Rare giant low surface brightness galaxies (gLSBGs) act as a stress test for the modern galaxy formation paradigm. To answer the question `How rare are they?' we estimate their volume density in the local Universe. A visual inspection of 120~sq.~deg. covered by deep Subaru Hyper Suprime-Cam data was performed independently by four team members. We detected 42 giant disky systems at z≤0.1 with either g-band 27.7~mag~arcsec−2 isophotal radius or four disc scalelengths 4h≥50~kpc, 37 of which had low central surface brightness (μ0,g​≥22.7 mag~arcsec−2). This corresponds to volume densities of 4.70×10−5 Mpc−3 for all galaxies with giant extended discs and 4.04×10−5 Mpc−3 for gLSBGs which converts to ∼11 thousand such galaxies in the entire sky out to z<0.1. These estimates agree well with the result of the EAGLE cosmological hydrodynamical simulation. Giant disky galaxies represent the large-size end of the volume density distribution of normal-sized spirals, suggesting the non-exceptional nature of giant discs. We observe a high active galactic nucleus fraction among the newly found gLSBGs. The result of the EAGLE simulation suggests that minor and major mergers are the dominant channels of gLSBG formation, and observed properties of newly found galaxies support this hypothesis