Leap year starting on Tuesday

A leap year starting on Tuesday is any year with 366 days (i.e. it includes 29 February) that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE, such as the years 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, and 2104 in the Gregorian calendar[1] or, likewise, 1964, 1992, and 2020 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th. This leap year has a Friday the 13th in June. Common years starting on Wednesday share this characteristic.

Calendars

Calendar for any leap 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
242526272829
 
March
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
April
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
May
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
June
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
2930  
 
July
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
August
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
September
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
October
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
November
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
December
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 

ISO 8601-conformant calendar with week numbers for
any leap year starting on Tuesday (dominical letter FE)

January
Wk Mo Tu We Th Fr Sa Su
01 010203040506
02 07080910111213
03 14151617181920
04 21222324252627
05 28293031  
   
April
Wk Mo Tu We Th Fr Sa Su
14 010203040506
15 07080910111213
16 14151617181920
17 21222324252627
18 282930  
   
July
Wk Mo Tu We Th Fr Sa Su
27 010203040506
28 07080910111213
29 14151617181920
30 21222324252627
31 28293031  
   
October
Wk Mo Tu We Th Fr Sa Su
40 0102030405
41 06070809101112
42 13141516171819
43 20212223242526
44 2728293031  
   
February
Wk Mo Tu We Th Fr Sa Su
05 010203
06 04050607080910
07 11121314151617
08 18192021222324
09 2526272829
   
May
Wk Mo Tu We Th Fr Sa Su
18 01020304
19 05060708091011
20 12131415161718
21 19202122232425
22 262728293031  
   
August
Wk Mo Tu We Th Fr Sa Su
31 010203
32 04050607080910
33 11121314151617
34 18192021222324
35 25262728293031
   
November
Wk Mo Tu We Th Fr Sa Su
44 0102
45 03040506070809
46 10111213141516
47 17181920212223
48 24252627282930
   
March
Wk Mo Tu We Th Fr Sa Su
09 0102
10 03040506070809
11 10111213141516
12 17181920212223
13 24252627282930
14 31  
June
Wk Mo Tu We Th Fr Sa Su
22 01
23 02030405060708
24 09101112131415
25 16171819202122
26 23242526272829
27 30  
September
Wk Mo Tu We Th Fr Sa Su
36 01020304050607
37 08091011121314
38 15161718192021
39 22232425262728
40 2930  
   
December
Wk Mo Tu We Th Fr Sa Su
49 01020304050607
50 08091011121314
51 15161718192021
52 22232425262728
01 293031  
   

Applicable years

Gregorian Calendar

Leap years that begin on Tuesday, like those that start on Wednesday, occur at a rate of approximately 14.4% of all total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is 3.5% (14 out of 400).

Gregorian leap years starting on Tuesday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 1608163616641692
18th century 1704173217601788
19th century 182818561884
20th century 192419521980
21st century 2008203620642092
22nd century 2104213221602188
Gregorian year types per leap cycle by Dominical letter (DL)[1] and Doomsday (DD)
Year starts Common years Leap years
1 JanCountRatio 31 DecDLDDCountRatio 31 DecDLDDCountRatio
Sun 5814.50 % SunATue4310.75 % MonAGWed1503.75 %
Sat 5614.00 % SatBMon4310.75 % SunBATue1303.25 %
Fri 5814.50 % FriCSun4310.75 % SatCBMon1503.75 %
Thu 5714.25 % ThuDSat4411.00 % FriDCSun1303.25 %
Wed 5714.25 % WedEFri4310.75 % ThuEDSat1403.50 %
Tue 5814.50 % TueFThu4411.00 % WedFEFri1403.50 %
Mon 5614.00 % MonGWed4310.75 % TueGFThu1303.25 %
∑ 400100.0 % 30375.75 % 9724.25 %

Julian Calendar

Like all leap year types, the one starting with 1 January on a Tuesday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. 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).

Julian leap years starting on Tuesday
Decade 1st2nd3rd4th5th6th7th8th9th10th
14th century 132013481376
15th century 1404143214601488
16th century 1516154415721600
17th century 162816561684
18th century 1712174017681796
19th century 182418521880
20th century 1908193619641992
21st century 202020482076
22nd century 2104213221602188

References

  1. 1 2 3 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
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