# 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:

$T = 2 \sqrt {\dfrac a g} \, \map K {\map \sin {\dfrac \alpha 2} }$

where:

$a$ is the length of the rod of $P$
$\map K k$ 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:

$T' = 2 \pi \sqrt {\dfrac a g}$