Common year starting on Tuesday

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, 2014 and 2025 in the obsolete Julian calendar, see below for more.

Any common year that starts on Sunday, Monday or 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 that precedes 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.

In this common year, Martin Luther King Jr. Day is on its latest possible date, January 21, Valentine's Day is on a Thursday, Presidents Day is on February 18, Saint Patrick's Day is on a Sunday, Memorial Day is on May 27, U.S. Independence Day and Halloween are on a Thursday, Labor Day is on September 2, Columbus Day is on its latest possible date, October 14, Election Day in the USA is on November 5th, Veterans Day is on a Monday, Thanksgiving is on its latest possible date, November 28, and Christmas is on a Wednesday.

Calendars

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

January
Su Mo Tu We Th Fr Sa
01 02 03 04 05
06 07 08 09 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
01 02
03 04 05 06 07 08 09
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
01 02
03 04 05 06 07 08 09
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
01 02 03 04 05 06
07 08 09 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
01 02 03 04
05 06 07 08 09 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
01
02 03 04 05 06 07 08
09 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
01 02 03 04 05 06
07 08 09 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
01 02 03
04 05 06 07 08 09 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
01 02 03 04 05 06 07
08 09 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
01 02 03 04 05
06 07 08 09 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
01 02
03 04 05 06 07 08 09
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
01 02 03 04 05 06 07
08 09 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 Tuesday (dominical letter F)

January
Wk Mo Tu We Th Fr Sa Su
01 01 02 03 04 05 06
02 07 08 09 10 11 12 13
03 14 15 16 17 18 19 20
04 21 22 23 24 25 26 27
05 28 29 30 31  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01 02 03
06 04 05 06 07 08 09 10
07 11 12 13 14 15 16 17
08 18 19 20 21 22 23 24
09 25 26 27 28
   
March
Wk Mo Tu We Th Fr Sa Su
09 01 02 03
10 04 05 06 07 08 09 10
11 11 12 13 14 15 16 17
12 18 19 20 21 22 23 24
13 25 26 27 28 29 30 31
   
April
Wk Mo Tu We Th Fr Sa Su
14 01 02 03 04 05 06 07
15 08 09 10 11 12 13 14
16 15 16 17 18 19 20 21
17 22 23 24 25 26 27 28
18 29 30  
   
May
Wk Mo Tu We Th Fr Sa Su
18 01 02 03 04 05
19 06 07 08 09 10 11 12
20 13 14 15 16 17 18 19
21 20 21 22 23 24 25 26
22 27 28 29 30 31  
   
June
Wk Mo Tu We Th Fr Sa Su
22 01 02
23 03 04 05 06 07 08 09
24 10 11 12 13 14 15 16
25 17 18 19 20 21 22 23
26 24 25 26 27 28 29 30
   
July
Wk Mo Tu We Th Fr Sa Su
27 01 02 03 04 05 06 07
28 08 09 10 11 12 13 14
29 15 16 17 18 19 20 21
30 22 23 24 25 26 27 28
31 29 30 31  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01 02 03 04
32 05 06 07 08 09 10 11
33 12 13 14 15 16 17 18
34 19 20 21 22 23 24 25
35 26 27 28 29 30 31  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01
36 02 03 04 05 06 07 08
37 09 10 11 12 13 14 15
38 16 17 18 19 20 21 22
39 23 24 25 26 27 28 29
40 30  
October
Wk Mo Tu We Th Fr Sa Su
40 01 02 03 04 05 06
41 07 08 09 10 11 12 13
42 14 15 16 17 18 19 20
43 21 22 23 24 25 26 27
44 28 29 30 31  
   
November
Wk Mo Tu We Th Fr Sa Su
44 01 02 03
45 04 05 06 07 08 09 10
46 11 12 13 14 15 16 17
47 18 19 20 21 22 23 24
48 25 26 27 28 29 30
   
December
Wk Mo Tu We Th Fr Sa Su
48 01
49 02 03 04 05 06 07 08
50 09 10 11 12 13 14 15
51 16 17 18 19 20 21 22
52 23 24 25 26 27 28 29
01 30 31  

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.

400 year cycle

century 1: 2, 13, 19, 30, 41, 47, 58, 69, 75, 86, 97

century 2: 109, 115, 126, 137, 143, 154, 165, 171, 182, 193, 199

century 3: 205, 211, 222, 233, 239, 250, 261, 267, 278, 289, 295

century 4: 301, 307, 318, 329, 335, 346, 357, 363, 374, 385, 391

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
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1409 1415 1426 1437 1443 1454 1465 1471 1482 1493 1499
16th century 1510 1521 1527 1538 1549 1555 1566 1577 1583 1594
17th century 1605 1611 1622 1633 1639 1650 1661 1667 1678 1689 1695
18th century 1706 1717 1723 1734 1745 1751 1762 1773 1779 1790
19th century 1801 1807 1818 1829 1835 1846 1857 1863 1874 1885 1891
20th century 1902 1913 1919 1930 1941 1947 1958 1969 1975 1986 1997
21st century 2003 2014 2025 2031 2042 2053 2059 2070 2081 2087 2098

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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