circumference

Circumference is the distance around a circle. It is the boundary length of a circle, a one-dimensional measure that depends on the circle’s size but not its interior. The circumference is related to the circle’s radius r by the formula C = 2πr, and to its diameter d by C = πd. Here π denotes the constant ratio of a circle’s circumference to its diameter, approximately 3.14159. The units of C match the units used for r or d.

In practice, circumference can be computed from known measurements. For example, a circle with radius 1 has a circumference of about 6.283 units. If the diameter is 10, the circumference is about 31.42 units. A common method of measurement is to wrap a flexible measuring device, such as a string, around the circle and then measure the string.

Circumference is connected to area by the formula A = πr^2. The derivative of area with respect to radius, dA/dr, equals 2πr, which is the circumference. The concept generalizes to spheres via great circles: the circumference of a great circle on a sphere of radius R is 2πR.

Applications of circumference appear in engineering, architecture, and everyday tasks, including wheel and tire sizing, fencing around circular plots, and fabric cutting layouts. The term is used to describe the boundary length of any circular object or shape, though in strict geometry it pertains to circles.