  We quantify the luminosity contribution of active galactic nuclei (AGN) to
the 12 $\mu$m, mid-infrared (MIR; 5-38 $\mu$m), and the total IR (5-1000
$\mu$m) emission in the local AGN detected in the all-sky 70-month Swift/Burst
Alert Telescope (BAT) ultra hard X-ray survey. We decompose the IR spectral
energy distributions (SEDs) of 587 objects into AGN and starburst components
using AGN torus and star-forming galaxy templates. This enables us to recover
the AGN torus emission also for low-luminosity end, down to $\log
(L_{14-150}/{\rm erg}~{\rm s}^{-1}) \simeq 41$, which typically have
significant host galaxy contamination. We find that the luminosity contribution
of the AGN to the 12 $\mu$m, the MIR, and the total IR band is an increasing
function of the 14-150 keV luminosity. We also find that for the most extreme
cases, the IR pure-AGN emission from the torus can extend up to 90 $\mu$m. The
obtained total IR AGN luminosity through the IR SED decomposition enables us to
estimate the fraction of the sky obscured by dust, i.e., the dust covering
factor. We demonstrate that the median of the dust covering factor is always
smaller than that of the X-ray obscuration fraction above the AGN bolometric
luminosity of $\log (L_{\rm bol}/{\rm erg}~{\rm s}^{-1}) \simeq 42.5$.
Considering that X-ray obscuration fraction is equivalent to the covering
factor coming from both the dust and gas, it indicates that an additional
neutral gas component, along with the dusty torus, is responsible for the
absorption of X-ray emission.
