how to find the diameter of a circle with the circumference

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Whether you're solving a math problem for school, making crafts, or putting fencing around your yard, knowing how to calculate the circumference of a circle will come in handy in a variety of circle-related problems. We'll teach you the key circumference formulas you need to figure out the circumference of a circle when you know either the diameter or radius.

Circumference Help

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]
- 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
Plug the given value of the diameter into the formula and solve. Check out the example problem below if you'd like extra practice.^[2]
- 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

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.^[3]
- 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.
- 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:^[4]
- C = 2πr
- C = 2π x 5
- C = 10π
- C = 31.4 inches

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Question

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

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

wikiHow Staff Editor

Staff Answer

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.
Question

What is the perimeter of a circle?

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

wikiHow Staff Editor

Staff Answer

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.
Question

What is a circumference?

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).
Question

If I know the radius of a circle, how I can find the circumference?

Double the radius to get the diameter. Then multiply by pi to get the circumference.
Question

How do I find the radius when I get the circumference?

The circumference = π x the diameter of the circle (Pi multiplied by the diameter of the circle). Simply divide the circumference by π and you will have the length of the diameter. The diameter is just the radius times two, so divide the diameter by two and you will have the radius of the circle!
Question

How can I find the diameter of the circle, once I know the circumference?

Circumference (C) = pi * diameter(d). To get the diameter of a circle take the circumference (C) and divide it by pi (3.14).
Question

How do I find the area of a circle when only given the circumference?

Divide the circumference by pi. That's the diameter. Divide by 2. That's the radius. Square the radius, and multiply by pi. That's the area.
Question

What is the formula used to calculate diameter?

The diameter is twice the radius. The circumference is diameter x pi, or 2 x radius x pi.
Question

How do I change the mixed number into radius?

If your radius is a mixed number, turn the number into an improper fraction. To do this, simply multiply the whole number part by the denominator and add that number to the numerator. The denominator should remain the same throughout the process. You can then use the improper fraction in your formula.
Question

What is the answer of the circumference of a circle?

The answer depends on your number. For example, pie or 3.14 is multiplied with your number which is the diameter or radius.

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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.
Remember: some worksheets will ask to replace pi with a subside, such as 3.14 or 22/7.
To find circumference from the diameter, just multiply pi by the diameter.
The radius is always going to be half of the diameter.^[5]

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Take your time. Remember the old adage—measure twice, cut once.
If you are stuck, ask a friend, family member, or teacher for help.
Remember to always double-check your work because one mistake will set off all your data.

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Article SummaryX

To calculate the circumference of a circle, use the formula C = πd, where "C" is the circumference, "d" is the diameter, and π is 3.14. If you have the radius instead of the diameter, multiply it by 2 to get the diameter. You can also use the formula for circumference of a circle using radius, which is C = 2πr. To see actual examples of the circumference of a circle being calculated, read the article!

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