  Infrared (IR) dust emission from galaxies is frequently used as an indicator
of star formation rate (SFR). However, the effect of the dust-to-gas ratio
(i.e., amount of the dust) on the conversion law from IR luminosity to SFR has
not so far been considered. Then, in this paper, we present a convenient
analytical formula including this effect. In order to obtain the dependence on
the dust-to-gas ratio, we extend the formula derived in our previous paper, in
which a theoretical formula converting IR luminosity to SFR was derived. That
formula was expressed as ${\rm SFR}/(M_\odot~{\rm yr}^{-1})=\{3.3\times
10^{-10}(1- \eta)/(0.4-0.2f+0.6\epsilon)\} (L_{\rm IR}/L_\odot)$, where f is
the fraction of ionizing photons absorbed by hydrogen, $\epsilon$ is the
efficiency of dust absorption for nonionizing photons, $\eta$ is the cirrus
fraction of observed dust luminosity, and $L_{\rm IR}$ is the observed
luminosity of dust emission in the 8-1000-$\mu$m range. Our formula explains
the IR excess of the Galaxy and the Large Magellanic Cloud. In the current
paper, especially, we present the metallicity dependence of our conversion law
between SFR and $L_{\rm IR}$. This is possible since both f and $\epsilon$ can
be estimated via the dust-to-gas ratio, which is related to metallicity. We
have confirmed that the relation between the metallicity and the dust-to-gas
ratio is applied to both giant and dwarf galaxies. Finally, we apply the result
to the cosmic star formation history. We find that the comoving SFR at z=3
calculated from previous empirical formulae is underestimated by a factor of
4-5.
