  We present newly-calibrated period-$\phi_{31}$-[Fe/H] relations for
fundamental mode RR Lyrae stars in the optical and, for the first time,
mid-infrared. This work's calibration dataset provides the largest and most
comprehensive span of parameter space to date with homogeneous metallicities
from $-3<\textrm{[Fe/H]}<0.4$ and accurate Fourier parameters derived from 1980
ASAS-SN ($V$-band) and 1083 WISE (NEOWISE extension, $W1$ and $W2$ bands) RR
Lyrae stars with well-sampled light curves. We compare our optical
period-$\phi_{31}$-[Fe/H] with those available in the literature and
demonstrate that our relation minimizes systematic trends in the lower and
higher metallicity range. Moreover, a direct comparison shows that our optical
photometric metallicities are consistent with both those from high-resolution
spectroscopy and globular clusters, supporting the good performance of our
relation. We found an intrinsic scatter in the photometric metallicities (0.41
dex in the $V$-band and 0.50 dex in the infrared) by utilizing large
calibration datasets covering a broad metallicity range. This scatter becomes
smaller when optical and infrared bands are used together (0.37 dex). Overall,
the relations derived in this work have many potential applications, including
large-area photometric surveys with JWST in the infrared and LSST in the
optical.
