I did this calc years ago.
The results of the above files are:
maximum holding capacity for the earth = 18.5 billion
Reached by about the year 2100.
It worked out that each person needs 1130sqm (about 1/4 acre) of arable land to sustainably grow their potatoes
This was calculated saying that:
- 13.31% of the earths surface is naturally arable.
- Based on my body using 195k KJ of food per week. (based on my personal intake when I am totally maxed out exercising and trying to increase sporting performance. I eat about 3 times the average adult male when training, but I expend 3 times the energy as well.)
- It did not include water, housing, clothing, transport, energy used in cooking.
- Based only on potato crops as they are amongst this simplest to grow. Therefore no protein, fat, mineral or vitamin considerations.
Other studies I came across, but did not rigorously verify said about 10billion by 2050ish.