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I figured I'd make a section for empires where sources have been found for the maximum extent but with no year specified (meaning they can't be included in the list). My hope is that this will be helpful when people try to locate sources. Feel free to add entries of your own to the list below. TompaDompa (talk) 23:38, 3 July 2020 (UTC)[reply]
^Hart, Hornell (1948). "The Logistic Growth of Political Areas". Social Forces. 26 (4): 402. doi:10.2307/2571873. ISSN0037-7732. In the Mediterranean area the earliest historic governments which extended their territory by major use of fleets were the Greek and the Phoenecian, reaching areas of approximately 250,000 square miles each
^Alcock, Susan E.; D'Altroy, Terence N.; Morrison, Kathleen D.; Sinopoli, Carla M. (2001-08-09). Empires: Perspectives from Archaeology and History. Cambridge University Press. p. 85. ISBN978-0-521-77020-0. The total spatial extent of the empire, not including the north coast, I estimate to have been some 320,000 square kilometers.
It is a bit confusing that the Xiongnu empire is listed at 9m km2 in 176 BC as the largest in history to date, but then in the table of largest at that time, the Han dynasty is still listed as the largest, with the Xiongnu empire appearing not until 150 BC at only ~5m km2 Samsledje (talk) 15:02, 27 October 2024 (UTC)[reply]
The latter table gives snapshot estimates at 50-year intervals at that point in time, following the cited source. The source makes an exception for the Macedonian Empire, so it gets an in-between entry at 323 BCE. The source also makes an exception for Assyria in 660 BCE, but that happens to fall between entries where Assyria is at the top regardless, so it doesn't show in our table apart from the maximum area estimate being higher than it otherwise would have been. TompaDompa (talk) 17:19, 27 October 2024 (UTC)[reply]
The table under Empires at their greatest extent uses "Million km^2" as the unit for land area. The cited source by Rein Taagepera ("Expansion and Contraction Patterns of Large Polities: Context for Russia") uses Mm^2 (Megameters squared). These are not equivalent units, and it does not appear that unit was converted correctly. 2600:8804:6F00:3D50:D19E:BB2F:53DF:629A (talk) 17:56, 28 October 2024 (UTC)[reply]
It's correct the way it is: 1 million km2 is the same thing as 1 Mm2. A square with side length 1,000 km = 1 Mm has an area of 1 million square kilometers, and equivalently an area of 1 square megameter. TompaDompa (talk) 19:15, 28 October 2024 (UTC)[reply]