Leap year starting on Monday

A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF, such as the years 1912, 1940, 1968, 1996, 2024, 2052, 2080, and 2120 in the Gregorian calendar[1] or, likewise, 2008, 2036, and 2064 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in September and December. Common years starting on Tuesday share this characteristic.

Calendars

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

January
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
February
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
2526272829
 
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 leap year starting on Monday (dominical letter GF)

January
Wk Mo Tu We Th Fr Sa Su
01 01020304050607
02 08091011121314
03 15161718192021
04 22232425262728
05 293031  
   
April
Wk Mo Tu We Th Fr Sa Su
14 01020304050607
15 08091011121314
16 15161718192021
17 22232425262728
18 2930  
   
July
Wk Mo Tu We Th Fr Sa Su
27 01020304050607
28 08091011121314
29 15161718192021
30 22232425262728
31 293031  
   
October
Wk Mo Tu We Th Fr Sa Su
40 010203040506
41 07080910111213
42 14151617181920
43 21222324252627
44 28293031  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01020304
06 05060708091011
07 12131415161718
08 19202122232425
09 26272829  
   
May
Wk Mo Tu We Th Fr Sa Su
18 0102030405
19 06070809101112
20 13141516171819
21 20212223242526
22 2728293031  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01020304
32 05060708091011
33 12131415161718
34 19202122232425
35 262728293031  
   
November
Wk Mo Tu We Th Fr Sa Su
44 010203
45 04050607080910
46 11121314151617
47 18192021222324
48 252627282930
   
March
Wk Mo Tu We Th Fr Sa Su
09 010203
10 04050607080910
11 11121314151617
12 18192021222324
13 25262728293031
   
June
Wk Mo Tu We Th Fr Sa Su
22 0102
23 03040506070809
24 10111213141516
25 17181920212223
26 24252627282930
   
September
Wk Mo Tu We Th Fr Sa Su
35 01
36 02030405060708
37 09101112131415
38 16171819202122
39 23242526272829
40 30  
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

Leap years that begin on Monday, along with those that start on Tuesday or Thursday, occur least frequently: 13 out of 97 (≈ 13.4%) total leap years of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400, with dominical letter FE).

Gregorian leap years starting on Monday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 162416521680
18th century 172017481776
19th century 181618441872
20th century 1912194019681996
21st century 202420522080
22nd century 212021482176
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 Monday 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 Monday
Decade 1st2nd3rd4th5th6th7th8th9th10th
14th century 1308133613641392
15th century 142014481476
16th century 1504153215601588
17th century 1616164416721700
18th century 172817561784
19th century 1812184018681896
20th century 192419521980
21st century 2008203620642092
22nd century 212021482176

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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