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.

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
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
February
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
2425262728
 
March
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
April
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
May
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
June
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
July
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
August
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
September
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
2930  
 
October
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
November
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
December
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
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 010203040506
02 07080910111213
03 14151617181920
04 21222324252627
05 28293031  
   
February
Wk Mo Tu We Th Fr Sa Su
05 010203
06 04050607080910
07 11121314151617
08 18192021222324
09 25262728
   
March
Wk Mo Tu We Th Fr Sa Su
09 010203
10 04050607080910
11 11121314151617
12 18192021222324
13 25262728293031
   
April
Wk Mo Tu We Th Fr Sa Su
14 01020304050607
15 08091011121314
16 15161718192021
17 22232425262728
18 2930  
   
May
Wk Mo Tu We Th Fr Sa Su
18 0102030405
19 06070809101112
20 13141516171819
21 20212223242526
22 2728293031  
   
June
Wk Mo Tu We Th Fr Sa Su
22 0102
23 03040506070809
24 10111213141516
25 17181920212223
26 24252627282930
   
July
Wk Mo Tu We Th Fr Sa Su
27 01020304050607
28 08091011121314
29 15161718192021
30 22232425262728
31 293031  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01020304
32 05060708091011
33 12131415161718
34 19202122232425
35 262728293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01
36 02030405060708
37 09101112131415
38 16171819202122
39 23242526272829
40 30  
October
Wk Mo Tu We Th Fr Sa Su
40 010203040506
41 07080910111213
42 14151617181920
43 21222324252627
44 28293031  
   
November
Wk Mo Tu We Th Fr Sa Su
44 010203
45 04050607080910
46 11121314151617
47 18192021222324
48 252627282930
   
December
Wk Mo Tu We Th Fr Sa Su
48 01
49 02030405060708
50 09101112131415
51 16171819202122
52 23242526272829
01 3031  

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]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 16021613161916301641164716581669167516861697
18th century 17091715172617371743175417651771178217931799
19th century 18051811182218331839185018611867187818891895
20th century 19011907191819291935194619571963197419851991
21st century 20022013201920302041204720582069207520862097
22nd century 21092115212621372143215421652171218221932199
23rd century 22052211222222332239225022612267227822892295
24th century 23012307231823292335234623572363237423852391
400-year cycle
0–99 213193041475869758697
100–199 109115126137143154165171182193199
200–299 205211222233239250261267278289295
300–399 301307318329335346357363374385391

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 1st2nd3rd4th5th6th7th8th9th10th
15th century 14091415142614371443145414651471148214931499
16th century 1510152115271538154915551566157715831594
17th century 16051611162216331639165016611667167816891695
18th century 1706171717231734174517511762177317791790
19th century 18011807181818291835184618571863187418851891
20th century 19021913191919301941194719581969197519861997
21st century 20032014202520312042205320592070208120872098

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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