The word circumference means the boundary of any shape. The circumference covers the round shapes body distance. Circumference is a Latin word in which circum means around and ferre means carry. In Latin ferre is a verb. In mathematics, the circumference is used to find out the distance around the circle. So, the circumference formula is used to find out the distance of the circle or round shape things. Round shape things like hat, boundary of ground etc. The distance of such kind of things is measured with the help of circumference formula.

**What is the Formula for Circumference?**

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As, we all get to know about what circumference is and in this section we are going to discuss about what is the formula of circumference? The formula of circumference is used to find out the distance of the circle. The distance of the circle is finding from the centre of the circle. And it covers the whole boundary of the round shape thing or body. Like if someone has covered the round shape distance then to find the distance covered by the person is measured with the help of circumference. Now, to find the circumference we need to know about the diameter of the circle. It is not necessary that the circumference can only be find out of circle, but can find out measurement of other circle shapes as well like we can also find out the circumference of ellipse, cylinder, sphere as well.

**Formula for Circumference**

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The formula of circumference consists of diameter, pie, and radius. Sometimes when the radius is given then first you need to find out the diameter which is double of the radius of the circle. The circle shaped bodies have same distance from the centre to the whole boundary. Here, the term pie is used which is mathematical constant and its value is 3.14 or 22/7 this value of pie is multiplied with the diameter. Diameter is defined by the distance of the across the boundary. And as I said above sometimes you get the value of radius then this radius is the distance of the boundary from the centre of the circle. That’s why when we double this value of radius we get the distance across the circle which is diameter of the circle.

Formula:

Where, C is the circumference of the circle d represents diameter and “this symbol is used to represent the pie.

**Circumference of a Circle Formula**

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To find out the circumference of the circle we use the above written formula and if the radius is given then you can use

And if you know the diameter of the circle then you can use above formula i.e.

Here, you need to put the value of pie as well to find out the accurate answer of the circumference of the circle that is 22/7 or 3.14 this is the standard constant value of the pie which is used in mathematics.

**Area and Circumference of a Circle Formula**

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You can find out area of a circle as well if you know the diameter of the circle. As the area of the circle deals with the value of the radius which can be find out from the diameter of the circle. As the radius of the circle from the diameter can be find out by half the value of diameter i.e.

r = d/2

Now, area of the circle is

And we can also find out the circumference of the circle from the radius as well. I.e. if the area of the circle is given to you and you have to find out the circumference of the circle then in this case you first need to find out the radius of the circle from the area of the circle. You can find out the radius with the help of square root of area of the circle divide by pie.

I.e.

r= √A/

After finding out the radius you can easily find out the circumference of the circle by putting the value of the radius in the circumference formula. And vice-versa can be used to find out the area of the circle from the circumference of the circle then you need to find out the radius of the circle by dividing the circumference of the circle by 2i.e.

r= C/2

And then put the value of r in the area of circle formula. Hence, these formula are correlated to each other and you can find out the values of missing terms from these formulas.

**Circumference to Diameter Formula**

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If the diameter is provided to you then you can simply find out the circumference of the circle from the diameter formula in which the term pie is multiplied with the diameter of the circle. I.e.

This formula does not need any complicated calculation if you know the diameter form this you can find out circumference of the circle very easily.

You can take example as well for the diameter formula of the circumference. Let us consider a circle shaped ground has diameter of 30 meter and you need to find out the circumference then you will just need to put the value of pie and diameter in the formula i.e.

C = 3.14 * 30 meter

C = 94.2 meter (Solution)

Hope this example has helped you to understand the concept of diameter formula.

*Circumference to Radius Formula*

*Circumference to Radius Formula*

Circumference of circle can also be find out if the diameter is not provided to you and radius is given. As I mentioned above also, the radius is twice the diameter of the circle so, if you have to find out the circumference of the circle using radius formula then you can use the below formula i.e.

And you can help of the example as well to know how to calculate the circumference of the circle using radius formula. If the radius of the circle is 17 meter and you are asked to find out the circumference then put the value of radius in r of the above formula i.e.

C = 2*3.14* 17 meter

C = 34 * 3.14 meter

C = 106.67 meter

**Pi Formula Circumference**

Pie formula can be used with the diameter or radius as well. Well, Pie is the Greek letter which has very long value when we divide 22/7 but round off value 3.14 is used to find out the accuracy of the measurement. This value provides the approximate value of the measurement. The value of pie always remains constant. That is in any formula when you find out the value of pie it always comes to the value 3.14 or 22/7 and if the value not come out to be this than it means you have done some wrong calculation. In case of circumference the pie can be find out from:

C/d =

And the pie formula of circumference is

**Circumference of a Sphere Formula**

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Sphere has same distance from the centre to all the sides. That is the diameter of the sphere does not vary horizontally or vertically it remain same from all the angles of the sphere. In this case the circumference formula of the circle is used as in case of sphere. Both possess same formula i.e.

**Circumference of the Sphere **

With the help of this you can find out the radius of the circle which helps you to find out the area, volume, surface area or other measurements of the sphere.

**Circumference of Cylinder Formula**

If you see the cylinder carefully then you will find the image of cylinder consists of two circles in the bottom and top and to find out the area of the cylinder you need to know the circumference of the circles and as you all know the formula to find out the circle is 2* pie*r. And after finding the circumference of one circle and with the help of circumference of the circle you can find out the area of outer edge of the circle by simply multiplying the circumference with the height of the cylinder. In this way, the circumference of the circle helps you to find out the surface area of the cylinder.

I.e. 2

And then surface area of cylinder is twice the area of circle and outer edge i.e.

A = 2 * ( * (2

**Ellipse Circumference Formula**

Circumference of the ellipse can also be known as perimeter of the ellipse and it is much difficult to find out the circumference of ellipse as it varies in the shape from the sphere. It has different diameter with respect to orientation vertical and horizontal. Here, you need to take the both values of horizontal radius as well as vertical radius. And the formula for finding circumference of ellipse is:

P = 4 * (a + b) * * *

Where, “a” and “b” is the horizontal and vertical radii of the ellipse. And P stands for the perimeter f the ellipse.

In Geometry, the shapes and there measurement can only be find out with the help of these formulas so you need to understand the concepts behind these formulas and remember these formulas as well so that you will be able to calculate the values and measurements easily.