• The Gregorian calendar divides years into BC (Before Christ) years and AD (Anno Domini) years. Note that there is no year 0 BC or year 0 AD; there is only 1 BC and 1 AD.
• Support for calculating BC years: Input negative numbers for years BC and positive numbers for years AD.
• Distinction between leap years and common years: A leap year has 366 days, with February having 29 days, while a common year has 365 days, with February having 28 days. Regardless of being a leap year or not, January, March, May, July, August, October, and December all have 31 days, while April, June, September, and November have 30 days.
• Rules for calculating leap years: For years AD, a leap year is determined by being divisible by 4 and not divisible by 100, or being divisible by 400. The same rule applies for years BC, calculated in reverse. It can be summarized as follows: a leap year occurs every four years, except for years that are multiples of 100 but not multiples of 400.

Why do we have leap years in the Gregorian calendar? The Earth's orbit around the sun takes approximately 365 days, 5 hours, 48 minutes, and 46 seconds (or 365.24219 days), known as a tropical year. The regular year in the Gregorian calendar only has 365 days, leaving a surplus of about 0.2422 days per year. This excess time accumulates to approximately one extra day every four years. Hence, an extra day is added at the end of February in the fourth year, creating a leap year with 366 days. In the current Gregorian calendar, there are 97 leap years in a 400-year period. By following the rule of having a leap year every four years, there is an average surplus of 0.0078 days per year. As a result, an extra day is accumulated every 128 years, leading to an excess of 3 days every 400 years. Therefore, it is necessary to reduce the number of leap years by 3 in a 400-year period. According to the Gregorian calendar, a year is considered a leap year if it is a multiple of 400; if it is a century year but not a multiple of 400, even if it is a multiple of 4, it is not a leap year.