
rüber
over
Colloquial short form of 'herüber' or 'hinüber', describing movement across a short distance or an imagined line.
Gib mir mal bitte das Salz rüber.
Please pass me the salt over here.
over
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over
Colloquial short form of 'herüber' or 'hinüber', describing movement across a short distance or an imagined line.
Gib mir mal bitte das Salz rüber.
Please pass me the salt over here.

to get across
Colloquial way of saying to communicate a message, emotion, or information clearly and effectively.
Sie ist eine tolle Rednerin, die ihre Begeisterung wirklich gut rüberbringen kann.
She's a great speaker who can really get her enthusiasm across well.

to go over
Colloquial and historical term for fleeing or moving from the former GDR to the Federal Republic of Germany.
Sein Onkel hat kurz vor dem Mauerbau noch 'rübermachen' können.
His uncle was still able to 'go over' shortly before the Berlin Wall was built.
'Rüber' (over) is the colloquial short form of 'herüber' (over here/across to here) or 'hinüber' (over there/across to there). It describes movement from one place to another, usually over a short distance.
Kommst du heute Abend zu mir rüber?
Are you coming over to my place tonight?
'Rüber' (over) often functions as a separable prefix for verbs like 'rüberkommen' (to come over), 'rübergehen' (to go over), or 'rüberreichen' (to pass over). In a main clause, the prefix stands at the end.
Kannst du mir bitte die Butter rüberreichen?
Can you please pass me the butter?
The separable verb 'etwas rüberbringen' (to get something across) has the figurative meaning of successfully communicating a message or feeling. What is communicated is the accusative object.
In seiner Rede hat er die Dringlichkeit des Problems gut rübergebracht.
In his speech, he got the urgency of the problem across well.
The expression 'rübermachen' (to go over) has a specific historical meaning. During the Cold War, it was the colloquial term for fleeing from East Germany (GDR) to West Germany.
Seine Familie hat kurz vor dem Mauerbau noch rübergemacht.
His family still managed to go over shortly before the Berlin Wall was built.
across / broken / gone
Rüber is a colloquial term for movement to the other side, without clearly distinguishing on its own between movement toward or away from the speaker. Hinüber explicitly indicates that the movement is away from the speaker or the place being considered. For this clear direction, hinüber is the better choice.

Ich gehe kurz rüber zu den Nachbarn.
I’m just going over to the neighbors for a moment.
Ich gehe von hier hinüber zu den Nachbarn.
I’m going across to the neighbors from here.