
unabsichtlich
unintentionally
Describes an action that happens without intention or deliberate purpose; by accident.
Ich habe die Vase unabsichtlich umgestoßen.
I unintentionally knocked over the vase.
unintentionally
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unintentionally
Describes an action that happens without intention or deliberate purpose; by accident.
Ich habe die Vase unabsichtlich umgestoßen.
I unintentionally knocked over the vase.
The word is structured simply: the prefix 'un-' negates the word 'absichtlich' (intentionally). 'Absichtlich' in turn comes from the noun 'die Absicht' (intention). So 'unabsichtlich' (unintentionally) literally means 'without intention.'
Entschuldigung, ich habe Sie unabsichtlich angerempelt.
Sorry, I bumped into you unintentionally.
As an adverb, 'unabsichtlich' (unintentionally) describes how an action happens. It usually comes after the conjugated verb and any objects.
Er hat die Datei unabsichtlich gelöscht.
He unintentionally deleted the file.
This word is very often used to apologize for a mistake or to explain that a negative action was an accident. It reduces one's own blame.
Ich habe dir unabsichtlich wehgetan, das tut mir sehr leid.
I unintentionally hurt you; I'm very sorry.
random / by chance
Zufällig and unabsichtlich can both express a lack of planning. Unabsichtlich only says that an action was not intended; zufällig additionally suggests that the specific outcome was determined by chance. Use zufällig for an outcome caused by chance and unabsichtlich for an unintended action.

Beim Sortieren legte ich den Brief unabsichtlich auf den falschen Stapel.
While sorting, I accidentally put the letter on the wrong pile.
Beim Sortieren legte ich den Brief zufällig auf den richtigen Stapel.
While sorting, I happened to put the letter on the correct pile.