Circle Perimeter Calculator

Q: 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.

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Luis Hoyos

Luis is a mechanical engineer who works at Omni Calculator as a content creator and researcher specializing in math and physics calculators with a focus on thermodynamics and classical mechanics. With a strong foundation in mechanical engineering, Luis is passionate about creating tools that simplify complex concepts and improve everyday life. Outside of work, Luis likes weightlifting and applying his engineering knowledge to optimize the thermal conditions of his home, all while caring for four beloved cats. See full profile

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Wojciech Sas, PhD

Wojciech SasPhD, Institute of Physics in Zagreb

Wojciech, PhD, is a physicist at the Institute of Physics in Zagreb, investigating materials under extreme conditions such as low temperatures and high pressures. He specializes in experimental work, including participation in Large-scale User Facilities such as synchrotrons. Wojciech uses his experience and knowledge to create calculators in physics, math, and statistics categories. In his free time, he likes swimming, playing board games, and looking for meteors while stargazing. See full profile

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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 for 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: you can use it to convert a circumference to a 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 interpret the results better. 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

Finally, let’s remember the circle area (A) can be expressed as A = πr², allowing us to obtain a new formula for the circle perimeter based on its area:

p = 2√(πA)

💡 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. Solving for π in the above equation 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:

p_half = πr

p_quarter = πr/2

How to calculate the perimeter of a circle — with example

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

Determine the radius of your circle. For example, let’s suppose it’s 7 cm.
Input the radius in the calculator, and you’ll know the circle’s circumference. The result should be 43.982 cm.
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

Now that you know how to find the perimeter of a circle, don’t forget this calculator is not our only tool for dealing with circular objects. We’re hopeful that the calculators below will help you with your day-to-day circular problems:

FAQs

How do I find the perimeter of a quarter circle?

To find the perimeter of a quarter circle:

Remember the perimeter of an ordinary circle, which is p = 2πr.
Divide it by four, as you only want the perimeter of a quarter circle.
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.