When you enter the U.S. you should receive a “F-1 D/S” notation on the U.S. entry stamp in your passport or on your I-94 electronic arrival record, indicating that you have permission to remain in the U.S. for “duration of status.”
The duration of your F-1 status ends as soon as your Form I-20 expires or as soon as you complete your program of study, whichever is sooner, plus up to 60-days of a “grace period” for you to prepare to depart the U.S. or take legal action that will allow you to remain in the U.S.
Your Form I-20 was issued for the estimated length of your program of study. If you need additional time to complete your program, you must submit a complete request for I-20 extension to OISA prior to your I-20 end date.
If you finish your degree earlier than expected, the end date on I-20 will be updated to reflect your actual date of program completion.