What is the approximate time span of Othello, and what evidence shows this?
We know the play begins in the evening, and that Othello and Desdemona leave for Cyprus that very night, concerned that they need to get there before the Turkish fleet.
There is somewhat of a gap then, between this departure and their arrival in the city. We cannot know for sure, but in the meantime there has also been a disaster for the Turkish fleet, so one could guess anywhere in the range of a couple days to a week or more, given the relatively difficult task of predicting travel time to Cyprus from Venice at the time.
The play then proceeds to move very, very quickly, but encompasses at least one more night and one more day as we have the scene with Othello meeting Iago after a sleepless night, as well as the night which yields all the action between Iago, Rodrigo and Cassio. Add in one more night in which the whole thing falls apart and Othello kills Desdemona, etc., and you are looking at at least several days.
So my rough estimate would be two weeks total. Of course most tragedies are said to last only 24 hours, so take your pick!