Polar-ring galaxies (PRGs) are fascinating systems in which the central object (typically, an early-type galaxy) is encircled by a large-scale ring of stars, gas, and dust with almost perpendicular spin. PRGs are rare objects and their formation mechanism is not entirely clear. In this paper, we present a new sample of 31 candidates to PRGs identified in the Sloan Digital Sky Survey (SDSS). Using their stacked gri-images, we determined geometrical parameters of these galaxies; the position angle and the size of the host galaxy and the ring. We compare our sample objects to the previously known PRGs and discuss their general characteristics; the frequency of faint outer structures, the luminosity.size relation, and the distribution by the apparent angle between the ring and the host galaxy. Our main results are: (i) Central galaxies of PRGs follow the luminosity-size relation for ordinary galaxies. The ring components are located along the similar relation but with a larger scatter. This increasing scatter may be the result of a secondary origin of polar structures. (ii) At least half of PRGs show a ring component within 20. from the perpendicular orientation.