I am replacing an old wooden barn post. The current post sits on a good size stone. I would like to sit the new oak post on a concrete footing. How deep does the footing have to be? What kind of concrete do I use? Thanks.

Is it necessary to bury the post under grade?

If not,don't.

Posts rot at contact to ground,not much below grade, but right at the level of ground to air. and using an oak post,not treated will become a problem in the long run(much less harder to remove when it has problems or needs repairs.)

I would never put an oak post in the ground, footer or not. Best thing is to fill a 48" hole with concrete and set the post on top of the concrete never to be covered with soil. Guess the answerr to your original question is 48" and slightly larger at the bottom than the top.