When I was in high school I read that Jesus was born in April of 3 AD.
The line in one of the tracks of “Jesus Christ, Superstar” goes, “Israel 4 BC has no mass communication”. Wow, those lyrics suck. But anyway, the calendar start date was figured out a bit wrong, it’s just that it is never settled (and perhaps never will be) just what the real theoretical start date is (I say theoretical because it was put together ad hoc), other than the one we’ve been using for 1600 years or so.