The formula for Circumference of circle is 2Πr. Circumference of circle is the length of a closed curve. In the above figure of a circle, the curve is in red. Its a closed curve. The length of this closed curve is circumference of circle. Circumference of circle is in fact, perimeter of circle. Perimeter of a polygon, i.e. a closed figure having three or more sides, is the length of the edge of the figure. Edges are the boundaries of any figure enclosing an amount of plane or space inside the closed boundary of the figure. The circumference of circle bears a constant ratio to the diameter of the circle. This ratio is called Pi, denoted by Π, a greek alphabet. If C is circumference of circle and D is diameter, then C: D = Π. The numerical value of this constant ratio is approximately 3.14. C/D = Π. Since diameter D = 2r, where r is radius of circle. So, C / 2r = Π, Finally C = 2 Π r

Properties of Circumference of Circle

1. If a square of side s cms is bent into a circle of radius r, then Circumference of circle = Perimeter of the square, i.e. 2Π r = 4s
2. In N revolutions, the distance traversed by a wheel or radius r is N × 2 Π r
3. Consider two wheels, one a large wheel of radius R, and another a smaller wheel of radius r. Let the two wheels travel a same distance, say D meters.

Let the first wheel take N revolutions to move the distance D meters; and the second, M revolutions. Then, N/M = r/R

Unit circle. Great circle.