Circumference of a circle - Definition, formula, and examples

The circumference of a circle, also called the perimeter of a circle, is the distance around a circle or any circular object such as a clock, a pizza, or a dinner plate. For example, the distance around a circular clock is the circumference of the clock. 

How to find the circumference of a circle?

Method 1: 

You could use a flexible measuring tape like the one used in the image above to measure the perimeter of the clock. As you wrap the tape measure around the clock, just stretch the measuring tape as much as possible so the measurement can be as accurate as possible. Then, read the number you see on the measuring tape.

Method 2

Mark a point on the margin of any circular object. This is shown below with a vertical red mark. Roll the circular object either to the left or to the right until it makes one revolution. The distance between the vertical red marks is the circumference of the circular object. 

Method 3

Another way to find the perimeter of a circle or any circular object is to use a special formula.

Circumference formula

The circumference is expressed in linear units.

• If r or d is measured in meters, then the circumference is also measured in meters or m.

• If r or d is measured in kilometers, then the circumference is measured in kilometers or km. 

• If r or d is measured in inches, then the circumference is measured in inches or in.

How to find circumference of a circle using the diameter?

The product of the constant π and the diameter of the circle is equal to the circumference of the circle.

C = π × d

You just have to find the length of the diameter and them multiply by 3.14 to get the circumference. To get the diameter, use a ruler or a measuring tape. Measure from one edge of the circle to another edge making sure that you go through the midpoint or center of the circle (or clock). After I measured the diameter of the clock you see below, I found something close to 11.90 inches. 

C = 3.14 × d = 3.14 × 11.9 = 37.36 inches. Looking at the measuring tape around the clock, we can see that the circumference is indeed close to 37.3 inches!

How to find circumference of a circle using the radius?

Twice the product of the constant π and the radius of the circle is equal to the circumference of the circle.

C = 2π × r

You just have to find the length of the radius r and them multiply by 2 and then by 3.14 to get the circumference. To get the radius, measure from the center of the circle(or clock) to the edge of the circle. After I measured the radius of the clock you see below, I found something close to 5.95 inches. 

C = 2(3.14) × r = 2(3.14) × 5.95 = 37.36 inches. Again, looking at the measuring tape around the clock, we can see that the circumference is indeed close to 37.3 inches!

A few more examples showing how to find the circumference of a circle

Examples #1

Calculate the circumference of a circle if r = 2 inches

C = 2 × π × r = 2 × 3.14 × 2 = 12.56 inches


Examples #2

Calculate the circumference of a circle if r = 4 inches

C = 2 × π × r = 2 × 3.14 × 4 = 25.12 inches


Examples #3

If D = 10 centimeters, find the circumference.

You have two choices. You can first find r and then substitute its value for r in the formula.

r is half the diameter, so r = 10 divided by 2

r = 5 cm

C = 2 × π × r = 2 × 3.14 × 5 = 31.4 cm

Otherwise, you can just use the formula C = π × D

C = 3.14 × 10 = 31.4 cm

A challenging exercise about the circumference of a circle

Examples #4

The circumference of circle A is four times the circumference of circle B

The diameter of circle B is 7. What is the diameter of circle A?

Let C_A be the circumference of circle A

Let C_B be the circumference of circle B

Let D_A be the diameter of circle A

Let D_B be the diameter of circle B

How to calculate the circumference if the area is given

C = 2π × r
A =  π × r²

Solve for r using A =  πr².

r² = A/π

r = √(A/π)

Substitute √(A/π) for r in C

C = 2π × √(A/π)

C = 2√(π)² × √(A/π)

C = 2√[(π)² × (A/π)]

C = 2√[(π)×(A)]

Circumference of a circle quiz. See how well you can calculate the circumference or perimeter of a circle