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We present Atacama Large Millimeter/submillimeter Array (ALMA) observations
of 85.69 and 99.02 GHz continuum emission and H42$\alpha$ and H40$\alpha$ lines
emission from the central 1~kpc of NGC 1808. These forms of emission are
tracers of photoionizing stars but unaffected by dust obscuration that we use
to test the applicability of other commonly star formation metrics. An analysis
of the spectral energy distributions shows that free-free emission contributes
about 60 to 90 per cent of the continuum emission in the 85-100 GHz frequency
range, dependent on the region. The star formation rate (SFR) derived from the
ALMA free-free emission is $3.1\pm0.3$~M$_\odot$~yr$^{-1}$. This is comparable
to the SFRs measured from the infrared emission, mainly because most of the
bolometric energy from the heavily obscured region is emitted as infrared
emission. The radio 1.5~GHz emission yields a SFR 25 per cent lower than the
ALMA value, probably because of the diffusion of the electrons producing the
synchrotron emission beyond the star-forming regions. The SFRs measured from
the extinction-corrected H$\alpha$ line emission are about 40 to 65 per cent of
the SFR derived from the ALMA data, likely because this metric was not
calibrated for high extinction regions. Some SFRs based on extinction-corrected
ultraviolet emission are similar to those from ALMA and infrared data, but
given that the ultraviolet terms in the extinction correction equations are
very small, these metrics seem inappropriate to apply to this dusty starburst.