
rauf
up
Colloquial short form of 'herauf' or 'hinauf', expressing movement upward.
Wir müssen den ganzen Berg zu Fuß rauf.
We have to go up the whole mountain on foot.
up
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up
Colloquial short form of 'herauf' or 'hinauf', expressing movement upward.
Wir müssen den ganzen Berg zu Fuß rauf.
We have to go up the whole mountain on foot.

up and down
An idiom meaning that something happens repeatedly or very thoroughly, often in relation to movement or searching through something.
Er ist die Liste rauf und runter gegangen, konnte den Namen aber nicht finden.
He went up and down the list but couldn't find the name.
'Rauf' (up) is the colloquial and very common short form of 'herauf' or 'hinauf' (upward/up here/up there). In formal or written texts, the full words are usually used.
Kommst du kurz rauf? Ich brauche deine Hilfe.
Can you come up for a moment? I need your help.
'Rauf' (up) is often combined as a separable prefix with verbs of movement (e.g. 'raufgehen' (to go up), 'raufklettern' (to climb up), 'rauffahren' (to drive/ride up)). In a main clause, 'rauf' goes at the end.
Wir gehen den Berg jetzt rauf.
We're going up the mountain now.
The expression 'rauf und runter' (up and down) means 'repeatedly' or 'very thoroughly'. For example, you can 'rauf und runter singen' (sing something over and over) a melody or 'rauf und runter beten' (recite something over and over) a poem.
Ich kenne den Text mittlerweile rauf und runter.
By now I know the text up and down.
high
In colloquial use, hoch and rauf can both express movement upward. Rauf clearly points to a destination higher up. In such expressions, hoch can also indicate this direction, but it is also used simply for lifting or raising something.

Bitte trag den schweren Karton vorsichtig nach oben rauf.
Please carry the heavy box carefully upward.
Bitte heb den schweren Karton vorsichtig hoch.
Please lift the heavy box carefully.