estimate vs compute

estimate is a noun but compute is not a noun.

Word	Noun	Adjective	Verb	Adverb
estimate	Yes	No	Yes	No
compute	No	No	Yes	No

As verbs, compute is a hypernym of estimate; that is, compute is a word with a broader meaning than estimate:

Other hypernyms of estimate include calculate, cipher, cypher, figure, reckon, work out.

estimate (noun)	compute (noun)
a judgment of the qualities of something or somebody
an approximate calculation of quantity or degree or worth
the respect with which a person is held
a document appraising the value of something (as for insurance or taxation)
a statement indicating the likely cost of some job

estimate (verb)	compute (verb)
judge tentatively or form an estimate of (quantities or time)	make a mathematical calculation or computation
judge to be probable