
hinauf
up
Expresses upward movement, from a lower to a higher position, often from the perspective of moving away from the speaker.
Wir sind langsam den steilen Bergpfad hinauf gewandert.
We slowly hiked up the steep mountain path.
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up
Expresses upward movement, from a lower to a higher position, often from the perspective of moving away from the speaker.
Wir sind langsam den steilen Bergpfad hinauf gewandert.
We slowly hiked up the steep mountain path.
The word is made up of 'hin' and 'auf'. 'Hin' describes movement away from the speaker, while 'auf' indicates the upward direction.
Schau mal, wie die Katze den Baum hinauf klettert!
Look how the cat is climbing up the tree!
'Hinauf' (up) is very often combined as a separable prefix with verbs of movement, e.g. 'hinaufgehen' (to go up), 'hinauffahren' (to ride/drive up), or 'hinaufsteigen' (to climb up). In a main clause, 'hinauf' comes at the end.
Wir fahren mit dem Aufzug in den zehnten Stock hinauf.
We're taking the elevator up to the tenth floor.
To name the path or destination of the upward movement, a noun in the accusative is often placed before 'hinauf' (up). Typical examples are 'die Treppe hinauf' (up the stairs) or 'den Berg hinauf' (up the mountain).
Er lief die Treppe schnell hinauf, weil er spät dran war.
He ran quickly up the stairs because he was late.
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Both words express upward movement. Hinauf is the full form and can emphasize movement away from the speaker; rauf is the colloquial short form of hinauf or herauf and often leaves this perspective open. Hinauf is more suitable in neutral standard language, while rauf is common in conversation.

Die Kinder gingen die Treppe hinauf, während ich unten blieb.
The children went up the stairs while I stayed downstairs.
Die Kinder gingen die Treppe rauf, während ich unten blieb.
The children went up the stairs while I stayed downstairs.