South Wales Police said around 50 officers are deployed in the "extensive" search for Ben Thompson, including a helicopter and search dogs.
Chief Inspector Eddie Ough said he believed Ben had left the city centre to try to walk back to where he was staying that night.
He asked people in the west of Cardiff to look in their outbuildings, as "Ben may have tripped, fallen, hurt himself, be unconscious."
More top news
A largely dry night but widespread frost will form under clear skies as temperatures drop.
Hywel Dda health board says its decision to remove its own online videos - critical of some of its hospitals - was part of 'normal process'
Police have been criticised by a support group after ten men escaped prosecution for naming innocent footballer Ched Evans’s accuser online.