How old is Hamlet at the end of the play?

31

Hamlet's age has two theories, both based on Act V Scene I material - the gravedigger scene. The gravedigger says that he has been in his current position since the day Young Hamlet was born, and then proceeds to say it was 30 years ago. However, in another version of the text, he actually says he's been working for 16 years and he's 30 years old in total. Either is possible, but 16 and 30 are very different interpretations of the character! Either way, this is close to the end of the play and would provide a good estimate of his age at that time.

Regarding the controversy over 16 years old vs 30 years old:

It appears Hamlet may have originally been written in as 16, but was changed to 30 to fit the actor's age.

In any case, the modern Hamlet should be read as being approx 30 years old.

However, this reading has the disadvantage that in the Folio the length of time Yorick has been in the ground is said to be twenty-three years, meaning that he had been dead seven years by the time Hamlet was born. Another theory offered is that the play was originally written with the view that Hamlet was 16 or 17, but since Shakespeare wrote his plays to be performed, and not read, these lines were likely changed so Burbage (who was almost always the protagonist in Shakespeare's plays) could play the role.

https://en.wikipedia.org/wiki/Prince_Hamlet