I am only a learner, and there will be multiple posts with additional reasons and instances where the circumflex is used, but here are 3 that comes to mind first. 1) It makes the vowel "closed" (for "o" and "e"). "avó" (open, meaning grandmother) as opposed to "avô" (closed, meaning grandfather) 2) For words of Greek origin, it tells you where the stress falls on. economia (stress falls on the usual place, penultimate) econômico (moved to the second "o") ciência (it's out of place at "e") emergência (ditto) 3) There are some orthographic differences between European Portuguese and Brazilian Portuguese. If I am not mistaken, in Brazilian Portuguese, they use the circumflex, and acute accent in European Portuguese. "quilómetro" (EP) while "quilômetro" (BP)

There're some possible situations to use it: The circumflex can be used to change the gender of the word, just like "avó" and "avô" To know if the stressed syllable has a closed sound or an open sound, just like: "sofá" and "você" or To give emphasis on a specific syllable, just like: metrô, camelô If you still have doubts, send me a message in the private chat. I'm a Brazilian, I'm sure I can help you out!!!

Diacritic grave áéíóú and circunflex êô and â ( â only in BP) are used to indicate the stressed silable in a word. We have two kinds of E and O, opened like in the words bed and tough, and closed like in bender and bow. Opened vowels receives the grave and closed receives the circunflex. Words with diferent pronounciation in BP and EP receives diferent diacritics, poop is cocô in BP and cocó in EP, also nasalised "a" receives the circunflex in Brazil because we pronounce this more closed, like in my last name Alcântara, in Portugal would be Alcántara. Vowels in unestressed silables are often reduced and their pronunciation, opened or closed, is optional.

As far as I am aware, it is not used for the same reason as in French, where it indicates the disappearance of an "s".