# Circumference

### Formula for Circumference

On this page, you can learn the formula to calculate circumference, as well as other geometric concepts for your ACT math examination.

Here is the formula for the circumference of a circle:

You will remember that the diameter is twice the length of the radius of the circle.

So, the formula can also be expressed as follows:

diameter × π

Problem 1:

If a circle has a diameter of 12, what is the circumference of the circle?

A. 6π

B. 12π

C. 24π

D. 36π

E. 144π

Here is the second formula from above again:  diameter × π

You could have also solved the problem with the first formula from above:

This circle has a diameter of 12, and since radius is always half of diameter, its radius is 6.

So, now we can substitute values into the other formula:

radius × 2 × π =

6 × 2 × π =

12π

Problem 2:

If a circle has a radius of 4, what is the circumference of the circle?

A. 4π

B. 8π

C. 12π

D. 16π

E. 24π

Here is the formula  again :

So now we can substitute values into the formula:

radius × 2 × π =

4 × 2 × π =

Alternatively, we can do the calculation with the diameter.

This circle has a radius of 4; in other words, its diameter is 8.

diameter = 4 × 2

diameter = 8

diameter × π = 8π

You might also have to work backwards to find the radius or the diameter from the facts provided.

Problem 3:

If a circle has a circumference of 4π, what is the diameter of the circle?

A. 4

B. 8

C. 12

D. 16

E. 24

circumference =  diameter × π = 4π

diameter = 4

#### Circumference vs. Area

Remember not to confuse the formula for the circumference of a circle with the formula for the area of a circle.

circle area = radius2 × π