Circumference Formula

Circumference Formula as the name suggests is the formula for calculating the circumference of a circle and as we know the circumference of a circle is defined as the length of the boundary of the circle. For ease of understanding, Circumference is the perimeter of the circle.

Circumference Formula is given by the product of twice the radius and the constant value π. A circle is a two-dimensional curved figure and a bangle is one of the best examples of the Circle. In this article, we will learn about the Circumference Formula and also learn how to calculate the Circumference of a Circle using Circumference Formula. We will also learn the Circumference Formula for semicircles, spheres, and other 3D objects whose at least one face is circular in nature.

What is the Circumference Formula?

Circumference Formula is a mathematical formula used to calculate the circumference of a circle which is also the perimeter of the circle. The Circumference Formula of a Circle is C = 2πr where ‘r’ is the radius of the circle or C = πd where d is the diameter of the circle. We can also say that the Circumference Formula is basically a mathematical equation to find the circumference of the circle.

Circumference Definition

The length of the boundary of a Circle is called the Circumference. The word Circumference is composed of two Latin Words Circum and Ferre. The word Circum means, around or about and Ferre means to carry. Hence, the word circumference means to carry around. For understanding, take a bangle and a thread. Put the thread around the circle in a closed manner. Now measure the length of this thread. The length of this thread will give you the measurement of the circumference of the Circle.

The use of thread is good at a beginner’s level but not for the advanced stage. Hence, we need to learn Circumference Formula for calculating the Circumference of the circle. Before learning the Circumference formula we should learn what is a Circle and what are its components.

What is a Circle?

A circle is two dimensional round shaped figure bounded by curved line. There are no edges or corner in a circle. The length of the curved line making the boundary of the circle is the circumference of the circle. The image showing the circle with all its components is attached below:

Components of Circle

There are the following components of a circle that define the nature of a circle.

Centre: Centre is the point inside a circle that is equidistant from the circumference of the circle.

Radius: The radius is the distance from the center of the circle to the circumference of the circle. A circle can have an infinite number of radii.

Diameter: Diameter is the length from one point on the circumference to another point passing through the center. The diameter is twice the length of the radius of the circle. A circle can have an infinite number of diameters.

Chord: The chord is the distance between any two points on the circumference of the circle. The diameter is the longest chord of the circle.

General Properties of Circle

Some general properties of circles are mentioned below:

• Circles with a common center are called Concentric Circles.
• Circles with the same radii measurement are congruent.
• The radius and tangent are perpendicular at the point of contact.
• A line segment from the radius and perpendicular to the chord bisects the chord.

Circle Circumference Formula

Circumference of a circle is the length of the boundary surrounding the circle. The Circumference of a circle is equal to twice the product of the numerical constant π and the radius ‘r’. The mathematical expression for Circumference Formula is given as follows:

Circumference of Circle Formula in terms of Radius

If C is the circumference of the circle and r is the radius of the circle then, Circumference of the circle is given as

C = 2πr

Circumference of Circle Formula in terms of Diamter

If C is the Circumference of the circle and ‘d’ is the diameter of the circle then the Circumference of the Circle is given as

C = πd

where, d = 2r

In both the above formulas, the value of π is constant and equal to approximately 3.14 in decimal and 22/7 in fractional form. The exact value of π can’t be found exactly. π is an irrational number.

Semi Circle Circumference Formula

Now one can think that if a semicircle is half of the circle then its circumference or perimeter would also be half of the circle. But that is actually wrong. If we see a semicircle, we see that arc is half of that of a circle but it is also enclosed by a line which is actually the diameter of the circle.

The formula for the circumference or perimeter of the semicircle is given by

Circumference of Semicircle = πr + 2r = 1/2(Circumference of Circle) + Diameter

where, r is the radius of the circle

Circumference Formula for Some Other Curved Objects

Apart from the circle, the circumference can be calculated for some other curved objects. Lets’s learn the circumference formula for cylinder, sphere, and ellipse.

