We present the most precise to date orbital and physical parameters of the well-known short period (P= 5.975 d), eccentric (e= 0.3) double-lined spectroscopic binary BY Draconis (BY Dra), a prototype of a class of late-type, active, spotted flare stars. We calculate the full spectroscopic/astrometric orbital solution by combining our precise radial velocities (RVs) and the archival astrometric measurements from the Palomar Testbed Interferometer (PTI). The RVs were derived based on the high-resolution echelle spectra taken between 2004 and 2008 with the Keck I/high-resolution echelle spectrograph, Shane/CAT/HamSpec and TNG/SARG telescopes/spectrographs using our novel iodine-cell technique for double-lined binary stars. The RVs and available PTI astrometric data spanning over eight years allow us to reach 0.20.5 per cent level of precision in Msin 3i and the parallax but the geometry of the orbit (i similar or equal to 154 degrees) hampers the absolute mass precision to 3.3 per cent, which is still an order of magnitude better than for previous studies. We compare our results with a set of YonseiYale theoretical stellar isochrones and conclude that BY Dra is probably a main-sequence system more metal rich than the Sun. Using the orbital inclination and the available rotational velocities of the components, we also conclude that the rotational axes of the components are likely misaligned with the orbital angular momentum. Given BY Dras main-sequence status, late spectral type and the relatively short orbital period, its high orbital eccentricity and probable spinorbit misalignment are not in agreement with the tidal theory. This disagreement may possibly be explained by smaller rotational velocities of the components and the presence of a substellar mass companion to BY Dra AB.