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Over the past decade, several works have used the ratio between total (rest 8−1000
μ
m) infrared and radio (rest 1.4 GHz) luminosity in star-forming galaxies (
q
IR
), often referred to as the infrared-radio correlation (IRRC), to calibrate the radio emission as a star formation rate (SFR) indicator. Previous studies constrained the evolution of
q
IR
with redshift, finding a mild but significant decline that is yet to be understood. Here, for the first time, we calibrate
q
IR
as a function of
both
stellar mass (
M
⋆
) and redshift, starting from an
M
⋆
-selected sample of > 400 000 star-forming galaxies in the COSMOS field, identified via (
NUV
−
r
)/(
r
−
J
) colours, at redshifts of 0.1 <
z
< 4.5. Within each (
M
⋆
,
z
) bin, we stacked the deepest available infrared/sub-mm and radio images. We fit the stacked IR spectral energy distributions with typical star-forming galaxy and IR-AGN templates. We then carefully removed the radio AGN candidates via a recursive approach. We find that the IRRC evolves primarily with
M
⋆
, with more massive galaxies displaying a systematically lower
q
IR
. A secondary, weaker dependence on redshift is also observed. The best-fit analytical expression is the following:
q
IR
(
M
⋆
,
z
) = (2.646 ± 0.024) × (1 +
z
)
( − 0.023 ± 0.008)
–(0.148 ± 0.013) × (log
M
⋆
/
M
⊙
− 10). Adding the UV dust-uncorrected contribution to the IR as a proxy for the total SFR would further steepen the
q
IR
dependence on
M
⋆
. We interpret the apparent redshift decline reported in previous works as due to low-
M
⋆
galaxies being progressively under-represented at high redshift, as a consequence of binning only in redshift and using either infrared or radio-detected samples. The lower IR/radio ratios seen in more massive galaxies are well described by their higher observed SFR surface densities. Our findings highlight the fact that using radio-synchrotron emission as a proxy for SFR requires novel
M
⋆
-dependent recipes that will enable us to convert detections from future ultra-deep radio surveys into accurate SFR measurements down to low-
M
⋆
galaxies with low SFR.