Leap year

A leap year is any year that has exactly 366 days, including February 29 (known as Leap Day). For example, the years 2016, 2020, and 2024 are leap years. Years that are not leap years are known as common years.

In the Julian calendar, leap years occur every 4 years without exception. On the other hand, in the Gregorian calendar, leap years usually still occur every 4 years, except that century years (those that end with "00") are not leap years unless divisible by 400. So, the years 2000 and 2400 are leap years, while the years 1800, 1900, 2100, 2200, and 2300 are not leap years. Century years divisible by 400 are also called century leap years.

Types of leap years
There are 7 types of leap years, one for each day of the week.

Starting on Sunday
For such a year, the dominical letter is AG, February 29 is on a Wednesday, and Friday the 13ths occur on January 13, April 13, and July 13. Such years occur 15 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

In the Julian calendar, such years occur when the year reduces to 8 mod 28.

Starting on Monday
For such a year, the dominical letter is GF, February 29 is on a Thursday, and Friday the 13ths occur on September 13 and December 13. Such years occur 13 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

In the Julian calendar, such years occur when the year reduces to 20 mod 28.

Starting on Tuesday
For such a year, the dominical letter is FE, February 29 is on a Friday, and a Friday the 13th occurs on June 13. Such years occur 14 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

In the Julian calendar, such years occur when the year reduces to 4 mod 28.

Starting on Wednesday
For such a year, the dominical letter is ED, February 29 is on a Saturday, and Friday the 13ths occur on March 13 and November 13. Such years occur 14 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

In the Julian calendar, such years occur when the year reduces to 16 mod 28.

Starting on Thursday
For such a year, the dominical letter is DC, February 29 is on a Sunday, and Friday the 13ths occur on February 13 and August 13. Such years occur 13 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

In the Julian calendar, such years occur when the year reduces to 0 mod 28 (or is divisible by 28).

Starting on Friday
For such a year, the dominical letter is CB, February 29 is on a Monday, and a Friday the 13th occurs on May 13. Such years occur 15 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

In the Julian calendar, such years occur when the year reduces to 12 mod 28.

Starting on Saturday
For such a year, the dominical letter is BA, February 29 is on a Tuesday, and a Friday the 13th occurs on October 13. Such years occur 13 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar. Any century leap year (divisible by 400) in the Gregorian calendar will always be such a year.

In the Julian calendar, such years occur when the year reduces to 24 mod 28.