Cylinder Circumference Formula

A cylinder is a 3D object whose two ends consist of a flat circular plane and the middle region is a curved region along which the cylinder can roll. The circumference formula in the cylinder is used to find the circumference of the two circles at two ends. The circumference formula for the circular ends of a cylinder is given as

C = 2πr

where r is the radius of the cylinder

Sphere Circumference Formula

A sphere is a three-dimensional round-shaped object. Like a circle, it has also a center, radius, and boundary. The circumference of a sphere can be found along any axis i.e. x, y, and z as it is the same along all directions. The sphere circumference formula is given as

C = 2πr

where r is the radius of the sphere

Ellipse Circumference Formula

The length of the boundary of an Ellipse is called its Circumference. We can’t exactly calculate the circumference of an ellipse rather we can approximate it. Let’s say an ellipse is defined by the equation (x²/a²) + (y²/b²) = 1 where a is the expansion of the ellipse along the x-axis and b is the expansion of the ellipse along the y-direction. If a is approximately equal to b then the expansion in both the x and y directions is the same and the ellipse will approximately become a circle. In this case, if a = b then the Circumference of the Ellipse is given by

C = π (a + b)

If a and b are not approximately equal then any other below formula can be used

C = π √[2(a² + b²)]

C = π [ (3/2)(a + b) – √(ab) ]

Read More,

• Area of Circle
• Perimeter of Triangle
• Quadrilateral

Sample Problems on Circumference Formula

Problem 1: Calculate the circumference of a circle having a radius of 24 cm.

Solution:

Given,

The radius of the circle is 24 cm

We have

Circumference = 2πr

= 2 × 3.14 × 24

= 150.72 cm

Hence, the circumference of the circle is 150.72 cm.

Problem 2: Calculate the circumference of a circle having a radius of 25 cm.

Solution:

Given:

The radius of the circle is 25 cm

Circumference = 2πr

C = 2 × 3.14 × 25

C = 157 cm

Hence, the circumference of the circle is 157 cm.

Problem 3: Calculate the circumference of a circle having a radius of 7 cm.

Solution:

Given:

The radius of the circle is 7 cm

Circumference = 2πr

C = 2 × 3.14 × 7

C = 44 cm

Hence, the circumference of the circle is 44 cm.

Problem 4: Calculate the circumference of a circle having a radius of 12 cm.

Solution:

Given:

The radius of the circle is 12 cm

Circumference = 2πr

C = 2 × 3.14 × 12

C = 113.04 cm

Hence, the circumference of the circle is 113.04 cm.

Problem 5: Calculate the circumference of a circle having a radius of 42 cm.

Solution:

Given:

The radius of the circle is 42 cm

Circumference = 2πr

C = 2 × 3.14 × 42

C = 263.76 cm

Hence, the circumference of the circle is 263.76 cm.

Problem 6: If a circle is given having a length of a radius of 14 cm, how the circumference of the circle can be calculated?

Solution:

Circumference = 2πr

= 2 × 3.14 × 14

= 87.92 cm

Hence, the circumference of the circle is 87.92 cm

Practice Questions on Circumference Formula

Q1: Using Circumference Formula, find the circumference of a circle of diameter 28 cm

Q2: What is the area of a circle if its circumference is 88 cm.

Q3: What is the circumference of a circle of a circle of radius 49 cm.

Q4: Find the ratio of diameter to circumference formula.

Q5: Find the ratio of Area to Circumference formula.

FAQs on Circumference Formula

1. What is the Circumference of a Circle?

The circumference of a circle is the length of the boundary of the circle. It is analogous to the perimeter of a two-dimensional figure.

2. What is Circle Circumference Formula?

The circumference formula of a circle is equal to 2πr.

3. Who Calculated the value of Pi?

The value of Pi was calculated by Archimedes of Syracuse.

4. What is the length of the Circumference of the Circle Formula?

The length of the circumference of the circle formula is given by 2πr.

5. How to find the Circumference of a Circle when the Diameter is given?

The circumference of a circle is calculated by multiplying diameter and π when the diameter of the circle is given.

6. What is Circle Area and Circumference Formula?

Circle Area formula is πr2 and the circle circumference formula is 2πr

7. What is the Circumference Formula in terms of Diameter?

Circumference Formula of Circle in terms of diameter is πd, where d is the diameter

8. What is Area of Circle with Circumference Formula?

The Area of Circle with Circumference is C2/4π where C is the Circumference of Circle.