How to Calculate the Circumference of a Circle

Calculating the circumference of a circle is an essential skill that is fundamental in middle school mathematics. It keeps coming back at the high school level and college level too. It should not be confused with calculating the area of a circle. Basically, the circumference of a circle is the perimeter or length of the circle. In other words, how long does it take to go around the circle?

What is the formula needed to calculate the circumference of a circle?

The circumference of a circle equals 2 times pi times the radius (C = 2πr). Pi is a mathematical constant that represents the ratio of the circumference to the diameter of a circle. Pi is an irrational number, a number that never ends and cannot be represented as a fraction. Pi is approximately equal to 3.14159...

The radius of a circle is half of the diameter, which is a special chord that goes from one end of the circle through the middle to another end on the opposite side. Since the radius is equal to half of the diameter, another representation of the circumference is equal to pi times the diameter (C = πd). Both of these formulas are equivalent (C = 2πr = πd).

Let's look at some examples.

1) What is the circumference of a circle whose radius is 5 inches?

C = 2πr

C = 2π*5 inches

C = 10π inches

2) What is the circumference of a circle whose radius is 1 cm?

C = 2πr

C = 2π*1 cm

C = 2π cm

3) What is the area of a circle whose diameter is 12 feet?

C = πd

C = π*12 feet

C = 12π feet