  The infrared-radio correlation (IRRC) underpins many commonly used radio
luminosity-star formation rate (SFR) calibrations. In preparation for the new
generation of radio surveys we revisit the IRRC of low-$z$ galaxies by (a)
drawing on the best currently available IR and 1.4 GHz radio photometry, plus
ancillary data over the widest possible area, and (b) carefully assessing
potential systematics. We compile a catalogue of $\sim$9,500 z $<$ 0.2 galaxies
and derive their 1.4 GHz radio ($L_{\mathrm{1.4}}$), total IR, and
monochromatic IR luminosities in up to seven bands, allowing us to parameterize
the wavelength-dependence of monochromatic IRRCs from 22-500 $\mu$m. For the
first time for low-$z$ samples, we quantify how poorly matched IR and radio
survey depths bias measured median IR/radio ratios,
$\overline{q}_{\mathrm{TIR}}$, and discuss the level of biasing expected for
low-z IRRC studies in ASKAP/MeerKAT fields. For our subset of $\sim$2,000
high-confidence star-forming galaxies we find a median
$\overline{q}_{\mathrm{TIR}}$ of 2.54 (scatter: 0.17 dex). We show that
$\overline{q}_{\mathrm{TIR}}$ correlates with $L_{\mathrm{1.4}}$, implying a
non-linear IRRC with slope 1.11$\pm$0.01. Our new $L_{\mathrm{1.4}}$-SFR
calibration, which incorporates this non-linearity, reproduces SFRs from
panchromatic SED fits substantially better than previous IRRC-based recipes.
Finally, we match the evolutionary slope of recently measured
$\overline{q}_{\mathrm{TIR}}$-redshift trends without having to invoke redshift
evolution of the IRRC. In this framework, the redshift evolution of
$\overline{q}_{\mathrm{TIR}}$ reported at GHz frequencies in the literature is
the consequence of a partial, redshift-dependent sampling of a non-linear IRRC
obeyed by low-$z$ {\it and} distant galaxies.
