\begin{definition}[Definition:Circular Error of Pendulum]
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:
:$T' = 2 \pi \sqrt {\dfrac a g}$
\end{definition}