
fest
solid
Having a hard, stable consistency; not liquid or gaseous.
Der Boden ist nach dem Frost wieder fest.
After the frost, the ground is firm again.
firm / fixed
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solid
Having a hard, stable consistency; not liquid or gaseous.
Der Boden ist nach dem Frost wieder fest.
After the frost, the ground is firm again.

firm
Stable, sturdy, and not easy to move or loosen.
Prüfe bitte, ob die Schrauben alle fest sind.
Please check whether all the screws are tight.

permanent / fixed
Set permanently, bindingly, or unchangeably.
Er hat eine feste Stelle in einer großen Firma bekommen.
He got a permanent position at a large company.

tightly
With force or fitting closely.
Der Knoten ist so fest, dass ich ihn nicht aufbekomme.
The knot is so tight that I can't get it open.

to sleep soundly
To sleep deeply and without interruption.
Das Baby hat die ganze Nacht fest geschlafen.
The baby slept soundly all night.

to be firmly convinced
To have a strong, unshakable conviction or belief.
Ich bin fest davon überzeugt, dass wir das Projekt erfolgreich abschließen werden.
I am firmly convinced that we will successfully complete the project.
The adjective 'fest' is also very often used as an adverb to intensify a verb. It then means 'strongly', 'firmly', or 'intensely'.
Sie drückte seine Hand ganz fest.
She squeezed his hand very tightly.
Words like 'befestigen' (to attach/fasten something), 'festhalten' (to hold on to something/not let go), or 'die Festung' (a stable fortified building/fortress) belong to the same word family and share the basic idea of stability.
Kannst du bitte das Bild an der Wand befestigen?
Can you please attach the picture to the wall?
In the meaning 'stable' or 'sturdy', 'fest' is often combined with things that provide support, e.g. 'fester Boden' (firm ground), 'festes Schuhwerk' (sturdy footwear), or 'ein fester Händedruck' (a firm handshake).
Für die Wanderung brauchst du festes Schuhwerk.
You need sturdy footwear for the hike.
In social and professional life, 'fest' expresses a binding, lasting relationship. Typical combinations are 'eine feste Stelle' (a permanent position), 'ein fester Termin' (a fixed appointment), or 'ein fester Freund / eine feste Freundin' (a steady boyfriend/girlfriend).
Wir haben noch keinen festen Plan für das Wochenende.
We don't have a fixed plan for the weekend yet.
When 'fest' means 'with force', it often appears as an adverb with verbs like 'halten' (to hold), 'ziehen' (to pull), 'drücken' (to press/squeeze), or 'umarmen' (to hug).
Er umarmte seine Mutter ganz fest zum Abschied.
He hugged his mother very tightly when saying goodbye.
The combination 'fest schlafen' (to sleep soundly) is a fixed expression and means that someone sleeps very deeply and well.
Trotz des Lärms hat das Kind die ganze Zeit fest geschlafen.
Despite the noise, the child slept soundly the whole time.
To express a strong, unshakable opinion, 'fest' is used in fixed expressions like 'fest davon überzeugt sein' (to be firmly convinced of it), 'fest daran glauben' (to firmly believe in it), or 'fest damit rechnen' (to fully expect it).
Sie rechnet fest damit, die Prüfung zu bestehen.
She fully expects to pass the exam.
sure / safe
Both words can express a strong conviction. „Sicher“ emphasizes that you have no doubt, while „fest“ highlights the particular strength and unshakable nature of the conviction. Use „sicher“ for clear certainty and „fest überzeugt“ for especially emphatic belief.

Ich bin fest überzeugt, dass die Mannschaft heute gewinnt.
I am firmly convinced that the team will win today.
Ich bin sicher, dass die Mannschaft heute gewinnt.
I am sure that the team will win today.