Circumference of a Circle
What is Circumference?
The circumference of a circle is the total distance around the circle — its perimeter. Just as the perimeter of a rectangle is found by adding the lengths of its sides, the perimeter of a circle is defined by a single elegant formula involving the constant π (pi).
Formal Definition
Given a circle with radius $r$ (the distance from the center to any point on the circle) or diameter $d$ (the distance across the circle through the center, from one side to the other), the circumference $C$ is:
$$ C = 2\pi r $$
or equivalently
$$ C = \pi d $$
Since $d = 2r$, both formulas are identical. The constant $\pi \approx 3.14159265...$ is the ratio of any circle's circumference to its diameter:
$$ \pi = \frac{C}{d} $$
This ratio is the same for every circle, regardless of its size — a profound geometric fact known since antiquity.