radius.

Here's how to use this calculator.

Enter a known value (radius, diameter, circumference or area) into the corresponding input field and select the desired unit (e.g. centimeters or inches). After entering it, the remaining three values will be automatically calculated and the circumference will be shown as the main result. It is not necessary to specify the type of entered value. If you want to start over with a different value, simply delete the previously entered field and enter a new value. To calculate the length of an arc segment and the circumference of a sector, open the "Sector" menu item and enter the central angle in degrees.

Formula for circumference of a circle:

The circumference is determined only by the radius. This formula doubles the radius and then multiplies it by pi.

Here P is the perimeter, r is the radius and pi is approximately 3.14159. This is the ratio between the circumference and diameter of any circle. As the diameter is twice the length of the radius this relationship can also be derived directly from the diameter or the circumference can be calculated from the area.

Let's say we have a circle with a radius of 7 centimeters, and then we double the radius and multiply it by pi.

Conversely, to determine the radius from the circumference, divide the circumference by twice pi.

List of measurement values for a circle:

Any one measurement of a circle is related to the other measurements by the radius. The following table summarizes the relationships used in the calculation tool and explains why it is possible to determine the remaining values once one has been entered.

Examples of calculations:

The following table shows the circumference for some common radii, with results rounded to two decimal places. The circumference increases as the radius does, and since the radius is not squared, they are directly proportional.

It is easier to calculate the circumference by using the diameter because the circumference equals pi times the diameter. If the diameter is 12 centimeters, then the circumference is equal to pi times 12 or approximately 37.70 cm. In this calculator tool, simply enter 12 in the field for the diameter and read off the circumference directly.

Arc length and sector, semicircle:

It doesn't always have to be a full circle whose circumference you need to calculate. A sector is the pie-shaped area cut out from the center of a circle and bounded by two radii and an arc in between. The length of the arc is a fraction of the entire circumference corresponding to the central angle, and to get the perimeter of the sector we add the two straight radii to it.

A semicircle is a special case of a circle, being half of it. Its perimeter consists of half the circumference of the whole circle plus the diameter that closes the opening. The result of the calculation is the result of Pi multiplied by the radius, plus the two radii. If you open the "Sector" option in the calculator and enter the central angle, then you can directly read off the arc length and perimeter of the sector.

Where is the circumference of a circle used?

Circular boundaries are found in many areas, from everyday tasks to technical applications. Gardeners buy curbs or fences that go around circular flower beds or ponds. Construction workers order decorative window sills or covers for manhole openings. Because a wheel with a known radius travels a distance equal to its circumference on each revolution, the circumference is crucial for determining the size of the wheel and the distance traveled. Tailors, mechanics, and track designers all use the same formula: 2πr.

Tips for accurate calculations:

Measure the radius exactly from the center or measure the diameter through the widest part of the circle and divide it by two in a calculator. Make sure your units are consistent. If the radius is given in centimeters, then the circumference must also be in centimeters. Unlike area, the circumference is directly proportional to the radius so even small errors in measurement will lead to results that change proportionally. There is no overestimation or underestimation.