Circumference Formula

The circumference formula is used to calculate the distance around a circle.

The diameter is the longest chord that runs through the center of the circle. The radius is the measure of the distance from the center of the circle to a point on the circle. The diameter is 2 times the measure of the radius. If we want an exact answer, we use π. If we want to approximate, we use 3.14.

Example 1:

Find the circumference of a circle with a radius of 5 centimeters.

Step 1:

Find variables necessary.

Radius, r = 5cm

Step 2:

Substitute into formula and multiply.

C = 2πr

C = 2π(5)

C = 10π

Exact Answer:

The circumference is 10π centimeters.

For an approximate answer, substitute 3.14 for π.

$C\approx 10\cdot 3.14\approx 31.4$

Approximate answer:

The circumference is about 31.4 centimeters.

Example 2:

Find the circumference of a circle with a diameter of 16 inches.

Step 1:

Find the variables

d=16

Since diameter is given, we will use the second formula.

Step 2:

Substitute.

C = πd

C = π . 16 = 16π

Exact answer:

The circumference is 16π inches.

$C\approx 16\cdot 3.14\approx 50.24$

Approximate answer:

The circumference is about 50.24 inches.