We derive the properties of dusty tori in active galactic nuclei from the comparison of observed spectral energy distributions (SEDs) of SDSS quasars and a precomputed grid of torus models. The observed SEDs comprise SDSS photometry, Two-Micron All-Sky Survey J, H and K data, whenever available, and mid-infrared (mid-IR) data from the Spitzer Wide-area InfraRed Extragalactic Survey. The adopted model is that of Fritz, Franceschini & Hatziminaoglou. The fit is performed by standard χ2-minimization; the model, however, can be a multicomponent comprising a stellar and a starburst component, whenever necessary. Models with low equatorial optical depth, τ9.7, were allowed as well as ‘traditional’ models with τ9.7≥ 1.0, corresponding to AV≥ 22 and the results were compared. Fits using high optical depth tori models only produced dust more compactly distributed than in the configuration where all τ9.7 models were permitted. Tori with decreasing dust density with the distance from the centre were favoured while there was no clear preference for models with or without angular variation of the dust density. The computed outer radii of the tori are of some tens of parsecs large but can reach, in a few cases, a few hundreds of parsecs. The mass of dust, MDust, and IR luminosity, LIR, integrated in the wavelength range between 1 and 1000 μm, do not show significant variations with redshift, once the observational biases are taken into account. Objects with 70-μm detections, representing 25 per cent of the sample, are studied separately and the starburst contribution (whenever present) to the IR luminosity can reach, in the most extreme but very few cases, 80 per cent.