estimate vs make a guess at

estimate

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. 

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

  • To calculate roughly, often from imperfect data. 

make a guess at

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