As my limited experience in English indicates, more contractions are used in spoken English than in written. Moreover, too many contractions favor casualness. Compare:
- I would not have come.
- I wouldn't have come.
- I wouldn't've come.
However, I've encountered plenty of contractions in formal contexts (textbooks, serious speeches, etc), which makes me unsure about associating contractions with informality.
What is the exact correlation between using contractions and formality?