'hard-on' originates from English compound formation in early 20th-century American slang, combining 'hard' (firm, rigid) with the particle 'on' indicating an ongoing state.

'hard' comes from Old English 'heard' meaning 'firm, solid' and 'on' from Old English 'on' meaning 'in a state of'; these elements were combined in modern slang to form 'hard-on' with an explicit sexual sense.

Originally the components literally suggested 'firm' + 'on' (a state of firmness); by the early 1900s the compound developed the specific vulgar sense of 'penile erection' and later acquired extended figurative meanings (obsession, hostility).