In this study we investigate the calibration of surface brightness--color (SBC) relations based solely on eclipsing binary stars. We selected a sample of 35 detached eclipsing binaries with trigonometric parallaxes from Gaia DR1 or Hipparcos, whose absolute dimensions are known with an accuracy better than 3% and that lie within 0.3 kpc from the Sun. For the purpose of this study, we used mostly homogeneous optical and near-infrared photometry based on the Tycho-2 and 2MASS catalogs. We derived geometric angular diameters for all stars in our sample with a precision better than 10%, and for 11 of them with a precision better than 2%. The precision of individual angular diameters of the eclipsing binary components is currently limited by the precision of the geometric distances ($sim$5% on average). However, by using a subsample of systems with the best agreement between their geometric and photometric distances, we derived the precise SBC relations based only on eclipsing binary stars. These relations have precisions that are comparable to the best available SBC relations based on interferometric angular diameters, and they are fully consistent with them. With very precise Gaia parallaxes becoming available in the near future, angular diameters with a precision better than 1% will be abundant. At that point, the main uncertainty in the total error budget of the SBC relations will come from transformations between different photometric systems, disentangling of component magnitudes, and for hot OB stars, the main uncertainty will come from the interstellar extinction determination. We argue that all these issues can be overcome with modern high-quality data and conclude that a precision better than 1% is entirely feasible.
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