The size of a ranch anywhere is dependent on what is being raised on that ranch. Cattle ranches are larger than say a place where chickens are raised. USDA has statistics on the average size of agricultural operations. Aa ranch needs space and water to be profitable, and I would bet that most small ranches are NOT profitable. That said, I think it would take more than 2000 acres to become profitable with cattle. In considering rates, the soils, climate, and water features would dictate carrying capacity. Carrying capacity in basic terminology is number of head of livestock (by species) that can be properly maintained without diminishing the health of the herd or the health of the land. That's my short answer. It is much more complicated than this, and hopefully you can see that the answer to your question is based on many variables. There are many ranches in Texas that are greater thn 50,000 acres, some as large as 250,000 acres, and a handful larger than that. A common sized ranch would be around 500 acres.
640 acres
1500 acres
1 Million acres
It has 825,000 acres.
Roughly 2,000,000 acres
20,000 plus acres - Barbara Moncrief
Rhode Island covers a total area of 776,960 acres.
10000
23,040 acres.
It depends on how large the ranch is. A ranch that is only 100 acres may only have 50 cows; "real" ranches that are over 1000 acres in size will have over 500 cows.
The University of Texas (at Dallas) has an area of 500 acres.
268,601, including water.