Leap year starting on Sunday

Last updated

A leap year starting on Sunday is any year with 366 days (i.e. it includes 29 February) that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG. The most recent year of such kind was 2012 and the next one will be 2040 in the Gregorian calendar [1] or, likewise 2024 and 2052 in the obsolete Julian calendar.

Contents

This is the only leap year with three occurrences of Friday the 13th: those three in this leap year occur three months (13 weeks) apart: in January, April, and July. Common years starting on Thursday share this characteristic, in the months of February, March, and November. Leap years starting on Wednesday also share the characteristic of three Friday the 13ths occurring three months (13 weeks) apart, wherein the third one occurs in the month of March, while the other two occur in the year preceding it.

In this type of year, all dates (except 29 February) fall on their respective weekdays 58 times in the 400 year Gregorian calendar cycle. Leap years starting on Friday share this characteristic. Additionally, these types of years are the only ones which contain 54 different calendar weeks (2 partial, 52 in full) in areas of the world where Monday is considered the first day of the week.

Calendars

Calendar for any leap year starting on Sunday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
February
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
26272829 
 
March
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
April
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
May
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
June
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
July
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
August
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
September
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
October
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
November
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
December
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
ISO 8601-conformant calendar with week numbers for
any leap year starting on Sunday (dominical letter AG)
January
WkMoTuWeThFrSaSu
5201
0102030405060708
0209101112131415
0316171819202122
0423242526272829
053031 
February
WkMoTuWeThFrSaSu
050102030405
0606070809101112
0713141516171819
0820212223242526
09272829 
  
March
WkMoTuWeThFrSaSu
0901020304
1005060708091011
1112131415161718
1219202122232425
13262728293031 
  
April
WkMoTuWeThFrSaSu
1301
1402030405060708
1509101112131415
1616171819202122
1723242526272829
1830 
May
WkMoTuWeThFrSaSu
18010203040506
1907080910111213
2014151617181920
2121222324252627
2228293031 
  
June
WkMoTuWeThFrSaSu
22010203
2304050607080910
2411121314151617
2518192021222324
26252627282930
  
July
WkMoTuWeThFrSaSu
2601
2702030405060708
2809101112131415
2916171819202122
3023242526272829
313031 
August
WkMoTuWeThFrSaSu
310102030405
3206070809101112
3313141516171819
3420212223242526
352728293031 
  
September
WkMoTuWeThFrSaSu
350102
3603040506070809
3710111213141516
3817181920212223
3924252627282930
  
October
WkMoTuWeThFrSaSu
4001020304050607
4108091011121314
4215161718192021
4322232425262728
44293031 
  
November
WkMoTuWeThFrSaSu
4401020304
4505060708091011
4612131415161718
4719202122232425
482627282930 
  
December
WkMoTuWeThFrSaSu
480102
4903040506070809
5010111213141516
5117181920212223
5224252627282930
0131 

Applicable years

Gregorian Calendar

Leap years that begin on Sunday, along with those starting on Friday, occur most frequently: 15 of the 97 (≈ 15.46%) total leap years in a 400-year cycle of the Gregorian calendar. Thus, their overall occurrence is 3.75% (15 out of 400).

Gregorian leap years starting on Sunday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1584
17th century 1612 1640 1668 1696
18th century 1708 1736 1764 1792
19th century 1804 1832 1860 1888
20th century 1928 1956 1984
21st century 2012 2040 2068 2096
22nd century 2108 2136 2164 2192
23rd century 2204 2232 2260 2288
24th century 2328 2356 2384
25th century 2412 2440 2468 2496
26th century 2508 2536 2564 2592
27th century 2604 2632 2660 2688
400-year cycle
0–9912406896
100–199108136164192
200–299204232260288
300–399328356384

Julian Calendar

Like all leap year types, the one starting with 1 January on a Sunday occurs exactly once in a 28-year cycle in the Julian calendar, i.e., in 3.57% of years. As the Julian calendar repeats after 28 years, it will also repeat after 700 years, i.e., 25 cycles. The formula gives the year's position in the cycle ((year + 8) mod 28) + 1).

Julian leap years starting on Sunday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1408 1436 1464 1492
16th century 1520 1548 1576
17th century 1604 1632 1660 1688
18th century 1716 1744 1772 1800
19th century182818561884
20th century1912194019681996
21st century202420522080
22nd century2108213621642192

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

Related Research Articles

The International Fixed Calendar is a proposed calendar reform designed by Moses B. Cotsworth, first presented in 1902. The International Fixed Calendar divides the year into 13 months of 28 days each. A type of perennial calendar, every date is fixed to the same weekday every year. Though it was never officially adopted at the country level, the entrepreneur George Eastman instituted its use at the Eastman Kodak Company in 1928, where it was used until 1989. While it is sometimes described as the 13-month calendar or the equal-month calendar, various alternative calendar designs share these features.

