Common year starting on Sunday

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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 letterhence 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, Memorial Day is on May 29, Labor Day is on September 4, Thanksgiving is on November 23, and Christmas is on a Monday.

Calendars[edit]

Calendar for any common year starting on Sunday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31
February
Su Mo Tu We Th Fr Sa
1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28
March
Su Mo Tu We Th Fr Sa
1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31
April
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30
May
Su Mo Tu We Th Fr Sa
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31
June
Su Mo Tu We Th Fr Sa
1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
July
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
August
Su Mo Tu We Th Fr Sa
1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31
September
Su Mo Tu We Th Fr Sa
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
October
Su Mo Tu We Th Fr Sa
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31
November
Su Mo Tu We Th Fr Sa
1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30
December
Su Mo Tu We Th Fr Sa
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
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 02 03 04 05 06 07 08
02 09 10 11 12 13 14 15
03 16 17 18 19 20 21 22
04 23 24 25 26 27 28 29
05 30 31
February
Wk Mo Tu We Th Fr Sa Su
05 01 02 03 04 05
06 06 07 08 09 10 11 12
07 13 14 15 16 17 18 19
08 20 21 22 23 24 25 26
09 27 28
March
Wk Mo Tu We Th Fr Sa Su
09 01 02 03 04 05
10 06 07 08 09 10 11 12
11 13 14 15 16 17 18 19
12 20 21 22 23 24 25 26
13 27 28 29 30 31
April
Wk Mo Tu We Th Fr Sa Su
13 01 02
14 03 04 05 06 07 08 09
15 10 11 12 13 14 15 16
16 17 18 19 20 21 22 23
17 24 25 26 27 28 29 30
May
Wk Mo Tu We Th Fr Sa Su
18 01 02 03 04 05 06 07
19 08 09 10 11 12 13 14
20 15 16 17 18 19 20 21
21 22 23 24 25 26 27 28
22 29 30 31
June
Wk Mo Tu We Th Fr Sa Su
22 01 02 03 04
23 05 06 07 08 09 10 11
24 12 13 14 15 16 17 18
25 19 20 21 22 23 24 25
26 26 27 28 29 30
July
Wk Mo Tu We Th Fr Sa Su
26 01 02
27 03 04 05 06 07 08 09
28 10 11 12 13 14 15 16
29 17 18 19 20 21 22 23
30 24 25 26 27 28 29 30
31 31
August
Wk Mo Tu We Th Fr Sa Su
31 01 02 03 04 05 06
32 07 08 09 10 11 12 13
33 14 15 16 17 18 19 20
34 21 22 23 24 25 26 27
35 28 29 30 31
September
Wk Mo Tu We Th Fr Sa Su
35 01 02 03
36 04 05 06 07 08 09 10
37 11 12 13 14 15 16 17
38 18 19 20 21 22 23 24
39 25 26 27 28 29 30
October
Wk Mo Tu We Th Fr Sa Su
39 01
40 02 03 04 05 06 07 08
41 09 10 11 12 13 14 15
42 16 17 18 19 20 21 22
43 23 24 25 26 27 28 29
44 30 31
November
Wk Mo Tu We Th Fr Sa Su
44 01 02 03 04 05
45 06 07 08 09 10 11 12
46 13 14 15 16 17 18 19
47 20 21 22 23 24 25 26
48 27 28 29 30
December
Wk Mo Tu We Th Fr Sa Su
48 01 02 03
49 04 05 06 07 08 09 10
50 11 12 13 14 15 16 17
51 18 19 20 21 22 23 24
52 25 26 27 28 29 30 31

Applicable years[edit]

Gregorian Calendar[edit]

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 only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Sunday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1589 1595
17th century 1606 1617 1623 1634 1645 1651 1662 1673 1679 — 1690
18th century 1702 1713 1719 — 1730 1741 1747 1758 1769 1775 1786 1797
19th century 1809 1815 1826 1837 1843 1854 1865 1871 1882 1893 1899
20th century 1905 1911 1922 1933 1939 — 1950 1961 1967 1978 1989 1995
21st century 2006 2017 2023 2034 2045 2051 2062 2073 2079 — 2090
22nd century 2102 2113 2119 — 2130 2141 2147 2158 2169 2175 2186 2197
23rd century 2209 2215 2226 2237 2243 2254 2265 2271 2282 2293 2299

Julian Calendar[edit]

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 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1402 1413 1419 1430 — 1441 1447 1458 1469 1475 1486 1497
16th century 1503 1514 1525 1531 1542 1553 1559 1570 — 1581 1587 1598
17th century 1609 1615 1626 1637 1643 1654 1665 1671 1682 1693 1699
18th century 1710 — 1721 1727 1738 1749 1755 1766 1777 1783 1794
19th century 1805 1811 1822 1833 1839 1850 — 1861 1867 1878 1889 1895
20th century 1906 1917 1923 1934 1945 1951 1962 1973 1979 1990 —
21st century 2001 2007 2018 2029 2035 2046 2057 2063 2074 2085 2091

References[edit]

Gregorian year types per leap cycle by Dominical letter (DL)[2] and Doomsday (DD)
Year starts Common years Leap years
1 Jan Count Ratio 31 Dec DL DD Count Ratio 31 Dec DL DD Count Ratio
Sun 58 14.50 % Sun A Tue 43 10.75 % Mon AG Wed 15 3.75 %
Sat 56 14.00 % Sat B Mon 43 10.75 % Sun BA Tue 13 3.25 %
Fri 58 14.50 % Fri C Sun 43 10.75 % Sat CB Mon 15 3.75 %
Thu 57 14.25 % Thu D Sat 44 11.00 % Fri DC Sun 13 3.25 %
Wed 57 14.25 % Wed E Fri 43 10.75 % Thu ED Sat 14 3.50 %
Tue 58 14.50 % Tue F Thu 44 11.00 % Wed FE Fri 14 3.50 %
Mon 56 14.00 % Mon G Wed 43 10.75 % Tue GF Thu 13 3.25 %
∑ 400 100.0 % 303 75.75 % 97 24.25 %
  1. ^ Jump up to:a b 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.