Solar cycle (calendar)

The solar cycle is a 28-year cycle of the Julian calendar, and 400-year cycle of the Gregorian calendar with respect to the week. It occurs because leap years occur every 4 years and there are 7 possible days to start a leap year, making a 28-year sequence.

This cycle also occurs in the Gregorian calendar, but it is interrupted by years such as 1800, 1900, 2100, 2200, 2300 and 2500, which are divisible by four but which are common years. This interruption has the effect of skipping 16 years of the solar cycle between February 28 and March 1. Because the Gregorian cycle of 400 years has exactly 146,097 days, i.e. exactly 20,871 weeks, one can say that the Gregorian so-called solar cycle lasts 400 years.

Calendar years are usually marked by Dominical letters indicating the first Sunday in a new year, thus the term solar cycle can also refer to a repeating sequence of Dominical letters.

Unless a year is not a leap year due to Gregorian exceptions, a sequence of calendars is reused every 28 years.

The name solar cycle comes from Sunday, the traditional first day of the week.

Examples

Dominical letter

The dominical letter in the Julian calendar depends only on the remainder of the year mod 28.

Year mod 28Dominical letter
0DC
1B
2A
3G
4FE
5D
6C
7B
8AG
9F
10E
11D
12CB
13A
14G
15F
16ED
17C
18B
19A
20GF
21E
22D
23C
24BA
25G
26F
27E

Doomsday

Year mod 28Doomsday
0Sunday
1Monday
2Tuesday
3Wednesday
4Friday
5Saturday
6Sunday
7Monday
8Wednesday
9Thursday
10Friday
11Saturday
12Monday
13Tuesday
14Wednesday
15Thursday
16Saturday
17Sunday
18Monday
19Tuesday
20Thursday
21Friday
22Saturday
23Sunday
24Tuesday
25Wednesday
26Thursday
27Friday

Friday the 13ths

Year mod 281st2nd3rd
0February 13August 13
1May 13
2January 13October 13
3April 13July 13
4June 13
5February 13March 13November 13
6August 13
7May 13
8January 13April 13July 13
9September 13December 13
10June 13
11February 13March 13November 13
12May 13
13January 13October 13
14April 13July 13
15September 13December 13
16March 13November 13
17August 13
18May 13
19January 13October 13
20September 13December 13
21June 13
22February 13March 13November 13
23August 13
24October 13
25April 13July 13
26September 13December 13
27June 13

Gregorian calendar

The years 1700, 1800, and 1900 were not leap years (unlike the Julian calendar) and do not fit in the tables of Dominical letters below.

Doomsday

Century Year
000102030405
060708091011
1213141516
171819202122
2324252627
282930313233
343536373839
4041424344
454647484950
5152535455
565758596061
626364656667
6869707172
737475767778
7980818283
848586878889
909192939495
96979899
16002000TueWedThuFriSatSunMon
17002100SunMonTueWedThuFriSat
18002200FriSatSunMonTueWedThu
19002300WedThuFriSatSunMonTue

