Leap year starting on Friday

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A leap year starting on Friday is any year with 366 days (i.e. it includes 29 February) 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 [1] or, likewise, 2000 and 2028 in the obsolete Julian calendar.

Contents

Any leap year that starts on Friday has only one Friday the 13th: the only one in this leap year occurs in May.

In this type of year, all dates (except 29 February) fall on their respective weekdays the maximal 58 times in the 400 year Gregorian calendar cycle. Leap years starting on Sunday share this characteristic.

Calendars

Calendar for any leap year starting on Friday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
February
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
2829 
 
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 leap year starting on Friday (dominical letter CB)
January
WkMoTuWeThFrSaSu
53010203
0104050607080910
0211121314151617
0318192021222324
0425262728293031
  
February
WkMoTuWeThFrSaSu
0501020304050607
0608091011121314
0715161718192021
0822232425262728
0929 
  
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 
  

Applicable years

Gregorian Calendar

Leap years that begin on Friday, along with those starting on Sunday, 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).

For this kind of year, the ISO week 10 (which begins March 7) and all subsequent ISO weeks occur later than in all other leap years.

Gregorian leap years starting on Friday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1588
17th century 1616 1644 1672
18th century 1712 1740 1768 1796
19th century 1808 1836 1864 1892
20th century 1904 1932 1960 1988
21st century 2016 2044 2072
22nd century 2112 2140 2168 2196
23rd century 2208 2236 2264 2292
24th century 2304 2332 2360 2388
25th century 2416 2444 2472
26th century 25122540 2568 2596
400-year cycle
0–99164472
100–199112140168196
200–299208236264292
300–399304332360388

Julian Calendar

Like all leap year types, the one starting with 1 January on a Friday 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 Friday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1412 1440 1468 1496
16th century 1524 1552 1580
17th century 1608 1636 1664 1692
18th century 1720 1748 1776
19th century1804183218601888
20th century1916194419722000
21st century202820562084
22nd century2112214021682196

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

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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 end 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 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 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.

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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.

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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.

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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.

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References

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