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 $0.25 mumathrm{Jy}$ 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.
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