I find this surprising. I help run an Atlanta-area non-profit that has a ~1 acre organic farm that donates everything it produces. For the year 2020 we have already donated 3120 lb / 1415 kg of food.
We're not trying to produce a nutritionally complete output on the farm, but that's still ~70 lb / 31.7 kg of food a week on average.
Now, let's assume a family of three - an average person needs around 2,000 kcal a day. That's 2,000 * 365 * 3, or around 2,200,000 kcal a year. So, you come quite a bit short. And that's on a good year; you're gonna have bad years, too.
Also a function of climate and soil. In the 19th century, settlers in the plains - Nebraska, Wyoming, etc - often couldn't make it work on 640 acres granted by the government. In contrast, there are eastern states where 20 acres would be more than enough.
(Farming in the West is now much more viable thanks to deep wells and mechanical irrigation, but that's a capital-intensive and resource-intensive approach that works best at a scale.)
The problem with your math is that it assumes the 3k lb yield from gp comment is for potatoes. Your crop yield depends a lot on the crop. Aparently you can get between 10-30 tons of potatoes per acre (that range is from beginner yields to expert) which would be 7-21 million calories per year. Plenty of room, then, to grow a number of other crops to eat a balanced diet.
Boring as hell after a while but it'd keep you alive.
On a typical day in 1844, the average adult Irishman ate about 13 pounds of potatoes. At five potatoes to the pound, that’s 65 potatoes a day. The average for all men, women, and children was a more modest 9 pounds, or 45 potatoes.
https://slate.com/culture/2001/03/putting-all-your-potatoes-...
While there are people who doubt these figures, eating 10 lbs of potatoes per day is definitely more plausible than your comment indicates.
Of course, the yields could probably be improved in order to get the 140 or so lbs needed to feed a family of 3
10 lbs of potatoes is only 3,500 calories. Which, while far in excess of a "normal" sedentary lifestyle, is completely reasonable for people working heavy labor jobs if that's their primary food source.
I have some family members who devoted about an acre and a half to a mix of crops, squashes mostly as they grow the best where they live, and for a family of 5 still had to supplement their diet pretty significantly.
At the same time, they ate more healthily than they ever had before, and often had too much of certain crops that they gave away or sold at the local farmer's market.
