Common year starting on Tuesday

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A common year starting on Tuesday is any non-leap year (i.e. a year with 365 days) 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, 2025 and 2031 in the obsolete Julian calendar, see below for more.

Contents

Any common year that starts on Tuesday has two Friday the 13ths: those two in this common year occur in September and December. Leap years starting on Monday share this characteristic. From July of the year preceding this year until September in this type of year is the longest period (14 months) that occurs without a Friday the 13th. Leap years starting on Saturday 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 Tuesday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
2728293031 
 
February
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
2425262728
 
March
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
24252627282930
31 
April
SuMoTuWeThFrSa
123456
78910111213
14151617181920
21222324252627
282930 
 
May
SuMoTuWeThFrSa
1234
567891011
12131415161718
19202122232425
262728293031 
 
June
SuMoTuWeThFrSa
1
2345678
9101112131415
16171819202122
23242526272829
30 
July
SuMoTuWeThFrSa
123456
78910111213
14151617181920
21222324252627
28293031 
 
August
SuMoTuWeThFrSa
123
45678910
11121314151617
18192021222324
25262728293031
 
September
SuMoTuWeThFrSa
1234567
891011121314
15161718192021
22232425262728
2930 
 
October
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
2728293031 
 
November
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
24252627282930
 
December
SuMoTuWeThFrSa
1234567
891011121314
15161718192021
22232425262728
293031 
 
ISO 8601-conformant calendar with week numbers for
any common year starting on Tuesday (dominical letter F)
January
WkMoTuWeThFrSaSu
01010203040506
0207080910111213
0314151617181920
0421222324252627
0528293031 
  
February
WkMoTuWeThFrSaSu
05010203
0604050607080910
0711121314151617
0818192021222324
0925262728
  
March
WkMoTuWeThFrSaSu
09010203
1004050607080910
1111121314151617
1218192021222324
1325262728293031
  
April
WkMoTuWeThFrSaSu
1401020304050607
1508091011121314
1615161718192021
1722232425262728
182930 
  
May
WkMoTuWeThFrSaSu
180102030405
1906070809101112
2013141516171819
2120212223242526
222728293031 
  
June
WkMoTuWeThFrSaSu
220102
2303040506070809
2410111213141516
2517181920212223
2624252627282930
  
July
WkMoTuWeThFrSaSu
2701020304050607
2808091011121314
2915161718192021
3022232425262728
31293031 
  
August
WkMoTuWeThFrSaSu
3101020304
3205060708091011
3312131415161718
3419202122232425
35262728293031 
  
September
WkMoTuWeThFrSaSu
3501
3602030405060708
3709101112131415
3816171819202122
3923242526272829
4030 
October
WkMoTuWeThFrSaSu
40010203040506
4107080910111213
4214151617181920
4321222324252627
4428293031 
  
November
WkMoTuWeThFrSaSu
44010203
4504050607080910
4611121314151617
4718192021222324
48252627282930
  
December
WkMoTuWeThFrSaSu
4801
4902030405060708
5009101112131415
5116171819202122
5223242526272829
013031 

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, along with Thursday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Tuesday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Tuesday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1585 1591
17th century 1602 1613 1619 1630 1641 1647 1658 1669 1675 1686 1697
18th century 1709 1715 1726 1737 1743 1754 1765 1771 1782 1793 1799
19th century 1805 1811 1822 1833 1839 1850 1861 1867 1878 1889 1895
20th century 1901 1907 1918 1929 1935 1946 1957 1963 1974 1985 1991
21st century 2002 2013 2019 2030 2041 2047 2058 2069 2075 2086 2097
22nd century 2109 2115 2126 2137 2143 2154 2165 2171 2182 2193 2199
23rd century 2205 2211 2222 2233 2239 2250 2261 2267 2278 2289 2295
24th century 2301 2307 2318 2329 2335 2346 2357 2363 2374 2385 2391
400-year cycle
0–99213193041475869758697
100–199109115126137143154165171182193199
200–299205211222233239250261267278289295
300–399301307318329335346357363374385391


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 7, 18 and 24 of the cycle are common years beginning on Tuesday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Tuesday.

Julian common years starting on Tuesday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1409 1415 1426 1437 1443 1454 1465 1471 1482 1493 1499
16th century 1510 1521 1527 1538 1549 1555 1566 1577 15831594
17th century16051611162216331639165016611667167816891695
18th century1706171717231734174517511762177317791790
19th century18011807181818291835184618571863187418851891
20th century19021913191919301941194719581969197519861997
21st century20032014202520312042205320592070208120872098

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.