
ruhig
quiet
Describing a state of silence and little background noise; quiet.
Wir wohnen in einer sehr ruhigen Straße ohne viel Verkehr.
We live on a very quiet street without much traffic.
quiet / calm
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quiet
Describing a state of silence and little background noise; quiet.
Wir wohnen in einer sehr ruhigen Straße ohne viel Verkehr.
We live on a very quiet street without much traffic.

calm
Describing a state of inner composure and relaxation; not nervous or excited.
Auch in stressigen Situationen bleibt sie immer ruhig und konzentriert.
Even in stressful situations, she always stays calm and focused.

go ahead
Used as a particle to give permission or encourage someone; means something like 'without hesitation' or 'feel free to'.
Du kannst ruhig schon ein Stück Kuchen nehmen, du musst nicht auf uns warten.
You can go ahead and take a piece of cake already; you don't have to wait for us.

still
Describing a state with little movement; still.
Das Meer war heute spiegelglatt und ganz ruhig.
The sea was mirror-smooth and completely still today.
The adjective 'ruhig' (quiet/calm) is derived directly from the noun 'die Ruhe' (quiet/calm/rest). When something is 'ruhig', then there is 'Ruhe' there.
Ich brauche am Abend meine Ruhe, deshalb mag ich ruhige Orte.
I need my peace and quiet in the evening, so I like quiet places.
'Ruhig' can be a normal adjective that describes a noun. But it can also be a particle that makes a statement friendlier or signals permission and is not translated literally.
Das ist ein ruhiges Hotel am Meer.
That is a quiet hotel by the sea.
The phrase 'ruhig bleiben' (to stay calm) is very common. It is advice or an instruction not to lose your nerve in a stressful or exciting situation.
Auch wenn es schwierig wird, ist es wichtig, ruhig zu bleiben und klar zu denken.
Even when things get difficult, it is important to stay calm and think clearly.
As a particle, 'ruhig' expresses permission or encouragement, similar to 'go ahead' or 'without hesitation'. It usually comes after the verb and the subject.
Frag ruhig, wenn du etwas nicht verstehst.
Go ahead and ask if you don't understand something.
only
Nur can strengthen a friendly invitation or permission without explicitly addressing possible concerns. Ruhig also encourages someone, but especially signals that the action is permitted and there is no reason to worry.

Komm ruhig herein, du störst mich nicht.
Go ahead and come in; you aren't disturbing me.
Komm nur herein, ich möchte dir etwas zeigen.
Come in, I want to show you something.