What is the difference between zu Hause and nach Hause?

zu Hause

→   means being at home

often used with verbs such as sein, bleiben, for example:

Ich bleibe morgen zu Hause.

Bist du schon zu Hause?

nach Hause

→   used when there is a movement towards home

often used with verbs such as gehen, fahren, kommen, for example:

Ich gehe jetzt nach Hause.

Wann bist du nach Hause gekommen?

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Dictionary with translations into various languages, with examples from the internet for the various meanings of a word.