The Circumference of a circle can be understood as the perimeter made on the outer line of the circle. What is a perimeter then? – a Perimeter can be understood the distance around the object. Then, the circumference of a circle can be defined as the perimeter outside of the circle with a fixed radius. For any other polygon, we would simply add the length of their sides but for a circle, there is a fixed formula that gives the circumference of the circle in absolute terms. Let us learn about some terms before we go on to calculate the circumference of the circle –

Diameter of a Circle

Diameter of a circle plays an important role in measuring the circumference. We can understand the diameter of a circle through following idea. To understand a circle, imagine your favorite pie. Now cut your pie into two halves. It would give you and your friend two large sides of a pie. So, the line which cuts the pie into two halves can be understood as the diameter of that pie which is like a circle. A diameter is a line that cuts the circle into two equal halves called the semi-circle. If we combine two semi circles of same diameter, we will get that circle back. So, the diameter is the line which cuts the circle in two equal parts.

Radius of the circle

Another important part of finding the circumference is understanding the radius of the circle. Take the example of the pie again. Cut the pie into four equal parts. This would give all your friends something to eat and savor that pie. So, two halves of the pie is cut into four. So, half of the diameter to the outer line of the pie can be defined as the radius of the circle. It is half the length of the diameter in a circle. From the centre of the circle, draw a line to any of the outer line of the circle, you would find the radius of the circle.

So, when you know the diameter of the circle, simply divide the diameter by two, you would get the radius of the circle. Conversely, if you know the radius of the circle, simply multiply it by two and you would get the diameter of the circle. It is very important to know the diameter or the radius of the circle to determine the circumference. In the problems of finding the circumference, either the diameter or the radius of the circle will definitely be given.

Know the Pi (π)

It is very important to know the Pi in order to find the circumference of the circle. It can be defined as the ratio between the circumference of a circle and its diameter. There has been so much effort to find the end number of the Pi but it is mostly said to be infinite. It can be rounded to the first two decimal points which is 3.14, or 22/7 to make it easier to solve the problems. . So, now you know the diameter or radius of the circle as well as the Pi, let us find out the circumference of the circle.

Finding the circumference of the circle when the Diameter if known

If the problem has declared the diameter of the circle, the task is rather easy for you. From the diameter, find out the radius by dividing it by two. Now when the radius is known, you can solve the problem using two processes –

• Circumference of the circle – πD , Where D is the diameter of the circle or
• Circumference of the circle – 2πR, where R is the Radius of the circle

There has always been discussion on the use of π and its value to determine the circumference of the circle. When the diameter is not known numerically, then either of the values of π can be used. So, if a circle has the diameter of 7 units, the circumference of the circle would be

• πD = π7 = 3.14 x 7 = 21.99 or
• πD = π7 = 22/7 x 7 = 22

Both the values of the circumference would be acceptable given the value of Pi is infinite. Alternatively, when the radius (R) is known, finding the value of the circumference of circle becomes easier. The same formula would get applied here as well. But the formula would get changed. Here, you would have to apply the following formula, C=2πR, where R is radius of the circle.

Even if either of the information is there, the students can get the value of the circumference. Both diameter and the radius of the circle is interconnected and hence finding becomes easy.