Common year starting on Saturday

Last updated

A common year starting on Saturday is any non-leap year (i.e. a year with 365 days) 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 2011 and the next one will be 2022 in the Gregorian calendar [1] or, likewise, 2006, 2017 and 2023 in the obsolete Julian calendar. See below for more.

Contents

Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th: the only one in this common year occurs in May. Leap years starting on Friday share this characteristic.

In this common year, Martin Luther King Jr. Day is on January 17, Valentine's Day is on a Monday, Presidents' Day is on its latest possible date, February 21, Saint Patrick's Day is on a Thursday, U.S. Independence Day and Halloween are on a Monday, Memorial Day is on May 30, Labor Day is on September 5, Election Day in the USA is on its latest possible date, November 8th, Thanksgiving is on November 24 and Christmas is on a Sunday.

Calendars

Calendar for any common 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
2728 
 
March
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
April
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
May
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
June
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
2627282930 
 
July
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
August
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
September
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
October
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
November
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
27282930 
 
December
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 

ISO 8601-conformant calendar with week numbers for
any common year starting on Saturday (dominical letter B)

January
WkMoTuWeThFrSaSu
52/53  0102
0103040506070809
0210111213141516
0317181920212223
0424252627282930
0531 
February
WkMoTuWeThFrSaSu
05010203040506
0607080910111213
0714151617181920
0821222324252627
0928 
  
March
WkMoTuWeThFrSaSu
09010203040506
1007080910111213
1114151617181920
1221222324252627
1328293031 
  
April
WkMoTuWeThFrSaSu
13010203
1404050607080910
1511121314151617
1618192021222324
17252627282930
  
May
WkMoTuWeThFrSaSu
1701
1802030405060708
1909101112131415
2016171819202122
2123242526272829
223031 
June
WkMoTuWeThFrSaSu
220102030405
2306070809101112
2413141516171819
2520212223242526
2627282930 
  
July
WkMoTuWeThFrSaSu
26010203
2704050607080910
2811121314151617
2918192021222324
3025262728293031
  
August
WkMoTuWeThFrSaSu
3101020304050607
3208091011121314
3315161718192021
3422232425262728
35293031 
  
September
WkMoTuWeThFrSaSu
3501020304
3605060708091011
3712131415161718
3819202122232425
392627282930 
  
October
WkMoTuWeThFrSaSu
390102
4003040506070809
4110111213141516
4217181920212223
4324252627282930
4431 
November
WkMoTuWeThFrSaSu
44010203040506
4507080910111213
4614151617181920
4721222324252627
48282930 
  
December
WkMoTuWeThFrSaSu
4801020304
4905060708091011
5012131415161718
5119202122232425
52262728293031 
  

If the preceding year is a common year starting on Friday, then the year begins in ISO week 52; if the preceding year is a leap year starting on Thursday, then the year begins in ISO week 53.

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Friday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Saturday. The 28-year sub-cycle will break at a century year which is not divisible by 400 (e.g. it broke at the year 1900 but not at the year 2000).

Gregorian common years starting on Saturday
1st2nd3rd4th5th6th7th8th9th10th
17th century 1605 1611 1622 1633 1639 1650 1661 1667 1678 1689 1695
18th century 1701 1707 1718 1729 1735 1746 1757 1763 1774 1785 1791
19th century 1803 1814 1825 1831 1842 1853 1859 - 1870 1881 1887 1898
20th century 1910 1921 1927 1938 1949 1955 1966 1977 1983 1994
21st century 2005 2011 2022 2033 2039 2050 2061 2067 2078 2089 2095
22nd century 2101 2107 2118 2129 2135 2146 2157 2163 2174 2185 2191
23rd century 2203 2214 2225 2231 2242 2253 2259 - 2270 2281 2287 2298
24th century 2310 2321 2327 2338 2349 2355 2366 2377 2383 2394

400 year cycle

century 1: 5, 11, 22, 33, 39, 50, 61, 67, 78, 89, 95

century 2: 101, 107, 118, 129, 135, 146, 157, 163, 174, 185, 191

century 3: 203, 214, 225, 231, 242, 253, 259, 270, 281, 287, 298

century 4: 310, 321, 327, 338, 349, 355, 366, 377, 383, 394

Julian Calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters, (one for January and February and the other for March to December in the Church of England, as 29 February has no letter). Each of the seven two-letter sequences occurs once within a cycle, and every common letter thrice.

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). Years 10, 16 and 27 of the cycle are common years beginning on Saturday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Saturday.

Julian common years starting on Saturday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1401 1407 1418 1429 1435 1446 1457 1463 1474 1485 1491
16th century 1502 1513 1519 1530 1541 1547 1558 1569 1575 15861597
17th century16031614162516311642165316591670168116871698
18th century17091715172617371743175417651771178217931799
19th century1810182118271838184918551866187718831894
20th century19051911192219331939195019611967197819891995
21st century2006201720232034204520512062207320792090

Related Research Articles

A leap year is a calendar year that contains an additional day 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 an additional day or month into some years, the drift between a civilization's dating system and the physical properties of the Solar System can be corrected. A year that is not a leap year is a common year.

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 2017 and the next one will be 2023 in the Gregorian calendar, or, likewise, 2007, 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 current year, 2021, is a common year starting on Friday in the Gregorian calendar. The last such year was 2010 and the next such year will be 2027 in the Gregorian calendar, or, likewise, 2005, 2011 and 2022 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, 2013, 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.

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 and 2024 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 most recent year of such kind was 1996 and the next one will be 2024 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, 2009, 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 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, 2010 and 2021 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, or likewise, 2004 and 2032 in the obsolete Julian calendar, see below for more.

The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the day of the week on which someone was born or a specific event occurred.

Doomsday rule Way of calculating the day of the week of a given date

The Doomsday rule 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. Applying the Doomsday algorithm involves three steps: Determination of the anchor day for the century, calculation of the anchor day for the year from the one for the century, and selection of the closest date out of those that always fall on the doomsday, e.g., 4/4 and 6/6, and count of the number of days between that date and the date in question to arrive at the day of the week. The technique applies to both the Gregorian calendar and the Julian calendar, although their doomsdays are usually different days of the week.

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.

A century leap year is a leap year in the Gregorian calendar that is evenly divisible by 400.

A century common year is a common year in the Gregorian Calendar that is divisible by 100 but not 400. Like all common years, these years do not get an extra day in February, meaning they have 365 days instead of 366. These years are the only common years that are divisible by 4.

References

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