Circumference is the linear distance around a circle.  This value is critical to know when finding the resolution of a measuring wheel, or when working with belts and pulleys.

Circumference is equal to the diameter of the circle (or twice the radius) multiplied by pi (π).

C = π · D = π · 2 · r


C = Circumference

π ≈ 3.14

D = Diameter

r = radius

Example 1

An encoder measuring wheel has a diameter of 3.815″.  Most measuring wheels are produced to this diameter, because when multiplied by pi, their circumference comes out to almost exactly 1′.

Diameter of circle

π · 3.815″ = 11.985″

Example 2

A pulley on a belt-driven actuator has a radius of 2″.


π · 2 · 2″ = 12.566″