Common year starting on Saturday

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 2022 and the next one will be 2033 in the Gregorian calendar[1] or, likewise, 2017 and 2023 in the obsolete Julian calendar. See below for more.

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.

From July of the year that precedes this year until September in this type of year is the longest period (14 months) that occurs without a Tuesday the 13th. Leap years starting on Wednesday share this characteristic, from August of the common year that precedes it to October in that type of year.

Calendars

Calendar for any common year starting on Saturday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
February
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728  
 
March
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
April
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
May
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
June
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
July
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
August
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
September
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
October
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
November
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
December
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
ISO 8601-conformant calendar with week numbers for
any common year starting on Saturday (dominical letter B) preceded by Common year starting on Friday (dominical letter C)
January
Wk Mo Tu We Th Fr Sa Su
52 0102
01 03040506070809
02 10111213141516
03 17181920212223
04 24252627282930
05 31  
February
Wk Mo Tu We Th Fr Sa Su
05 010203040506
06 07080910111213
07 14151617181920
08 21222324252627
09 28  
   
March
Wk Mo Tu We Th Fr Sa Su
09 010203040506
10 07080910111213
11 14151617181920
12 21222324252627
13 28293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 010203
14 04050607080910
15 11121314151617
16 18192021222324
17 252627282930
   
May
Wk Mo Tu We Th Fr Sa Su
17 01
18 02030405060708
19 09101112131415
20 16171819202122
21 23242526272829
22 3031  
June
Wk Mo Tu We Th Fr Sa Su
22 0102030405
23 06070809101112
24 13141516171819
25 20212223242526
26 27282930  
   
July
Wk Mo Tu We Th Fr Sa Su
26 010203
27 04050607080910
28 11121314151617
29 18192021222324
30 25262728293031
   
August
Wk Mo Tu We Th Fr Sa Su
31 01020304050607
32 08091011121314
33 15161718192021
34 22232425262728
35 293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01020304
36 05060708091011
37 12131415161718
38 19202122232425
39 2627282930  
   
October
Wk Mo Tu We Th Fr Sa Su
39 0102
40 03040506070809
41 10111213141516
42 17181920212223
43 24252627282930
44 31  
November
Wk Mo Tu We Th Fr Sa Su
44 010203040506
45 07080910111213
46 14151617181920
47 21222324252627
48 282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 01020304
49 05060708091011
50 12131415161718
51 19202122232425
52 262728293031  
   
ISO 8601-conformant calendar with week numbers for
any common year starting on Saturday (dominical letter B) preceded by Leap year starting on Thursday (dominical letter DC)
January
Wk Mo Tu We Th Fr Sa Su
53 0102
01 03040506070809
02 10111213141516
03 17181920212223
04 24252627282930
05 31  
February
Wk Mo Tu We Th Fr Sa Su
05 010203040506
06 07080910111213
07 14151617181920
08 21222324252627
09 28  
   
March
Wk Mo Tu We Th Fr Sa Su
09 010203040506
10 07080910111213
11 14151617181920
12 21222324252627
13 28293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 010203
14 04050607080910
15 11121314151617
16 18192021222324
17 252627282930
   
May
Wk Mo Tu We Th Fr Sa Su
17 01
18 02030405060708
19 09101112131415
20 16171819202122
21 23242526272829
22 3031  
June
Wk Mo Tu We Th Fr Sa Su
22 0102030405
23 06070809101112
24 13141516171819
25 20212223242526
26 27282930  
   
July
Wk Mo Tu We Th Fr Sa Su
26 010203
27 04050607080910
28 11121314151617
29 18192021222324
30 25262728293031
   
August
Wk Mo Tu We Th Fr Sa Su
31 01020304050607
32 08091011121314
33 15161718192021
34 22232425262728
35 293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01020304
36 05060708091011
37 12131415161718
38 19202122232425
39 2627282930  
   
October
Wk Mo Tu We Th Fr Sa Su
39 0102
40 03040506070809
41 10111213141516
42 17181920212223
43 24252627282930
44 31  
November
Wk Mo Tu We Th Fr Sa Su
44 010203040506
45 07080910111213
46 14151617181920
47 21222324252627
48 282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 01020304
49 05060708091011
50 12131415161718
51 19202122232425
52 262728293031  
   

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
16th century prior to first adoption (proleptic)15831594
17th century 16051611162216331639165016611667167816891695
18th century 17011707171817291735174617571763177417851791
19th century 1803181418251831184218531859-1870188118871898
20th century 1910192119271938194919551966197719831994
21st century 20052011202220332039205020612067207820892095
22nd century 21012107211821292135214621572163217421852191
23rd century 2203221422252231224222532259-2270228122872298
24th century 2310232123272338234923552366237723832394
25th century 24052411242224332439245024612467247824892495
400-year cycle
0–99 511223339506167788995
100–199 101107118129135146157163174185191
200–299 203214225231242253259270281287298
300–399 310321327338349355366377383394

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
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 14011407141814291435144614571463147414851491
16th century 15021513151915301541154715581569157515861597
17th century 16031614162516311642165316591670168116871698
18th century 17091715172617371743175417651771178217931799
19th century 1810182118271838184918551866187718831894
20th century 19051911192219331939195019611967197819891995
21st century 2006201720232034204520512062207320792090

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

References

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