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

Where:

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′.

C = π · D

11.985″ = π · 3.815″

**Example 2**

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

C = 2π · r

12.566″ = 2 π · 2″