
die Angst
fear
A strong, unpleasant feeling of threat or worry.
Bei dem Gedanken an die Prüfung spürte er große Angst.
At the thought of the exam, he felt great fear.
fear
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fear
A strong, unpleasant feeling of threat or worry.
Bei dem Gedanken an die Prüfung spürte er große Angst.
At the thought of the exam, he felt great fear.

to be afraid of
To be afraid of a specific person, thing, or situation.
Viele Menschen haben Angst vor Spinnen.
Many people are afraid of spiders.

to fear for
To worry about someone's well-being or safety.
Die Mutter hat Angst um ihr krankes Kind.
The mother fears for her sick child.
The preposition after 'Angst haben' (to be afraid) is very important. 'Angst vor' (+ dative) describes the source of fear. 'Angst um' (+ accusative) expresses worry about someone or something.
Das Kind hat Angst vor der Dunkelheit.
The child is afraid of the dark.
Common verbs with 'Angst' (fear) are 'Angst haben' (to be afraid), 'Angst bekommen' (to suddenly feel afraid), and 'jemandem Angst machen' (to scare someone).
Als das Licht ausging, bekam ich große Angst.
When the light went out, I became very afraid.
To explain the reason for the fear more precisely, you can use a subordinate clause with 'dass' (that) or an infinitive construction with 'zu' (to).
Ich habe Angst, dass ich den Zug verpasse.
I'm afraid that I'll miss the train.
panic
Die Angst is the more general word for a strong, unpleasant feeling of threat. Die Panik, on the other hand, refers to sudden, extreme fear in which people lose control and may act irrationally. Use Angst for the feeling in general and Panik for this kind of sudden escalation.

Vor dem brennenden Haus hatte sie große Angst.
She was very afraid in front of the burning house.
Als der Rauch dichter wurde, bekam sie Panik und rannte unkontrolliert hinaus.
As the smoke grew thicker, she panicked and ran out uncontrollably.