  We employ newly computed grids of spectra reprocessed by dust for estimating
the total dust production rate (DPR) of carbon stars in the Small Magellanic
Cloud (SMC). For the first time, the grids of spectra are computed as a
function of the main stellar parameters, i.e. mass-loss rate, luminosity,
effective temperature, current stellar mass and element abundances at the
photosphere, following a consistent, physically grounded scheme of dust growth
coupled with stationary wind outflow. The model accounts for the dust growth of
various dust species formed in the circumstellar envelopes of carbon stars,
such as carbon dust, silicon carbide and metallic iron. In particular, we
employ some selected combinations of optical constants and grain sizes for
carbon dust which have been shown to reproduce simultaneously the most relevant
color-color diagrams in the SMC. By employing our grids of models, we fit the
spectral energy distributions of $\approx$3100 carbon stars in the SMC,
consistently deriving some important dust and stellar properties, i.e.
luminosities, mass-loss rates, gas-to-dust ratios, expansion velocities and
dust chemistry. We discuss these properties and we compare some of them with
observations in the Galaxy and LMC. We compute the DPR of carbon stars in the
SMC, finding that the estimates provided by our method can be significantly
different, between a factor $\approx2-5$, than the ones available in the
literature. Our grids of models, including the spectra and other relevant dust
and stellar quantities, are publicly available at
http://starkey.astro.unipd.it/web/guest/dustymodels
