ABSTRACT Rare giant low surface brightness galaxies (gLSBGs) act as a stress test for the current 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 deg2 covered by deep Subaru Hyper Suprime-Cam data was performed independently by four team members. We detected 42 giant disky systems (30 of them isolated) at z ≤ 0.1 with either g-band 27.7 mag arcsec−2 isophotal radius or four disc scale lengths 4h ≥ 50 kpc, 37 of which (including 25 isolated) 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 ∼12 700 such galaxies in the entire sky out to z < 0.1. These estimates agree well with the result of the Evolution and Assembly of GaLaxies and their Environments (EAGLE) cosmological hydrodynamical simulation. Giant disky galaxies represent the large-sized 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.