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It's well-known that intellectuals in the West have accepted a spherical Earth since antiquity, but I'm not sure how long it took for this to become common knowledge, worldwide. So a more concrete answer is possible, I'll say it's "common knowledge" if >50% of adult humans know it.
Earlier, I asked this question regarding what pre-Columbian Americans thought about the shape of the Earth. There is no evidence that any society arrived at the idea of a spherical Earth, though of course, it's hard to prove a negative. I also read this thread, which explains that most Chinese scholars favored the flat Earth model before the 17th century.
My hypothesis: the true shape of the Earth was not well-known before the 19th century. I have two points:
Public education. While it had been the consensus in academic circles for centuries beforehand, the lack of public education meant that this knowledge did not reach most of the public. In the 1800s, a large number of countries began mandating formal education, starting in Europe and soon spreading to the Americas and the Asia-Pacific.
Population. The European public was early in learning about the shape of the Earth, but before the industrial and agricultural revolutions of the 1800s, Europe had only a small slice of the global population. In 1500, Europe's population was 18% of the world total. By 1913, it was a more significant 28%. Many high-population regions, such as China and SE Asia, were among the last places to accept the spherical Earth model. West Asia, where the idea was popular since antiquity, has a relatively small population.
I'm not completely convinced yet, and I've also heard that nearly all people have known the shape of the Earth since prehistory. The argument is that it's too obvious not to see; for example, you can watch mountains and other tall features disappear below the horizon as you move away from them. A reason to be skeptical about this: it's hard to then explain why so many early religions (e.g. ancient Sumerian religion) describe a flat Earth.
The Wikipedia article Myth of the flat Earth gives a general summary for the Western world as:
According to Stephen Jay Gould, "there never was a period of 'flat Earth darkness' among scholars (regardless of how the public at large may have conceptualized our planet both then and now).
Historian Jeffrey Burton Russell says the flat-Earth error flourished most between 1870 and 1920, and had to do with the ideological setting created by struggles over biological evolution. Russell claims "with extraordinary few exceptions no educated person in the history of Western Civilization from the third century B.C. onward believed that the Earth was flat", and ascribes popularization of the flat-Earth myth to histories by John William Draper, Andrew Dickson White, and Washington Irving.
The article goes further into great detail who believed what and when in Europe.
A more global summary of beliefs about the Flat Earth is in a separate article which starts with the following general summary:
The flat Earth model is an archaic conception of Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat Earth cosmography, including Greece until the classical period, the Bronze Age and Iron Age civilizations of the Near East until the Hellenistic period, India until the Gupta period (early centuries AD), and China until the 17th century.
Further details, region for region, are then given.
Both sources, taken together, should offer a good overview of the different viewpoints and how they evolved.
Based on these sources, no general answer can be given.
Different regions evolved differently, thus conclusions were arrived at at different times.
In Europe, this knowledge was gained early but refuted later by others. Thus certain groups in one area both believed differently, so a common date of acceptance cannot determined.
This is only one of many topics where a specific group, pushing their own absolute truth, are intolerant of any contradictory opinions.
When both groups are pushing their own absolute truths in the same intolerant way, war is often not far away.
It is very hard to know know when more than 50 % of Humans over the age of 16 knew that the Earth is roughly spherical.
The two regions with the largest populations are China and the Indian subcontinent. It is quite possible that at various times they had a total of two thirds of the world's population.
It is said that intellectual elites in India learned that the world is spherical in the Gupta Era and so by about the time of the fall of the Gupta Empire in AD 543, and that intellectual elites in China learned that the world is spherical in the 17th century (1601-1700).
But how rapidly did such fascinating knowledge with little use in everyday life spread from intellectual elites to more and more common people until the majority of adults knew that? How many years, decades, centuries, or millennia would it take?
European sailors began circumnavigating the Earth in the 16th century and news of those voyages was big news in Europe. And of course many of those voyages reached ports in highly populated regions of Asia, where the voyagers may have told the locals that the world is spherical and they were sailing around it. So how much did that news spread in those regions?
And eventually mass education programs were introduced in India and China beginning in the 19th century and much more so in the 20th century and the majority of the people there received education by the time they were adults. Including some basic science, I presume.
And the space age began in 1957 with the first satellites, and presumably everyone who explained to someone what a satellite was had to explain that the Earth is spherical if the other person didn't already know. And a few years later famous pictures of the spherical Earth began to be taken from space, often with recognizable parts of continents as seen on maps and globes.
So by the end of the 20th century 19 or 20 years ago the vast majority of adults and schoolchildren in the world knew that IS Earth more or less shaped like a sphere.
But it seems uncertain to me when the percentage of Humans above the age of 16 (as asked in the question) that knew that the Earth was roughly spherical first reached and exceeded 50 percent. Was that in the 20th century or in the 19th century or possibly even earlier?