The difference between "zu Hause" vs. "nach Hause" easily trips up German learners, but it doesn't have to trip you up if you use the tips below.
1. "zu Hause" = (at) home
"zu" is usually used as a preposition, so it would stand by itself and you might think that "zu Hause" means "to home." This is an exception. When you say "zu Hause," you're really using it as one block of language.
Think of the sentence "Ich bin zu Hause" and picture it like two wooden blocks:
[Ich] [bin] [zu Hause].
So just as you learn "der Tisch" and not just "Tisch," learn this as one piece of language or one idea. Learn "zu Hause" meaning home just as you would "der Tisch" for table.
You're at home and your friend calls. "Wo bist du?" You answer "Ich bin zu Hause."
You and your spouse fancy a night in. Your friends call and ask you to go get pizza, but really you just want to stay home. Your response is "Wir bleiben heute Abend zu Hause."
2. "nach Hause" = to home / toward home
"Nach Hause" is what you say when you're leaving somewhere and you're going to go home. Think of this also like a block:
[Ich] [fahre] [nach Hause].
When you're at a friend's for dinner, but it's late and it's time to go, you say "Ich fahre nach Hause. Gute Nacht!"
You're out shopping with your sister and you're all shopped out. You look at each other and say "Wir fahren nach Hause."
You're in Germany and have had a wonderful vacation, but now you must return to your home country. "Ich fliege jetzt nach Hause."
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