<span class="mw-page-title-main">Week</span> Time unit equal to seven days

A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are often mapped against yearly calendars, but are typically not the basis for them, as weeks are not based on astronomy.

A common year starting on Sunday is any non-leap year that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2023 and the next one will be 2034 in the Gregorian calendar, or, likewise, 2018 and 2029 in the obsolete Julian calendar, see below for more.

A common year starting on Friday is any non-leap year that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2021 and the next one will be 2027 in the Gregorian calendar, or, likewise, 2022 and 2033 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 100 when divided by 400. The most recent such year was 1700 and the next one will be 2100.

A common year starting on Monday is any non-leap year that begins on Monday, 1 January, and ends on Monday, 31 December. Its dominical letter hence is G. The most recent year of such kind was 2018 and the next one will be 2029 in the Gregorian calendar, or likewise, 2019 and 2030 in the Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on and occurs in century years that yield a remainder of 300 when divided by 400. The most recent such year was 1900 and the next one will be 2300.

Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter depending on which day of the week the year starts. The Dominical letter for the current year 2024 is GF.

A common year starting on Tuesday is any non-leap year that begins on Tuesday, 1 January, and ends on Tuesday, 31 December. Its dominical letter hence is F. The most recent year of such kind was 2019 and the next one will be 2030, or, likewise, 2014 and 2025 in the obsolete Julian calendar, see below for more.

A leap year starting on Monday is any year with 366 days that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF. The current year, 2024, is a leap year starting on Monday in the Gregorian calendar. The last such year was 1996 and the next such year will be 2052 in the Gregorian calendar or, likewise, 2008 and 2036 in the obsolete Julian calendar. 29 February falls on Thursday.

A common year starting on Wednesday is any non-leap year that begins on Wednesday, 1 January, and ends on Wednesday, 31 December. Its dominical letter hence is E. The most recent year of such kind was 2014, and the next one will be 2025 in the Gregorian calendar or, likewise, 2015 and 2026 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 200 when divided by 400. The most recent such year was 1800 and the next one will be 2200.

A leap year starting on Tuesday is any year with 366 days that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE. The most recent year of such kind was 2008 and the next one will be 2036 in the Gregorian calendar or, likewise 2020 and 2048 in the obsolete Julian calendar.

A common year starting on Saturday is any non-leap year that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2022 and the next one will be 2033 in the Gregorian calendar or, likewise, 2023 and 2034 in the obsolete Julian calendar. See below for more.

A common year starting on Thursday is any non-leap year that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar or, likewise, 2021 and 2027 in the obsolete Julian calendar, see below for more.

A leap year starting on Saturday is any year with 366 days that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA. The most recent year of such kind was 2000 and the next one will be 2028 in the Gregorian calendar or, likewise 2012 and 2040 in the obsolescent Julian calendar. In the Gregorian calendar, years divisible by 400 are always leap years starting on Saturday. The most recent such occurrence was 2000 and the next one will be 2400, see below for more.

A leap year starting on Friday is any year with 366 days that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB. The most recent year of such kind was 2016 and the next one will be 2044 in the Gregorian calendar or, likewise, 2000 and 2028 in the obsolete Julian calendar.

A leap year starting on Thursday is any year with 366 days that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC. The most recent year of such kind was 2004 and the next one will be 2032 in the Gregorian calendar or, likewise, 2016 and 2044 in the obsolete Julian calendar.

A leap year starting on Wednesday is any year with 366 days that begins on Wednesday 1 January and ends on Thursday 31 December. Its dominical letters hence are ED. The most recent year of such kind was 2020 and the next one will be 2048 in the Gregorian calendar, or likewise, 2004 and 2032 in the obsolete Julian calendar, see below for more.

<span class="mw-page-title-main">Doomsday rule</span> Way of calculating the day of the week of a given date

The Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for mental calculation was devised by John Conway in 1973, drawing inspiration from Lewis Carroll's perpetual calendar algorithm. It takes advantage of each year having a certain day of the week upon which certain easy-to-remember dates, called the doomsdays, fall; for example, the last day of February, 4/4, 6/6, 8/8, 10/10, and 12/12 all occur on the same day of the week in any year.

The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.

The Hanke–Henry Permanent Calendar (HHPC) is a proposal for calendar reform. It is one of many examples of leap week calendars, calendars that maintain synchronization with the solar year by intercalating entire weeks rather than single days. It is a modification of a previous proposal, Common-Civil-Calendar-and-Time (CCC&T). With the Hanke–Henry Permanent Calendar, every calendar date always falls on the same day of the week. A major feature of the calendar system is the abolition of time zones.

References

  1. 1 2 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.