
satt
full
The feeling of having eaten enough and no longer being hungry.
Nach dem großen Stück Kuchen bin ich jetzt pappsatt.
After that big piece of cake, I'm completely stuffed now.
full / fed up
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full
The feeling of having eaten enough and no longer being hungry.
Nach dem großen Stück Kuchen bin ich jetzt pappsatt.
After that big piece of cake, I'm completely stuffed now.

to be fed up with something
A colloquial expression that means you have had enough of something or someone and are annoyed.
Ich habe deine ständigen Ausreden wirklich satt!
I am really fed up with your constant excuses!

rich
Describes a color as intense, strong, and deep.
Die Wiese leuchtete nach dem Regen in einem satten Grün.
After the rain, the meadow glowed in a rich green.
In the meaning 'nicht mehr hungrig' (no longer hungry), 'satt' (full) is almost always used as a predicative adjective. So you say 'Ich bin satt' (I am full), but rarely 'ein satter Mensch' (a full person). Another typical construction is 'sich satt essen' (to eat one's fill).
Danke für das Essen, ich bin satt.
Thank you for the meal, I'm full.
The expression 'etwas satt haben' (to be fed up with something) means that you are annoyed by something. The structure is always: person + haben + accusative object (what is annoying) + satt. This phrasing is colloquial.
Ich habe das schlechte Wetter so satt!
I am so fed up with the bad weather!
To describe a color as intense and strong, 'satt' (rich) is placed directly before the color. Typical combinations are 'sattes Grün' (rich green), 'sattes Rot' (rich red), or 'sattes Blau' (rich blue).
Der Himmel hatte ein sattes Blau.
The sky had a rich blue color.
full
When talking about eating, both words can express that you do not want to eat anything more. „Satt“ is the neutral term for having eaten enough. „Voll“ is more colloquial and can additionally suggest that your stomach feels uncomfortably full.

Nach dem großen Mittagessen bin ich satt und möchte keinen Nachtisch mehr.
After the big lunch, I’m full and don’t want any dessert.
Nach dem großen Mittagessen bin ich so voll, dass ich keinen Nachtisch mehr möchte.
After the big lunch, I’m so full that I don’t want any dessert.