The New World became common knowledge in Europe only after Christopher Columbus "discovered" it. Surely they had to have an accurate guess of the circumference of the Earth then, too. So was Columbus over-packed when he made his voyage, as though he expected there to be more ocean beyond when he actually made landfall?
Columbus' trip's intent was to reach China/India to find another route to 'the riches of the east' with the effectively closing of the overland route after the disintegration of the Mongol and Timurid Khanates and fall of Constantinople. Columbus and others had no idea there was another continent between them. As far as we can tell, they believed it was just open ocean between the west coast of Europe and China's east coast. Part of the reason Columbus had difficulty getting support for his trip was because he guessed the circumference was much smaller than other Europeans believed, and they thought, based on his measurements, he'd get half way across and run out of supplies. He got lucky with Ferdinand and Isabella of Spain, who had money to burn from the conquest of last Moorish stronghold in Spain, Granada. From what I can recall from memory, Columbus had JUST enough supplies to reach the Caribbean, and would have been in serious danger if he had not.
How accurate were the general European measurements, I don't know, and I don't know if they were the same ones used by the Greeks. There would have been several means of getting at a number, which seem to have tended towards larger estimates than what Columbus had come up with.
John Man's "The Mongol Empire: Genghis Khan, his Heirs and the Founding of Modern China," discusses the European belief in sailing to China. Columbus appears to have expected to find a descendant of Kublai still on the Dragon Throne.
Here's a link to Columbus' journal, if you're interested. http://eada.lib.umd.edu/text-entries/journal/