down
A colloquial expression for a state of emotional dejection, sadness, or lack of energy.
Nach der Absage war er den ganzen Tag ziemlich down.
After the rejection, he was pretty down all day.

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A colloquial expression for a state of emotional dejection, sadness, or lack of energy.
Nach der Absage war er den ganzen Tag ziemlich down.
After the rejection, he was pretty down all day.

The word 'down' is borrowed directly from English and is used mainly in colloquial speech. It keeps its English pronunciation.
Ich fühle mich heute irgendwie down.
I feel kind of down today.
As an adjective, 'down' is not declined and almost always comes after a verb like 'sein' (to be) or 'sich fühlen' (to feel). You cannot place it before a noun.
Der Server ist schon wieder down.
The server is down again.
You can recognize the meaning from the subject of the sentence. If 'down' refers to a person, it means 'niedergeschlagen' (dejected/down). If it refers to a technical system, it means 'außer Betrieb' (out of service/down).
Mein Freund ist seit gestern down.
My friend has been down since yesterday.
sad
'traurig' and 'down' can both describe that someone is not doing well emotionally. 'traurig' is the neutral German word and fits many situations, including when an event is regrettable. 'down' is colloquial and often means a mix of sad, tired, and lacking energy. It sounds more casual and is more suitable for conversations among friends. If you simply want to express sorrow or sadness, 'traurig' is more precise and appropriate everywhere. If someone feels bad and has no energy, 'down' can sound natural.

Nach der schwierigen Prüfung ist die ganze Gruppe ziemlich down.
After the difficult exam, the whole group is pretty down.
Frau Klein wirkt traurig, weil ihre Freundin weggezogen ist.
Ms. Klein seems sad because her friend moved away.