As long as your return is time stamped on the due date (April 15, or October 15 if you have an extension), it will be considered on time.
On the other hand, if you owe a tax bill and file even one day after the deadline, you’ll have the failure-to-file and failure-to pay penalties added to your bill. That’s 5% interest on your taxes added each month your return isn’t filed, so it’s always best to file on time or as soon as possible.
If you file after the deadline but don’t owe any taxes, you won’t have any penalties or fees applied until more than 60 days after the due date. After that, you’ll owe $135 (the minimum penalty when you don’t owe tax or when you expect to get a refund), so you should still file as soon as possible. Also, remember that you won’t receive your refund until your return has been filed, accepted and approved.