Gregorian calendar

How it works

The year is twelve months. Dates run inside each month from 1 to that month’s last day. A seven-day week overlays the month grid. The weekday of the 1st changes from year to year. The number of dates in a given month does not, except for February.

The leap rule exists so named seasons do not drift through the months. A year divisible by 4 is a leap year, unless it is a century year. A century year is a leap year only when it is also divisible by 400. So 2000 was a leap year, 1900 was not, and 2100 will not be. 2026 is not a leap year. 2028 is.

That rule decides whether February ends on the 28th or the 29th, and therefore whether the year contains 365 or 366 dates. It does not, by itself, move Easter. It does not name holidays. It is a filter on February.

Pope Gregory XIII introduced this calendar in 1582 to replace the Julian calendar, which had been inserting too many leap days. Countries switched at different times. Britain and its colonies skipped from 2 September 1752 to 14 September 1752 when they adopted it. Until a place switched, its civil dates were not Gregorian dates.

Month lengths and leftover weekdays

Apart from February, month lengths are fixed: 31 days: January, March, May, July, August, October, December. 30 days: April, June, September, November. 28 days in a common February; 29 in a leap February.

Over 400 years the leap rule inserts 97 leap days, not 100, because three century years in each 400 are skipped. The average Gregorian year is therefore 365.2425 days: 365 plus 97 divided by 400. That average is a property of the rule. Any given year is still 365 or 366 dates long. You will not see 0.2425 of a day on a wall calendar.

A week is seven days and is not an integer factor of 365 or 366. Fifty-two weeks are 364 days. The leftover day, or two in a leap year, is what walks 1 January to a new weekday. That is why a year is not a round number of weeks, and why you cannot reuse last year’s weekday table without adjusting for the leftover.

How to test a year

Divide by 4. If there is a remainder, February has 28 days. If not, look at the century. Years such as 2016, 2024, and 2028 are leap years because they divide by 4 and are not centuries. 1900 divides by 4 and still is not a leap year. 2000 divides by 400 and is.

The calendar is a dating system. It does not tell you when the Sun rises. Solstices and equinoxes still wander a little inside their months because the average year and Earth’s orbit are not the same length to the last fraction. The job of the leap rule is to keep that wander small, not to print sunrise tables.

The Gregorian year is slightly embarrassed about February on purpose. That embarrassment is the whole trick. If you only needed today’s date, the machine has already done the work. If you needed to know whether next February has a 29th, run the year through the filter. Do not copy a leap day into June or August. Those months do not take leftovers.