Circle Perimeter Calculator

Created by Luis Fernando
Reviewed by Wojciech Sas, PhD candidate
Last updated: Mar 15, 2022

Our circle perimeter calculator can be of great help if you're struggling to solve geometry problems. One common problem is to find the perimeter of a circle, also called its circumference, which measures the length of the line forming this geometric figure. Keep reading if you want to know:

  • What is the formula of circle perimeter.
  • How to find the perimeter of a circle using the circle perimeter formula and our circle circumference calculator.
  • What are the perimeters of a quarter circle and a half-circle.

🔎 Remember that, as with the rest of our tools, this circle circumference calculator works both ways - it is also a circumference to radius calculator - and you can use it to convert circumference to radius.

The circle perimeter formula

If you don't know how to find the circumference of a circle, our calculator is the fastest option. Even so, it's helpful to understand how equations work to have a better interpretation of the results. The circle perimeter formula is:

p = 2πr,

where p is the circle's perimeter, r is the radius, and π is a constant equal to approximately 3.14159265...
You can also express the perimeter in terms of the diameter (d), remembering that r=d/2:

p = πd

💡 The number π is a constant equal to the ratio of the circumference to the diameter (or twice the radius). It'll always have the same value, independently of the size of the circle.

If you solve for π in the above equation, it results in the mentioned ratio: π = p/(2r).

Half circle and quarter circle perimeter formulas

Sometimes we need to calculate portions of a circle instead of a whole one. We can obtain the formulas for the perimeters of a half-circle and a quarter-circle by dividing the above equation by 2 and 4, respectively:

phalf = πr

pquarter = πr/2

How to calculate the perimeter of a circle?

If you want to use the circle perimeter calculator to find the circumference of a circle, follow these steps:

  1. Determine the radius of your circle. For example, let's suppose it's 7 cm.
  2. Input the radius in the calculator, and you'll know the circle's circumference. The result should be 43.982 cm.
  3. To double-check your result, enter the radius in the circle perimeter formula: p = 2 × π × (7 cm) = 43.982 cm.

Other helpful tools beyond the circle perimeter calculator

FAQ

How do I find the perimeter of a quarter circle?

To find the perimeter of a quarter circle:

  1. Remember the perimeter of an ordinary circle, which is p = 2πr.
  2. Divide it by four, as you only want the perimeter of a quarter circle.
  3. The result should be p = πr/2. That is the perimeter of a quarter circle for any radius.

How do I find the perimeter of a half-circle?

Multiply the radius by π (pi), and you'll get the half-circle perimeter. The perimeter of a half-circle is simply the perimeter of an ordinary circle divided by two, which results in p = πr.

What is the perimeter of a 10-inch circle?

31.416 inches. To find the perimeter of any circle, multiply the diameter by the number pi (π). In this case, 10 in × π = 31.416 in.

Luis Fernando
Image of a circle with radius, diameter, and perimeter marked.
Radius (r)
in
Diameter (d)
in
Perimeter (p)
in
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