Definition:Circular Error of Pendulum

Definition
The period of a pendulum $P$ is dependent upon the angle from the vertical from which the bob is released.

That period of $P$ is described by Motion of Pendulum as being:
 * $T = 2 \sqrt {\dfrac a g} K \left({\sin \left({\dfrac \alpha 2}\right)}\right)$

where:
 * $a$ is the length of the rod of $P$
 * $K \left({k}\right)$ is the complete elliptic integral of the first kind.

The circular error of $P$ is the difference between $T$ and its approximate period as described by period Approximate Motion of Pendulum:
 * $T' = 2 \pi \sqrt {\dfrac a g}$