  Systematic local structural studies of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system are
undertaken at room temperature using atomic pair distribution function (PDF)
analysis. The local structure of the Ba$_{1-x}$K$_x$Fe$_2$As$_2$ is found to be
well described by the long-range structure extracted from the diffraction
experiments, but with anisotropic atomic vibrations of the constituent atoms
($U_{11}$ = $U_{22} \ne U_{33}$). The crystal unit cell parameters, the
FeAs$_4$ tetrahedral angle and the pnictogen height above the Fe-plane are seen
to show systematic evolution with K doping, underlining the importance of the
structural changes, in addition to the charge doping, in determining the
properties of Ba$_{1-x}$K$_x$Fe$_2$As$_2$.
