Using a recently completed survey of faint (sub-mJy) radio sources, selected at 1.4 GHz, a dust-free estimate of the local star formation rate (SFR) is carried out. The sample is 50% complete to 0.2 mJy, with over 50% of the radio sources having optical counterparts brighter than R = 21.5. Spectroscopic observations of 249 optically identified radio sources have been made, using the 2-degree Field (2dF) facility at the Anglo-Australian Telescope (AAT). Redshifts and equivalent widths of several spectral features (e.g., Halpha and [OII]3727) sensitive to star formation have been measured and used to identify the star-forming and absorption-line systems. The spectroscopic sample is corrected for incompleteness and used to estimate the 1.4 GHz and Halpha luminosity functions (LFs) and luminosity density distributions. The 1.4 GHz LF of the star-forming population has a much steeper faint-end slope (1.85) than that for the ellipticals (1.35). This implies an increasing preponderance of star-forming galaxies among the optically identified (i.e., z < 1) radio sources at fainter flux densities. The Halpha LF of the faint radio population agrees with published Halpha LFs derived from local samples selected by Halpha emission. This suggests that the star-forming faint radio population is coincident with the Halpha selected galaxies. The 1.4 GHz and Halpha luminosity densities have been used to estimate the SFRs. The two estimates agree, both giving a SFR density of $0.032 M_odot yr^{-1} Mpc^{-3}$ in the range z < 1.
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