Upcoming radio telescopes will allow us to study the radio sky at low frequencies with unprecedented sensitivity and resolution. New surveys are expected to discover a large number of new radio sources, in particular those with a steep radio spectrum. Here we investigate the abundance of radio relics, i.e. steep-spectrum diffuse radio emission coming from the periphery of galaxy clusters, which is believed to trace shock waves induced by cluster mergers. With the advent of comprehensive relic samples, a framework is needed to analyse the relic abundance statistically. To this end, we introduce the probability of finding a relic located in a galaxy cluster with given mass and redshift, which allows us to relate the halo mass function of the Universe to radio-relic number counts. To date, about 45 relics have been reported in the literature and we compile the resulting counts, N(>S1.4). In principle, the parameters of the distribution could be determined using a sufficiently large relic sample. However, since the number of known relics is still small, for that purpose we use the MareNostrum Universe simulation to determine the relic radio-power scaling with cluster mass and redshift. Our model is able to reproduce the recently found tentative evidence for an increase in the fraction of clusters hosting relics, both with X-ray luminosity and redshift, using an X-ray flux-limited cluster sample. Moreover, we find that a considerable fraction of faint relics (S1.4≲ 10 mJy) reside in clusters with an X-ray flux below ≲ 3 × 10−12 erg s-1 cm−2. Finally, we estimate the number of radio relics that await discovery by future low-frequency surveys proposed for the Low Frequency Array (LOFAR) and the Westerbork Synthesis Radio Telescope (WSRT). We estimate that the Westerbork Observations of the Deep APERTIF Northern-Sky (WODAN) survey proposed for WSRT may discover 900 relics and that the LOFAR–Tier 1–120 MHz survey may discover about 2500 relics. However, the actual number of newly discovered relics will depend crucially on the existence of sufficiently complete galaxy cluster catalogues.