# Calculate the circumference of a circle using the circumference formula

As seen in the lesson about the number pi, the circumference formula of a circle is

C = 2 × π × r      or  C = π × D

If either the radius of a circle (r) or the diameter of the circle (D) is known, you can find the circumference by simply substituting the known value for r or D in the formula. Use 3.14 for π.

Examples #1

Calculate C if r = 2 inches

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

Examples #2

Calculate C if r = 4 inches

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

Examples #3

If D = 10 cm, find the circumference.

You have two choices. You can first find r and then replace its value

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

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 CA be the circumference of circle A

Let CB be the circumference of circle B

Let DA be the diameter of circle A

Let DB be the diameter of circle B

Since the ratio of circumference to diameter is the same for all circles, you can use the following proportion to solve this problem

 CA / DA =    CB / DB

Things that we know:

CA = 4 × CB

DB = 7

Replace these in the proportion

 4 × CB / DA =    CB / 7

 If   2 / 5 =    8 / 20   then, 2 × 20 = 5 × 8

 If   4 × CB / DA =    CB / 7   then, 4 × CB × 7 = DA × CB

28 × CB = DA × CB

DA = 28 since 28 × CB = 28 × CB no matter what CB is

 CA / DA =    CB / DB

Things that we know:

CA = 4 × CB

DB = 7

Replace these in the proportion

 4 × CB / DA =    CB / 7

 If   2 / 5 =    8 / 20   then, 2 × 20 = 5 × 8

 If   4 × CB / DA =    CB / 7

Then, 4 × CB × 7 = DA × CB

28 × CB = DA × CB

DA = 28 since 28 × CB = 28 × CB no matter what CB is

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