Common year starting on Sunday

A common year starting on Sunday is any non-leap year (i.e. a year with 365 days) 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,[1] or, likewise, 2018 and 2029 in the obsolete Julian calendar. See below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in January and October. In this common year, U.S. Independence Day and Halloween are on a Tuesday, Thanksgiving is on November 23, and Christmas is on a Monday.

Calendars

Calendar for any common year starting on Sunday,
presented as common in many English-speaking areas

January
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
February
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728  
 
March
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
April
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
May
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
June
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
July
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
August
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
September
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
October
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
November
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
December
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  

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

January
Wk Mo Tu We Th Fr Sa Su
52 01
01 02030405060708
02 09101112131415
03 16171819202122
04 23242526272829
05 3031  
February
Wk Mo Tu We Th Fr Sa Su
05 0102030405
06 06070809101112
07 13141516171819
08 20212223242526
09 2728  
   
March
Wk Mo Tu We Th Fr Sa Su
09 0102030405
10 06070809101112
11 13141516171819
12 20212223242526
13 2728293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 0102
14 03040506070809
15 10111213141516
16 17181920212223
17 24252627282930
   
May
Wk Mo Tu We Th Fr Sa Su
18 01020304050607
19 08091011121314
20 15161718192021
21 22232425262728
22 293031  
   
June
Wk Mo Tu We Th Fr Sa Su
22 01020304
23 05060708091011
24 12131415161718
25 19202122232425
26 2627282930  
   
July
Wk Mo Tu We Th Fr Sa Su
26 0102
27 03040506070809
28 10111213141516
29 17181920212223
30 24252627282930
31 31  
August
Wk Mo Tu We Th Fr Sa Su
31 010203040506
32 07080910111213
33 14151617181920
34 21222324252627
35 28293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 010203
36 04050607080910
37 11121314151617
38 18192021222324
39 252627282930
   
October
Wk Mo Tu We Th Fr Sa Su
39 01
40 02030405060708
41 09101112131415
42 16171819202122
43 23242526272829
44 3031  
November
Wk Mo Tu We Th Fr Sa Su
44 0102030405
45 06070809101112
46 13141516171819
47 20212223242526
48 27282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 010203
49 04050607080910
50 11121314151617
51 18192021222324
52 25262728293031
   

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Monday, Wednesday, Friday or Saturday, 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 Sunday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Sunday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic)15891595
17th century 160616171623163416451651166216731679—1690
18th century 170217131719—17301741174717581769177517861797
19th century 18091815182618371843185418651871188218931899
20th century 19051911192219331939—195019611967197819891995
21st century 200620172023203420452051206220732079—2090
22nd century 210221132119—21302141214721582169217521862197
23rd century 22092215222622372243225422652271228222932299

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, as 29 February has no letter). This sequence occurs exactly 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 11, 22 and 28 of the cycle are common years beginning on Sunday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Sunday.

Julian common years starting on Sunday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 1402141314191430—1441144714581469147514861497
16th century 15031514152515131542155315591570—158115871598
17th century 16091615162616371643165416651671168216931699
18th century 1710—172117271738174917551766177717831794
19th century 180518111822183318391850—18611867187818891895
20th century 1906191719231934194519511962197319791990—
21st century 20012007201820292035204620572063207420852091

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