# What's the difference between revolutions and radians?

Jul 5, 2015

A factor of $2 \pi$.

One revolution traces out $2 \pi$ radians.

#### Explanation:

The circumference of a circle of radius $r$ has length $2 \pi r$

A radian is the angle subtended by an arc of length equal to the radius. That is, if the radius is $r$, then the length of the arc is $r$.

For an arc to subtend a full revolution its length must be $2 \pi r$ so the angle is $2 \pi$ radians.

I hope that helps!