by accident

Short definition from Wiktionary

Adverb

1. 1
   Accidentally; unintentionally; without meaning to; as the result of an event not expected, aided, or willingly planned.
2. 2
   As the result of some undesigned, unintended, unrelated, natural, or random occurrence; as the unexpected and unforeseen result of formerly unrelated factors.
3. 3
   By chance; unexpectedly; as the result of an unrelated series of events.

Adjective

1. 1
   Accidental; as the result of some unforeseen happening or series of events; unexpected; resulting from an event without the foresight, expectation, aid, or design of the person by whose agency it was caused; unintentional.