approximate vs estimate

approximate

verb
  • To come near to; to approach. 

  • To carry or advance near; to cause to approach. 

  • To estimate. 

adj
  • Nearing correctness; nearly exact; not perfectly accurate. 

  • Approaching; proximate; nearly resembling. 

estimate

verb
  • To judge and form an opinion of the value of, from imperfect data. 

  • To calculate roughly, often from imperfect data. 

noun
  • A rough calculation or assessment of the value, size, or cost of something. 

  • A document (or verbal notification) specifying how much a job is likely to cost. 

  • An upper limitation on some positive quantity. 

How often have the words approximate and estimate occurred in a corpus of books? (source: Google Ngram Viewer )