It all depends.
We have a tiny runway, only 120 feet x 18 feet. A bit limiting in terms of aircraft type and its suitability for novice flyers.
Used to have 180 x 24, which was much better ... and acceptable for most purposes.
So, If you have such an area, with clear approaches, you can get by with very little. Obviously, you have to be able to overfly the surrounding fields. If there is a standing crop at the runway edges, then your effective length is much reduced.
If you want to fly ic sport models, and stay within the bounds of your own property, I can hazard a good guess, based upon my own observations of the ranges at which people fly. At our field, the sport flyers rarely exceed a range of 120 yards from the pilot' box. That'd provide for minimum dimensions of 120 x 240 yards, which is about 6 acres. That's if you have only one runway.
But, I would suggest that a 6-acre site would require disciplined flyers, if they are to remain within its boundaries.
A more realistic size might be based upon a flying range of 150 yards from the pilot box. Based on that range, and encompassing only one runway, you'd need 9 acres. Plus a bit for the pits and for parking, most probably.
I know that I tried to buy a field, a few years ago. That was 15 acres ... and I considered it to be ample. But, it was bounded by other fields of crops; no houses within half-a-mile or so. Given what you said in the OP, I would judge that 15 acres would be good for you, too; if the shape of the field is right. A field of 400 yds x 180 yards would give you about 15 acres, and a lot of options.
Last edited by bogbeagle; 01-19-2015 at 08:04 AM.