A unit circle has radius 1, and thus circumference
.
Since an angle of
is one eighth of a whole turn, the length of an arc that subtends an angle of
radians will be one eighth of the whole circumference:

In fact, the radians have the property that, in the unit circle, the length of the arc is exactly the measure of the angle. In general, you have

where l is the length of the arc, r is the radius and
is the angle in radians. So, if
, you have 