calm down vs silence

calm down is not a noun while silence is a noun.

Word	Noun	Adjective	Verb	Adverb
calm down	No	No	Yes	No
silence	Yes	No	Yes	No

As verbs, silence is a hypernym of calm down; that is, silence is a word with a broader meaning than calm down:

Other hypernyms of calm down include hush, hush up, quieten, shut up, still.

calm down (noun)	silence (noun)
	the absence of sound
	a refusal to speak when expected
	the trait of keeping things secret
	the state of being silent (as when no one is speaking)

calm down (verb)	silence (verb)
become quiet or less intensive	cause to be quiet or not talk
make calm or still	keep from expression, for example by threats or pressure
become quiet or calm, especially after a state of agitation