Leap year starting on Friday

A leap year starting on Friday is any year with 366 days (i.e. it includes 29 February) that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB, such as the years 1808, 1836, 1864, 1892, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2112, 2140, 2168, 2196, and 2208 in the Gregorian calendar[1] or, likewise, 2000 and 2028 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; the only Friday the 13th in this leap year occurs in May. Common years starting on Saturday share this characteristic.

Calendars

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

January
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
February
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
2829  
 
March
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
April
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
May
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
June
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
July
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
August
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
September
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
October
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
November
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
December
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 

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

January
Wk Mo Tu We Th Fr Sa Su
53 010203
01 04050607080910
02 11121314151617
03 18192021222324
04 25262728293031
   
February
Wk Mo Tu We Th Fr Sa Su
05 01020304050607
06 08091011121314
07 15161718192021
08 22232425262728
09 29  
   
March
Wk Mo Tu We Th Fr Sa Su
09 010203040506
10 07080910111213
11 14151617181920
12 21222324252627
13 28293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 010203
14 04050607080910
15 11121314151617
16 18192021222324
17 252627282930
   
May
Wk Mo Tu We Th Fr Sa Su
17 01
18 02030405060708
19 09101112131415
20 16171819202122
21 23242526272829
22 3031  
June
Wk Mo Tu We Th Fr Sa Su
22 0102030405
23 06070809101112
24 13141516171819
25 20212223242526
26 27282930  
   
July
Wk Mo Tu We Th Fr Sa Su
26 010203
27 04050607080910
28 11121314151617
29 18192021222324
30 25262728293031
   
August
Wk Mo Tu We Th Fr Sa Su
31 01020304050607
32 08091011121314
33 15161718192021
34 22232425262728
35 293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01020304
36 05060708091011
37 12131415161718
38 19202122232425
39 2627282930  
   
October
Wk Mo Tu We Th Fr Sa Su
39 0102
40 03040506070809
41 10111213141516
42 17181920212223
43 24252627282930
44 31  
November
Wk Mo Tu We Th Fr Sa Su
44 010203040506
45 07080910111213
46 14151617181920
47 21222324252627
48 282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 01020304
49 05060708091011
50 12131415161718
51 19202122232425
52 262728293031  
   

Applicable years

Gregorian Calendar

Leap years that begin on Friday, along with those that start on Sunday, occur most frequently: 15 out of the 97 (≈ 15.46%) total leap years in a 400-year cycle of the Gregorian calendar. Thus, the overall occurrence is thus 3.75% (15 out of 400).

Gregorian leap years starting on Friday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 161616441672
18th century 1712174017681796
19th century 1808183618641892
20th century 1904193219601988
21st century 201620442072
22nd century 2112214021682196

Julian Calendar

Like all leap year types, the one starting with 1 January on a Friday 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 Friday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 1412144014681496
16th century 152415521580
17th century 1608163616641692
18th century 172017481776
19th century 1804183218601888
20th century 1916194419722000
21st century 202820562084
22nd century 2112214021682196
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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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