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
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