Leap year starting on Saturday

Last updated

A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) 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. [1]

Contents

Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th: the only one in this leap year occurs in October. Common years starting on Sunday share this characteristic, but also have another in January. From August of the common year preceding that year until October in this type of year is also the longest period (14 months) that occurs without a Friday the 13th. Common years starting on Tuesday share this characteristic, from July of the year that precedes it to September in that type of year.

This is the only type of year in which all dates (except 29 February) fall on their respective weekdays the minimal 56 times in the 400 year Gregorian Calendar cycle. 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 Sunday is considered the first day of the week, and also the only type of year to contain 53 full weekends.

Calendars

Calendar for any leap year starting on Saturday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
February
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
272829 
 
March
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
April
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
May
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
June
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
July
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
August
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
September
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
October
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
November
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
2627282930 
 
December
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
ISO 8601-conformant calendar with week numbers for
any leap year starting on Saturday (dominical letter BA)
January
WkMoTuWeThFrSaSu
520102
0103040506070809
0210111213141516
0317181920212223
0424252627282930
0531 
February
WkMoTuWeThFrSaSu
05010203040506
0607080910111213
0714151617181920
0821222324252627
092829 
  
March
WkMoTuWeThFrSaSu
090102030405
1006070809101112
1113141516171819
1220212223242526
132728293031 
  
April
WkMoTuWeThFrSaSu
130102
1403040506070809
1510111213141516
1617181920212223
1724252627282930
  
May
WkMoTuWeThFrSaSu
1801020304050607
1908091011121314
2015161718192021
2122232425262728
22293031 
  
June
WkMoTuWeThFrSaSu
2201020304
2305060708091011
2412131415161718
2519202122232425
262627282930 
  
July
WkMoTuWeThFrSaSu
260102
2703040506070809
2810111213141516
2917181920212223
3024252627282930
3131 
August
WkMoTuWeThFrSaSu
31010203040506
3207080910111213
3314151617181920
3421222324252627
3528293031 
  
September
WkMoTuWeThFrSaSu
35010203
3604050607080910
3711121314151617
3818192021222324
39252627282930
  
October
WkMoTuWeThFrSaSu
3901
4002030405060708
4109101112131415
4216171819202122
4323242526272829
443031 
November
WkMoTuWeThFrSaSu
440102030405
4506070809101112
4613141516171819
4720212223242526
4827282930 
  
December
WkMoTuWeThFrSaSu
48010203
4904050607080910
5011121314151617
5118192021222324
5225262728293031
  

Applicable years

Gregorian Calendar

Leap years that begin on Saturday, along with those starting on Monday and Thursday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).

Gregorian leap years starting on Saturday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1600
17th century 1628 1656 1684
18th century 1724 1752 1780
19th century 1820 1848 1876
20th century 1916 1944 1972 2000
21st century 2028 2056 2084
22nd century 2124 2152 2180
23rd century 2220 2248 2276
24th century 2316 2344 2372 2400
25th century 2428 2456 2484
400-year cycle
0–990285684
100–199124152180
200–299220248276
300–399316344372

Julian Calendar

Like all leap year types, the one starting with 1 January on a Saturday 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 that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1).

Julian leap years starting on Saturday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1424 1452 1480
16th century 1508 1536 1564 1592
17th century 1620 1648 1676
18th century 1704 1732 1760 1788
19th century 1816 1844 1872 1900
20th century192819561984
21st century2012204020682096
22nd century212421522180

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

Related Research Articles

A leap year is a calendar year that contains an additional day compared to a common year. The 366th day is added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have a constant number of days in each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting ("intercalating") an additional day, a leap day, or month, a leap month, into some years, the drift between a civilization's dating system and the physical properties of the Solar System can be corrected.

<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 is a calendar year with 365 days, as distinguished from a leap year, which has 366 days. More generally, a common year is one without intercalation. The Gregorian calendar employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

A leap year starting on Sunday is any year with 366 days 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 or, likewise, 1996, 2024 and 2052 in the obsolete Julian calendar.

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.

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 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.

References

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