das Motiv
motive
The reason, cause, or occasion for a person's action.
Die Polizei ist sich über das Motiv des Täters noch im Unklaren.
The police are still unclear about the perpetrator's motive.

motive / motif
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motive
The reason, cause, or occasion for a person's action.
Die Polizei ist sich über das Motiv des Täters noch im Unklaren.
The police are still unclear about the perpetrator's motive.

'Das Motiv' is closely related to the verb 'motivieren' (to motivate). This connection helps you understand the meaning 'Beweggrund' (motive): A 'Motiv' is what moves or motivates a person to take an action.
Seine guten Noten motivieren ihn, weiter zu lernen.
His good grades motivate him to keep studying.
The German word 'Motiv' is broader than the English 'motive'. It does not only mean 'Beweggrund' (motive), but also 'wiederkehrendes Thema' (motif) and 'Bildgegenstand' (subject).
Das Schloss Neuschwanstein ist ein weltberühmtes Motiv für Fotografen.
Neuschwanstein Castle is a world-famous subject for photographers.
The meaning depends strongly on the topic. In a crime story, it is about the reason for the crime. In art analysis, it is about a recurring theme. In photography or painting, it is about what is being depicted.
Das Motiv der Rache ist in vielen Filmen zentral.
The motif of revenge is central in many films.
As 'Beweggrund' (motive), 'Motiv' often appears with the preposition 'für' ('das Motiv für etwas' — the motive for something) or in the phrase 'aus ... Motiven handeln' (to act for ... reasons/motives).
Er handelte aus rein persönlichen Motiven.
He acted for purely personal motives.
As 'Bildgegenstand' (subject of an image), 'Motiv' is often used as part of a compound such as 'Fotomotiv' (photo subject) or 'Postkartenmotiv' (postcard scene). You can also say 'ein Motiv suchen' (to look for a subject), 'ein Motiv finden' (to find a subject), or 'ein Motiv auswählen' (to choose a subject).
Der Sonnenuntergang am Meer ist ein klassisches Postkartenmotiv.
The sunset by the sea is a classic postcard scene.
reason / ground
'der Grund' and 'das Motiv' can both explain why someone does something. 'der Grund' is more general and can be used for people, events, or states. 'das Motiv' refers especially to a person's inner motive, that is, what drives them to take an action. You often hear 'Motiv' with intentional actions, for example in reports about conflicts or crimes. Learners may confuse the words because both ask about the why. When it is generally about an explanation, 'Grund' fits. When it is about a person's intention, 'Motiv' is more precise.

Die Polizei prüft, welches Motiv der Täter hatte.
The police are checking what motive the perpetrator had.
Könnt ihr mir den Grund nennen, warum der Kurs heute ausfällt?
Can you tell me the reason why the course is canceled today?