Calculate the circumference of a circle

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

C = 2 × π × r      or  C = π × D

If either r or D is known, you can calculate 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, calculate 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

Examples #5

If the circumference of a circle is 50.24 inches, calculate r.

 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

Examples #5

If the circumference of a circle is 50.24 inches, calculate r.

Recent Articles

1. Conjugate in Algebra

Oct 16, 17 09:34 AM

What is the conjugate in algebra? A concise and clear explanation.

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Recent Lessons

1. Conjugate in Algebra

Oct 16, 17 09:34 AM

What is the conjugate in algebra? A concise and clear explanation.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.