"When a 10-month calendar didn't do the trick, the Romans borrowed from the Greeks and Egyptians, who figured out that 12 lunar cycles fit into a solar cycle. So Roman King Numa Pompilius extended their calendar to 12 months by adding February and January, named after Janus, the Roman god of beginnings. Jan. 1 was then made the start of the calendar, Hayton said."
"In 45 B.C.E., while Julius Caesar was high priest, he stretched the 12-month calendar to 365 days and a quarter of a day. But that quarter amounted to a full day after four years. So he implemented leap years to catch the calendar back up with the solar year, Hayton said. But there was still a problem. The astronomers of Caesar's day who calculated the length of a solar year were off by about 11 minutes, a misalignment that would grow significantly over time."
The Gregorian calendar and Jan. 1 start date trace to ancient Rome. Early Roman calendars sought to align lunar cycles, solar years and seasons because religious festivals depended on equinoxes and moon phases. Romans adopted a 12-month system; King Numa Pompilius added February and January, named for Janus, making Jan. 1 the calendar start. Julius Caesar reformed the calendar in 45 B.C.E., setting a 365.25-day year and introducing leap years. A small error in the solar year calculation accumulated over centuries. In 1582, Pope Gregory XIII issued a correction to remedy the misalignment.
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