Biggest possible population of medieval Hungary

With the presented borders below, theoretically how big population could the area of Kingdom of Hungary support in the Middle Ages? What are the biggest possible numbers?
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Thank you in advance for your answers!
 
Here's the very rough math I came up with so feel free to correct me. I'm also just assuming ideal conditions so realistic numbers are probably significantly less.

Your map looks like roughly like modern Hungary and Croatia combined which have 12,892,000 acres of arable land although about half would be kept fallow at any one time.
Yield in western Europe in medieval times was in the range of 8-12 bushels of grain per acre (I have no idea what yield was in Hungary), and half of it was kept as seed. So total food output is 32,230,000 bushels a year. This number will improve over time as well as yields rise.

I've seen some numbers that say the average person needed 14-24 bushels a year to survive so that puts the total population at ~1.7 million people. But again this is an ideal situation and I wouldn't be surprised if the maximum sustainable was half that.
 
Here's the very rough math I came up with so feel free to correct me. I'm also just assuming ideal conditions so realistic numbers are probably significantly less.

Your map looks like roughly like modern Hungary and Croatia combined which have 12,892,000 acres of arable land although about half would be kept fallow at any one time.
Yield in western Europe in medieval times was in the range of 8-12 bushels of grain per acre (I have no idea what yield was in Hungary), and half of it was kept as seed. So total food output is 32,230,000 bushels a year. This number will improve over time as well as yields rise.

I've seen some numbers that say the average person needed 14-24 bushels a year to survive so that puts the total population at ~1.7 million people. But again this is an ideal situation and I wouldn't be surprised if the maximum sustainable was half that.
Thank you for answering, but your numbers are a little bit strange. In the 14th century, the estimated population of this area is 3 million, while for the end of the 15th century some estimations put the population around 5 million.
I'm not sure, but the flaw in your calculation might have been that you only counted with the areas of modern Hungary and Croatia as you said, but actually it's much bigger, than that. On the map you can see the modern borders as well with the narrow lines.
 
Here's the very rough math I came up with so feel free to correct me. I'm also just assuming ideal conditions so realistic numbers are probably significantly less.

Your map looks like roughly like modern Hungary and Croatia combined which have 12,892,000 acres of arable land although about half would be kept fallow at any one time.
Yield in western Europe in medieval times was in the range of 8-12 bushels of grain per acre (I have no idea what yield was in Hungary), and half of it was kept as seed. So total food output is 32,230,000 bushels a year. This number will improve over time as well as yields rise.

I've seen some numbers that say the average person needed 14-24 bushels a year to survive so that puts the total population at ~1.7 million people. But again this is an ideal situation and I wouldn't be surprised if the maximum sustainable was half that.
Also, you're calculating using only open-field grain yields. While this was a major component of the average person's diet, there were also home gardens (which could be quite extensive, with both perennial and annual food-bearing plants). These were heavily manured from household waste and some livestock manure, so they were quite productive. Livestock also represented a large source of calories, and would be pastured on much of the non-arable land, AND on the fallow land between planting seasons.

For the yields, the volumetric measures varied between every culture, so most historians use a 'seeds harvested-to-seeds planted measurement; i.e., a good yield on the fields around Paris in the 1300s was about 9-11 seeds for every one planted, with some river-bottom lands with good fertility achieving 15-1 ratios. And so the idea of keeping back half of the harvest for seed is a bit excessive, except for the most poorly producing lands.

I'll do some better calculations when I'm not grading papers, but I'd say Fehervari's citing of 3-5 million is OTL. With a four-crop rotation, different crops, improved livestock breeds, more intensive cultivation on the best soils...maybe 10 million??
 
Also, you're calculating using only open-field grain yields. While this was a major component of the average person's diet, there were also home gardens (which could be quite extensive, with both perennial and annual food-bearing plants). These were heavily manured from household waste and some livestock manure, so they were quite productive. Livestock also represented a large source of calories, and would be pastured on much of the non-arable land, AND on the fallow land between planting seasons.

For the yields, the volumetric measures varied between every culture, so most historians use a 'seeds harvested-to-seeds planted measurement; i.e., a good yield on the fields around Paris in the 1300s was about 9-11 seeds for every one planted, with some river-bottom lands with good fertility achieving 15-1 ratios. And so the idea of keeping back half of the harvest for seed is a bit excessive, except for the most poorly producing lands.

I'll do some better calculations when I'm not grading papers, but I'd say Fehervari's citing of 3-5 million is OTL. With a four-crop rotation, different crops, improved livestock breeds, more intensive cultivation on the best soils...maybe 10 million??
Sounds plausible. In OTL the population of Hungary reached 10 million by the end of 18th century and it was still relatively sparsely populated though. How much difference can be between the population cap in the 14th and 18th century? (No industrialisation)
 
With the presented borders below, theoretically how big population could the area of Kingdom of Hungary support in the Middle Ages? What are the biggest possible numbers?
View attachment 348535
Thank you in advance for your answers!
In terms of arable land, France has 215,029km^2. The territory which is now France had a population of around 20,000,000 people in the early 1300s. This means France had about 93 people per square km of arable land.

The Kingdom of Hungary had at least 68,322km^2 of arable land (I got that number by putting modern Hungary, Croatia, and Slovakia together, it's not perfect by any means). At 93 people per square km it would have at least 6,353,946 people. I think "wanking" it to 10 million is reasonable.
 
In terms of arable land, France has 215,029km^2. The territory which is now France had a population of around 20,000,000 people in the early 1300s. This means France had about 93 people per square km of arable land.

The Kingdom of Hungary had at least 68,322km^2 of arable land (I got that number by putting modern Hungary, Croatia, and Slovakia together, it's not perfect by any means). At 93 people per square km it would have at least 6,353,946 people. I think "wanking" it to 10 million is reasonable.
You really need Transylvania to boost that land area.
France is sort of the limit for medieval pop density, they had extremely fertile lands, so I don't think going too far over that is reasonable without industrialization.
 
You really need Transylvania to boost that land area.
Sadly I couldn't find that value. Or the Value for Transcarpathia or Burgenland for that matter.

France is sort of the limit for medieval pop density, they had extremely fertile lands, so I don't think going too far over that is reasonable without industrialization.
Couldn't early adoption of more efficient farming methods boost that? Of course such methods would likely spread producing many much more populous states.
 
What about a more urbanized Hungary overall? Even in medieval times, Western Europe had to import large amounts of food from Eastern Europe to sustain its (relatively) high populations. The same would be true of any large relatively urbanized country: food could be imported through trade for manufactured products of the cities.
 
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