About 5 acres seems to be the absolute minimum for self sufficiency, providing you make use of all the modern technical advances available, and supplement with wild game and fish, or buy your meat elsewhere, and you choose the right type of land and plants.

It is going to be one of the most strenuous jobs you will ever have trying to get that amount of land to produce enough to feed a family for a year, but it can be done.

Done right, it should provide at least 4 months of fresh produce a year and allow for an additional 1,000 quarts canned. It should also produce about 100 bushels of wheat. A good root cellar ought to allow for an additional 400-800 lbs of storable produce (pumpkin, winter squash, certain root vegetables, apples, etc).

If you hunt and fish, you should be able to garner another 1,200 lbs or so of meat, depending on where you are in the country. To be that successful will take a fair investment in equipment and practice, as well as finding the animals. Domestic livestock would cost more in resources than they will provide, so best if you can get it wild. In my heyday, after amortizing the cost of all my hunting and fishing gear, I could usually bring in 1,000 lbs or more of meat a year on less than $500. Most of it was fish, but I got my fair share of birds, and the occasional deer and elk filled the deep freeze to capacity.