When I wrote my MA, I spent months wracking my brains and scouring libraries in hopes that I could estimate the population of the Achaemenid empire within a factor of two or three. Little did I know that a much more precise figure was available!
By share of population, the largest empire was the Achaemenid Empire, better known as the Persian Empire, which accounted for approximately 49.4 million of the world’s 112.4 million people in around 480 BC – an astonishing 44%. Originating in modern-day Iran, the empire was first established by Cyrus the Great and included parts of Central Asia, the Mediterranean, North Africa, and even European territories such as ancient Thrace and Macedonia.
Guinness Book of World Records, “Largest Empire, by Percentage of World Population,” accessed September 2014 http://www.guinnessworldrecords.com/records-9000/largest-empire-by-percentage-of-world-population
While I hope that everyone who remembers their high-school science classes is smiling (do they really think they know whether the world population was closer to 112.4 million than 112.3 million or 112.5 million?) this is a real problem. However you define “the population of the Achaemenid empire” that population was a number, and shaped the lives of everyone who lived within the empire. Many people venture to estimate the population in writing without giving a basis for their calculation, while many cautious estimates deal with earlier or later periods or only cover part of the empire. For myself, I would be satisfied if I knew the population of the empire within an order of magnitude (eg. “tens of millions” or “30 to 300 million”), and I won’t repeat a figure unless I can show how it was estimated or at least from whom it was cribbed. This one was cribbed from Wikipedia, and I think that tracing it further would be futile.
Edit 2015-10-04: Specifically, back in September 2011 the Wikipedia page “List of largest empires” gave a population of 49.4 million in 480 BCE with no source for that particular number given. The version of September 2011 estimated that this was 20% of the population of the world, citing a book by Barry Strauss which indeed estimates that Xerxes ruled 20 million of the 100 people living in the world in 480 BCE, but does not cite a single source for either number; by September 2013 this estimate of the world population in 480 BCE had been ‘improved’ to 112.4 million and attributed to an Encyclopaedia Iranica article on Darius the Great which says nothing whatsoever about the population of the world. By the same date the estimate of the population of the empire in 480 BCE had been rounded to 50 million, a guess which commonly appears in books.
Further Reading: My MA thesis discusses research on the population of the Achaemenid empire. A writer at Nature http://www.nature.com/news/2011/111019/full/478300a.html assumed a 1% margin of error in world population estimates, the Indian Government decided that their 1951 census missed at least 1% of the population (source) and Gerhard Heilig of the UN estimates that their world population figures have a margin of error of 1-2% (source). No census data for any significant part of the Achaemenid empire survives, and in many regions archaeologists have not even tried to count the remains of villages and measure the area of towns to allow some sort of systematic estimate.