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.

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.
already
'schon' and 'ruhig' can both have a reassuring or encouraging effect. 'schon' is often used to say: it will be okay, or it is not so bad. 'ruhig' is used when you allow or recommend someone to do something without hesitation. That is why they are not simply interchangeable. Learners confuse them because both can sound friendly and reassuring. Memory tip: 'schon' reassures about the outcome, while 'ruhig' gives permission or encourages an action.

Du kannst die Ärztin ruhig fragen, wenn du etwas nicht verstehst.
Feel free to ask the doctor if you do not understand something.
Keine Sorge, der Termin klappt schon.
Don't worry, the appointment will work out.