How to Calculate the Circumference of a Circle

Reviewed by Grace Imson, MA

Last Updated: July 20, 2023 Fact Checked

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Need to know how to find the circumference of a circle? Can't remember the circumference formula? Don't sweat it—we've got you covered. If you know the diameter, simply plug it into this formula: C=πd. Were you given the radius, instead? No problem, just use this formula: C=2πr. Keep reading for everything you need to know about how to figure out the circumference of a circle using either the diameter or the radius. We've even got a circumference calculator to make things easy.

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Method 1

Method 1 of 2:

Using the Diameter

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1
Use the formula C = πd to find the circumference if you know the diameter. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7.^{[1]
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- Diameter means a straight line segment that passes through the center of the circle and has its endpoints on the sides of the circle.^{[2]
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2
Plug the given value of the diameter into the formula and solve. Check out the example problem below if you'd like extra practice.^{[3]
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- Example problem: You have a circle tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub.
- To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub, plus the space between the tub and fence.
- The diameter for your circular fence is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference:
- C = πd
- C = π x 20
- C = 62.8 feet

Method 2

Method 2 of 2:

Using the Radius

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1
Use the formula C = 2πr to find the circumference using the radius. In this formula, "r" represents the radius of the circle. Again, you can plug π into your calculator to get its numeral value, which is a closer approximation of 3.14.^{[4]
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- A radius is any line segment that extends from the center of the circle and has its other endpoint on the edge of the circle.^{[5]
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- You might notice this is similar to the C = πd formula. That’s because the radius is half as long as the diameter, so the diameter can be thought of as 2r.
2
Plug the given radius into the equation and solve. For this example, let's say you're cutting out a decorative strip of paper to wrap around the edge of a pie you've just made. The radius of the pie is 5 inches. To find the circumference that you need, just plug the radius into the equation:^{[6]
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- C = 2πr
- C = 2π x 5
- C = 10π
- C = 31.4 inches

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What is the perimeter of a circle?

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This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

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The perimeter of a circle is the same as its circumference, the distance around it. The term "perimeter" refers to the distance around any closed shape, and “circumference” applies specifically to a circle or arc.

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What’s the difference between the circumference and the diameter?

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This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

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The diameter is the length of a straight line drawn through the center of a circle from one side to the other. The circumference is the length all the way around the outside of the circle.

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What is a circumference?

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Circumference is the distance around the perimeter of a circle. It is calculated by multiplying the distance across the center (diameter) by Pi (3.1416).

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Tips

The radius is always going to be half of the diameter.^{[7]
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Consider buying a scientific or graphing calculator that already has π as one of the buttons. This will mean less typing for you and a more accurate answer because the π button produces an approximation to π that is much more accurate than 3.14.

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Remember: some worksheets will ask to replace pi with a subside, such as 3.14 or 22/7.

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Warnings

If you are stuck, ask a friend, family member, or teacher for help.

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Take your time. Remember the old adage—measure twice, cut once.

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Remember to always double-check your work because one mistake will set off all your data.

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