First days of months

Year Month
JanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember
2000202820562084SaturdayTuesdayWednesdaySaturdayMondayThursdaySaturdayTuesdayFridaySundayWednesdayFriday
2001202920572085MondayThursdayThursdaySundayTuesdayFridaySundayWednesdaySaturdayMondayThursdaySaturday
2002203020582086TuesdayFridayFridayMondayWednesdaySaturdayMondayThursdaySundayTuesdayFridaySunday
2003203120592087WednesdaySaturdaySaturdayTuesdayThursdaySundayTuesdayFridayMondayWednesdaySaturdayMonday
2004203220602088ThursdaySundayMondayThursdaySaturdayTuesdayThursdaySundayWednesdayFridayMondayWednesday
2005203320612089SaturdayTuesdayTuesdayFridaySundayWednesdayFridayMondayThursdaySaturdayTuesdayThursday
2006203420622090SundayWednesdayWednesdaySaturdayMondayThursdaySaturdayTuesdayFridaySundayWednesdayFriday
2007203520632091MondayThursdayThursdaySundayTuesdayFridaySundayWednesdaySaturdayMondayThursdaySaturday
2008203620642092TuesdayFridaySaturdayTuesdayThursdaySundayTuesdayFridayMondayWednesdaySaturdayMonday
2009203720652093ThursdaySundaySundayWednesdayFridayMondayWednesdaySaturdayTuesdayThursdaySundayTuesday
2010203820662094FridayMondayMondayThursdaySaturdayTuesdayThursdaySundayWednesdayFridayMondayWednesday
2011203920672095SaturdayTuesdayTuesdayFridaySundayWednesdayFridayMondayThursdaySaturdayTuesdayThursday
2012204020682096SundayWednesdayThursdaySundayTuesdayFridaySundayWednesdaySaturdayMondayThursdaySaturday
2013204120692097TuesdayFridayFridayMondayWednesdaySaturdayMondayThursdaySundayTuesdayFridaySunday
2014204220702098WednesdaySaturdaySaturdayTuesdayThursdaySundayTuesdayFridayMondayWednesdaySaturdayMonday
2015204320712099ThursdaySundaySundayWednesdayFridayMondayWednesdaySaturdayTuesdayThursdaySundayTuesday
201620442072FridayMondayTuesdayFridaySundayWednesdayFridayMondayThursdaySaturdayTuesdayThursday
201720452073SundayWednesdayWednesdaySaturdayMondayThursdaySaturdayTuesdayFridaySundayWednesdayFriday
201820462074MondayThursdayThursdaySundayTuesdayFridaySundayWednesdaySaturdayMondayThursdaySaturday
201920472075TuesdayFridayFridayMondayWednesdaySaturdayMondayThursdaySundayTuesdayFridaySunday
202020482076WednesdaySaturdaySundayWednesdayFridayMondayWednesdaySaturdayTuesdayThursdaySundayTuesday
202120492077FridayMondayMondayThursdaySaturdayTuesdayThursdaySundayWednesdayFridayMondayWednesday
202220502078SaturdayTuesdayTuesdayFridaySundayWednesdayFridayMondayThursdaySaturdayTuesdayThursday
202320512079SundayWednesdayWednesdaySaturdayMondayThursdaySaturdayTuesdayFridaySundayWednesdayFriday
202420522080MondayThursdayFridayMondayWednesdaySaturdayMondayThursdaySundayTuesdayFridaySunday
202520532081WednesdaySaturdaySaturdayTuesdayThursdaySundayTuesdayFridayMondayWednesdaySaturdayMonday
202620542082ThursdaySundaySundayWednesdayFridayMondayWednesdaySaturdayTuesdayThursdaySundayTuesday
202720552083FridayMondayMondayThursdaySaturdayTuesdayThursdaySundayWednesdayFridayMondayWednesday

1583–1699

1583–16001601–16281629–16561657–16841685–1699Dominical letter
1601162916571685G
1602163016581686F
1603163116591687E
1604163216601688DC
1605163316611689B
1606163416621690A
1607163516631691G
1608163616641692FE
1609163716651693D
1610163816661694C
15831611163916671695B
15841612164016681696AG
15851613164116691697F
15861614164216701698E
15871615164316711699D
1588161616441672CB
1589161716451673A
1590161816461674G
1591161916471675F
1592162016481676ED
1593162116491677C
1594162216501678B
1595162316511679A
1596162416521680GF
1597162516531681E
1598162616541682D
1599162716551683C
1600162816561684BA

1701–1799

1701–17281729–17561757–17841785–1799Dominical letter
1701172917571785B
1702173017581786A
1703173117591787G
1704173217601788FE
1705173317611789D
1706173417621790C
1707173517631791B
1708173617641792AG
1709173717651793F
1710173817661794E
1711173917671795D
1712174017681796CB
1713174117691797A
1714174217701798G
1715174317711799F
171617441772ED
171717451773C
171817461774B
171917471775A
172017481776GF
172117491777E
172217501778D
172317511779C
172417521780BA
172517531781G
172617541782F
172717551783E
172817561784DC

1801–1899

1801–18281829–18561857–18841885–1899Dominical letter
1801182918571885D
1802183018581886C
1803183118591887B
1804183218601888AG
1805183318611889F
1806183418621890E
1807183518631891D
1808183618641892CB
1809183718651893A
1810183818661894G
1811183918671895F
1812184018681896ED
1813184118691897C
1814184218701898B
1815184318711899A
181618441872GF
181718451873E
181818461874D
181918471875C
182018481876BA
182118491877G
182218501878F
182318511879E
182418521880DC
182518531881B
182618541882A
182718551883G
182818561884FE

1901–2099

1901–19281929–19561957–19841985–20122013–20402041–20682069–20962097–2099Dominical letter
19011929195719852013204120692097F
19021930195819862014204220702098E
19031931195919872015204320712099D
1904193219601988201620442072CB
1905193319611989201720452073A
1906193419621990201820462074G
1907193519631991201920472075F
1908193619641992202020482076ED
1909193719651993202120492077C
1910193819661994202220502078B
1911193919671995202320512079A
1912194019681996202420522080GF
1913194119691997202520532081E
1914194219701998202620542082D
1915194319711999202720552083C
1916194419722000202820562084BA
1917194519732001202920572085G
1918194619742002203020582086F
1919194719752003203120592087E
1920194819762004203220602088DC
1921194919772005203320612089B
1922195019782006203420622090A
1923195119792007203520632091G
1924195219802008203620642092FE
1925195319812009203720652093D
1926195419822010203820662094C
1927195519832011203920672095B
1928195619842012204020682096AG

See also

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