bad luck vs calamity

bad luck and calamity both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad luck	Yes	No	No	No
calamity	Yes	No	No	No

As nouns, calamity is a hyponym of bad luck; that is, calamity is a word with a more specific, narrower meaning than bad luck:

bad luck: unnecessary and unforeseen trouble resulting from an unfortunate event
calamity: an event resulting in great loss and misfortune

bad luck (noun)	calamity (noun)
unnecessary and unforeseen trouble resulting from an unfortunate event	an event resulting in great loss and misfortune
an unpredictable outcome that is unfortunate
an unfortunate state resulting from unfavorable outcomes