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Circumference of Circle
The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park, or a circular table to be bordered requires this metric of the circumference of a circle. The circumference is a linear value and its units are the same as the units of length.
A circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center. The two important metrics of a circle are the area of a circle and the circumference of a circle. Here we shall aim at understanding the formula and calculation of the circumference of a circle.
1.  What is Circumference of a Circle? 
2.  Circumference of Circle Formula 
3.  How to Find the Circumference of Circle? 
4.  Circumference to Diameter 
5.  FAQs Circumference of Circle? 
What is Circumference of a Circle?
The circumference of a circle is its boundary or the length of the complete arc of a circle. Let us understand this concept using an example. Consider a circular park shown below.
If a boy starts running from point 'A' and reaches the same point after taking one complete round of the park, a distance is covered by him. This distance or boundary is called the circumference of the park which is in the shape of a circle. The circumference is the length of the boundary.
Circumference of a Circle Definition
The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.
Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.
 Center: The center of the circle is a point that is at a fixed distance from any other point from the circumference.
 Diameter: The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.
 Radius: The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.
Circumference of Circle Formula
The formula for the circumference of a circle is expressed using the radius 'r' of the circle and the value of 'pi'. It is expressed as, Circumference of a circle formula = 2πr. While using this circumference formula, if we do not have the value of the radius, we can find it using the diameter. That is, if the diameter is known, it can be divided by 2 to obtain the value of the radius because of the diameter of a circle = 2 × radius. Another way to calculate the circumference of a circle is by using the formula: Circumference = π × Diameter. If we need to calculate the radius or diameter, when the circumference of a circle is given, we use the formula: Radius = Circumference/2π
How to Find the Circumference of Circle?
Although the circumference of a circle is the length of its boundary, it cannot be calculated with the help of a ruler (scale) like it is usually done for other polygons. This is because a circle is a curved figure. Therefore, to calculate the circumference of a circle, we apply a formula that uses the radius or the diameter of the circle and the value of Pi (π).
Pi is a special mathematical constant with a value approximated to 3.14159 or π = 22/7. The value of π = 22/7 is used in various formulas. It is the ratio of circumference to diameter, where C = πD. Let us consider a practical illustration to understand how to calculate the circumference of a circle with the help of the circumference formula.
Example: If the radius of the circle is 25 units, find the circumference of the circle. (Take π = 3.14)
Solution: Given, radius = 25 units
Let us write the circumference formula and then we will substitute the value of r (radius) in it.
Circumference of circle formula = 2πr
C = 2 × π × 25
C = 2 × 3.14 × 25 = 157 units
Therefore, the circumference of a circle is 157 units.
Circumference to Diameter
The circumference to diameter of a circle is a ratio used to define the standard definition of Pi (π). If you know the diameter 'd' of a circle, then you can easily find the circumference C using the relation: C = πd. So, when the circumference C is placed in a ratio with the diameter d, the answer we get is π.
Important Notes on Circumference of a Circle
 π(Pi) is a mathematical constant that is the ratio of the circumference of a circle to its diameter. It is approximated to π = 22/7or 3.14
 If the radius of a circle is extended further and touches the boundary of the circle, it becomes the diameter of a circle. Therefore, Diameter = 2 × Radius
 The circumference is the distance around a circle or the length of a circle.
 We can find the circumference of a circle using the radius or diameter.
 Circumference formula = π× Diameter; Circumference = 2πr.
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Circumference of Circle Examples

Example 1: If the radius of a circle is 28 cm find the circumference of the circle.
Solution:
Given, Radius of the circle = 28 cm. To find the circumference of the circle, we will use the circumference formula: 2πr = 2 × 22/7 × 28 = 176 cm.
Therefore, the circumference of the circle is 176 cms.

Example 2: The circumference of a wheel is 440 cm. Find its radius and diameter.
Solution:
Given, the Circumference of the wheel = 440 cm
Circumference of a circle formula = 2πr
Let us substitute the known values to find the radius first.
440 = 2πr
440 = 2 × (22/7) × r
radius = 70 cm
Diameter = 2 × radius
Diameter = 2 × 70
Therefore, the radius is 70 cm, and the diameter is 140 cm.

Example 3: The perimeter of a rectangular wire is 264 m. The same wire is bent into the shape of a circle. Find the radius of the circle formed using the circumference formula.
Solution:
We know that the perimeter of the rectangle = Total length of the wire used = Circumference of the circle formed.
Hence, the Circumference of the circle formed = 264 m
Circumference of a circle formula = 2πr
Circumference of the circle = 264
Let us substitute the known values to find the radius.
264 = 2πr
264 = 2 × (22/7) × r
Therefore, the radius of the circle is 42 m.
FAQs on Circumference of Circle
What is the Circumference of a Circle in Geometry?
The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle. The circumference of the circle is the product of π (pi) and the diameter of the circle. The circumference of a circle is a linear quantity that has the same units of length.
How to Find the Circumference of a Circle?
The circumference of a circle is calculated with the help of the circumference formula that needs the value of the radius of the circle and the value of π (pi). Circumference of a circle = 2πr, where, 'r' is the radius of the circle and π(pi) is a special mathematical constant with a value approximated to 3.14159 or π = 22/7.
How to Find the Diameter From the Circumference of a Circle?
If we need to calculate the diameter when the circumference of a circle is given, we use the formula: Circumference = π × Diameter, or, Diameter = Circumference/π
How to Find the Circumference of the Circle with the Area?
The circumference of a circle can be calculated if the area of the circle is given. Using the formula for the area of a circle the radius can be calculated. Once the radius is known, the circumference can be calculated. Area of circle = πr^{2}, \(radius = \sqrt{\frac{A}{\pi}}\), and C = 2πr = 2\(\pi\sqrt{\frac{A}{\pi}}\).
What is the Unit of the Circumference of a Circle?
The circumference of the circle is a onedimensional linear quantity and the unit of the circumference of a circle is expressed in m, inch, cm, feet, and so on. The circumference of a circle is related to other linear quantities such as the radius and diameter of the circle.
What is the Perimeter of the Circle?
The perimeter of a circle is the same as the circumference of a circle. It is the total length of the outer boundary of the circle. The perimeter or circumference of a circle is the product of the constant 'pi' and the diameter of the circle. It is expressed in linear units like m, inch, cms, feet.
What is the Value of Pi?
Pi is a constant value used for the measurement of the area and circumference of a circle or other circular figures. The symbol of pi is π and its numeric value is equal to 22/7 or 3.14. Further, these numeric values are used based on the context of the equation.
What is the Difference Between the Diameter and the Circumference of a Circle?
The diameter of the circle is the longest chord that passes through the center of the circle. The circumference of the circle is the length of the outer boundary of the circle. Both the diameter and the circumference are lengths and are expressed in linear units. The circumference of the circle is equal to the product of the diameter and the constant π (pi).
How to Find the Circumference of a Circle with Diameter?
The circumference of the circle can be calculated if the diameter is known because the relationship between the circumference and diameter of the circle is expressed as, Circumference = π × Diameter, or, diameter = Circumference/π.
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