Circumference Of A Circle

Circumference of a circle is the total length of the circular curve. In other words if we cut a circle and straight it to make a rod (line) then the length of this line is the circumference of the circle. It is also known as the perimeter of the circle.

Consider a bicycle wheel, the distance travelled in one full revolution (spin) of this wheel gives the circumference of this bicycle wheel.

Some of the circle basic terms are very important to find its circumference. These basic terms include; center, diameter, pi and radius of the circle.

This page contains various types of lessons and worksheets to find the perimeter of circles. Skim through this page to find lessons and worksheets of your own choice.

Sample worksheet on the concept 


What is the circumference?


Let's solve the following problems to understand it further:

1. Find the circumference of a circle whose diameter is 6 inches. (pi = 3.14)

Solution: Given diameter of the circle = d = 6 in.

               Formula >>>>    C = pi x diameter of the circle

                                         C = 3.14 x 6 = 18.84 inches

Note: Remember that the units of circumference is same as that of the diameter of radius of the circle. Many students confuse with the units of area and circumference. Don't square the units for circumference (perimeter) of a circle because it represent a length not the area.

2. A circle has a radius of 2.5 cm, find its circumference. Use pi = 3.14

Solution: Given the radius of the circle = r = 2.5 cm

Formula to find the circumference of a circle when its radius is given, shown below:

C = 2 x pi x radius (r)

C = 2 x 3.14 x 2.5      

C = 15.7 cm 

Worksheets on the above concept: Print the following worksheets to practice how to find the circumference of a circle when its diameter of radius is given.

Worksheet - 1                  Worksheet - 2                  Word Problems Worksheet


How to find circumference when area of a circle is given?

3. The area of a circle is 35 square units. What is its circumference? Use pi = 22/7.

Solution: This is a typical question and we can't answer it direct. To find the circumference of the circle when its area is given we need to find its radius from area. Let's use the formula for area of a circle to find its radius first.

When area of a circle is given and the question is to find its perimeter, then the best approach is to use the formula.

The basic knowledge of algebraic equations and square root is mandatory to preform the calculations. So, make sure you know how to solve a simple equation involving square and square roots.

Procedure starts with equating the given area of the circle with the formula to find the area of a circle using radius. From this radius of the circle can be obtained in couple of the steps.

Once the radius for the circle is known, it is very easy to find its circumference by using the radius in the formula.

Now go through the whole procedure at left and be ready to do related problems given ahead.

Now copy and complete the following word problems on circumference:

1. The diameter of a ferry wheel is 67 feet. Find its circumference.

2. A dinner plate has a radius of 5 cm, what is the circumference of this plate.

3. Paul wants to protect his garden from pigs in his farm. Garden is a circle in shape whose diameter is  110 yards. Find the length of fencing needed to cover all around the garden.

4. There are two wheels of two different bicycles. One wheel has a diameter of 2.5 feet, and a smaller one has a diameter of 1.2 feet. How much bigger is the circumference of the larger wheel as compared to the smaller one?

5. The area of a circular window is 57 square feet. Find the length of the plastic lining which covers all around the window. If 1 foot of lining costs $1.09, find the total cost of the lining.