This answer was written before the question was edited, so not sure if I'll need to adjust it.
Well, it is really arable area multiplied by crop productivity per area divided by food requirement per unit of population. Only real complication is that you need to also consider the type of arable area (temperature, humidity, soil) when calculating productivity. Potato, for example, was huge not only because it had high productivity, but because it was less demanding of climate and soil than the more productive cereals. You also have to consider that people do change their environment to be both more and less productive by clearing forests, levelling ground, and building irrigation systems.
But, yeah, the basic math is simple. They have more arable area, more productive crops, or people who need less food.
Arable area can be increased by having less deserts, tundra, taiga, sea or other types of areas not suited for agriculture. Or by having magic that can make such areas arable. A fantasy civilization could feasibly use magic to adjust temperature, moisture, or even soil. This could even happen invisible by the gods intervening to help their worshippers. Or the world could simply be bigger.
Magic could easily make crops more productive. A simple protective blessing by a village priest could easily replace fertilizers and protect plants from pests and disease. Fantasy civilizations generally have long history of agriculture and access to supernatural guidance. Their cultivars could actually be better than ours are. So the agricultural productivity per area of common magic fantasy civilization could be comparable to modern agriculture. And thus it might be able to support similar populations.
Food consumption might vary by race. Non-humans might need less food and thus increase maximum possible population. Magic might reduce spoilage. Fantasy civilizations might eat less meat, which would vastly decrease resources needed.
An issue that needs to be addressed is productivity per person. While productivity per area will tell you how many people an area can support, you also need to know how many of those people are stuck tending the fields and how many will migrate to cities to other work. Typically low tech would imply that almost everyone lives in small villages producing food, but golems, elemental servants, or zombies can be used to tend to fields instead and allow an urbanized society.
Logistics is also important. Typically low tech would have lots of small cities with few political, religious, or commercial centers becoming larger. But if you can use magic to transport food, you could have population distribution more similar to modern times.
You also need to think about how good the people are in handling disease, particularly epidemics, as that has impact on how good large cities are to live in. (ckersch covers this in his answer) Medical technology will also determine the rate of growth that is possible for the population. Better you control disease, lower the childhood mortality will be and faster your population can grow in response to changes in its ability to support more people.
And also think how people actually cook their food. If people use wood fires, you'll have acute deforestation and eventual ecological collapse. If magic can be used, you'll have (probably) sustainability similar to modern electricity based solutions. The energy still is coming from somewhere even if you use magic so something similar to global warming might exist.
And one thing people tend to forget. Building houses and roads requires land that then can't be used for agriculture. So then population increases you'll need new agricultural area to not only cover the increased consumption, but also to replace the area taken by infrastructure.