Circumference Formula - Circumference of a Circle Formula

Circumference of a Circle Formula

Whether you’re doing craft work, putting fencing around your hot tub, or just solving a math problem for school, knowing how to find the circumference of a circle will come in handy in a variety of circle-related problems.

Method1: Using the Diameter


Write down the formula for finding the circumference of a circle using the diameter. The formula is simply this: C = πd. 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.

Plug the given value of the diameter into the formula and solve.
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 and fence. The diameter 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

Method2: Using the Radius

Write down the formula for finding the circumference of a circle using the radius. The radius is half as long as the diameter, so the diameter can be thought of as 2r. Keeping this in mind, you can write down the formula for finding the circumference of a circle given the radius: C = 2πr. 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.

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:
C = 2πr
C = 2π x 5
C = 10π
C = 31.4 inches

Circumference Formula - Circumference of a Circle Formula is the length of an arc of a circle which has been straightened out in a line.
Every day example for easy understanding
Well let’s understand this concept in an easier way. If you have a perfect round balloon and you take a string, roll it over the surface of a balloon at its exact center, then the length of a string that has been rolled over the balloon is circumference of a circle. As we know, Circumference formula is as follows :
C= Diameter * π
C= d * π
C= 2r * π
The value of π is fixed i.e. 3.14159 or 22/7. So we need to know the radius of a given arc length only in order to find out the circumference. Let’s say we have a radius equals to 3 meter then the diameter would become 6 meter and resultantly circumference would become 18.85 meter. It is calculated as described below.
C = 2 * 3 * 3.14159
C= 18.85 meter
Physically, if we carry on the example of a balloon, it means the distance of a perfect ballon surface from its center is 3 meter and the length of a piece of string required to roll over its surface at its exact center is 18.85 meters.
Let me give you an other simple example from a daily life so that you can understand the significance of Circumference Formula - Circumference of a Circle Formula
Significance in Daily Life
If you have a bicycle whose tyre has a diameter of 0.5 meter and if such a tyre is cut open and straightened out into a rubber belt then the length of such a rubber belt would be 1.57 meter. It is calculated using Circumference Formula - Circumference of a Circle Formula.
C = 2πr
C=1.57 meter
By now, it has been made quite clear on how to use Circumference Formula - Circumference of a Circle Formula and what is its significance in daily life.

Circumference of a circle and Formula

If a circle is opened to make a line then length of that line are going to be the circle’s circumference.

How to calculate the circumference of the circle?

For calculating the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference also can be calculated by multiplying 2×radius with pi (π=3.14).

What is radius?

The radius of a circle is that the length of the line from the middle to any point on its edge.

Circumference with radius

As radius is half diameter than
and circumference is
Formula for circumference is when radius is given
Put values in the formula and find circumference.

What is the unit of circumference?

Circumference, like perimeter, is measured in linear units centimeters, inches, feet, yards, meters, kilometers, miles, etc.

Value of pi π?

After division of circumference by the diameter we get 3.141592654…
which is that the number π (Pi)

What is Area of circle?

Circle’s area is π times the radius squared, which is written:
A = π r2
A is Area
r is radius

What are the special names of lines?

A line that “just touches” the circle because it passes by is named as Tangent.
A line that cuts the circle at two points is named as Secant.
A line segment that goes from one point to a different one on the circle’s circumference is named as a Chord.
If it passes through a middle it is known as Diameter.
And which is near the circumference is called an Arc.

How many slices of the circle?

There are two main “slices” of a circle.The “pizza” slice is named a Sector and the slice made by a chord is named a Segment.

What are common sectors?

Two special types of Sectors are Quadrant and Semicircle.
Quarter of a circle is called a Quadrant.
Half a circle is called a Semicircle.
Angle of sector from center with180° is named a half-disk and is bounded by a diameter and a semicircle. Angles of sectors from center are sometimes given special names, these include quadrants (90°), sextants (60°) and octants (45°), which come from the sector being one 4th, 6th or 8th a part of a full circle, respectively. Confusingly, the arc of a quadrant also can be termed a quadrant.

What is arc length?

Formula for the length of an arc is
L denotes the arc length, r denotes the radius of the circle and θ denotes the angle in radians made by the arc at the centre of the circle.

What is the length of chord?

Chord’s length formed with the extremal points of the arc is given by

C=2R θ/2

C denotes the chord length, R represents the radius of the circle, and θ represents the angular width of the sector in radians.

Area of a sector of a circle?

Finding the area of a sector, actually finding a fractional part of the area of the entire circle. The fraction is find by the ratio of the central angle of the sector to the “entire central angle” of 360 degrees.
Find the area of a sector by expressing the fraction is possible when
ratio of the arc length (s) to the whole circumference.