If Every Fourth Year Is a Leap Year, Why Isn’t 2100?

A familiar shortcut says that a year divisible by four is a leap year. Yet 2100 is divisible by four and will not contain 29 February. The shortcut states only the first layer of the Gregorian rule.

The tropical year that tracks the seasonal cycle is about 365.2422 days, not 365.25. If a calendar added one day without exception every four years, its average year would be 365.25 days—about 0.0078 day too long. Over enough time, calendar dates would still drift slowly against the seasons.

The Gregorian calendar therefore says that years divisible by four are normally leap years; century years divisible by 100 lose that leap day; century years divisible by 400 regain it. Thus 2000 was a leap year, 2100, 2200 and 2300 will not be, and 2400 will be.

Across 400 years, this gives 97 leap years and 146,097 days, averaging 365.2425 days per year. That is much closer to the tropical year than 365.25. The central point is not that century years are mysteriously special. The calendar uses a convenient rule involving whole numbers to approximate an astronomical cycle that is not a whole number of days. It remains an approximation, but one accurate enough for long-term civil use.

https://aa.usno.navy.mil/faq/calendars
https://www.britannica.com/science/Gregorian-calendar