  We matched the 1.4 GHz local luminosity functions of star-forming galaxies
(SFGs) and active galactic nuclei to the 1.4 GHz differential source counts
from $0.25 \ \mu\mathrm{Jy}$ to 25 Jy using combinations of luminosity and
density evolution. We present the most robust and complete local far-infrared
(FIR)/radio luminosity correlation to date in a volume-limited sample of
$\approx 4.3 \times 10^3$ nearby SFGs, finding that it is very tight but
distinctly sub-linear: $L_\mathrm{FIR} \propto L_\mathrm{1.4\,GHz}^{0.85}$. If
the local FIR/radio correlation does not evolve, the evolving 1.4 GHz
luminosity function of SFGs yields the evolving star-formation rate density
(SFRD) $\psi (M_\odot \ \mathrm{year}^{-1} \ \mathrm{Mpc}^{-3}$) as a function
of time since the big bang. The SFRD measured at 1.4 GHz grows rapidly at early
times, peaks at "cosmic noon" when $t \approx 3 \ \mathrm{Gyr}$ and $z \approx
2$, and subsequently decays with an $e$-folding time scale $\tau = 3.2 \
\mathrm{Gyr}$. This evolution is similar to, but somewhat stronger than, SFRD
evolution estimated from UV and FIR data.
