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 1904, 1932, 1960, 1988, 2016, 2044, 2072, and 2112 in the Gregorian calendar[1] or, likewise, 2000 and 2028 in the obsolete Julian calendar. Like common years starting on Saturday, this leap year has a Friday the 13th in May.

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
   
April
Wk Mo Tu We Th Fr Sa Su
13 010203
14 04050607080910
15 11121314151617
16 18192021222324
17 252627282930
   
July
Wk Mo Tu We Th Fr Sa Su
26 010203
27 04050607080910
28 11121314151617
29 18192021222324
30 25262728293031
   
October
Wk Mo Tu We Th Fr Sa Su
39 0102
40 03040506070809
41 10111213141516
42 17181920212223
43 24252627282930
44 31  
February
Wk Mo Tu We Th Fr Sa Su
05 01020304050607
06 08091011121314
07 15161718192021
08 22232425262728
09 29  
   
May
Wk Mo Tu We Th Fr Sa Su
17 01
18 02030405060708
19 09101112131415
20 16171819202122
21 23242526272829
22 3031  
August
Wk Mo Tu We Th Fr Sa Su
31 01020304050607
32 08091011121314
33 15161718192021
34 22232425262728
35 293031  
   
November
Wk Mo Tu We Th Fr Sa Su
44 010203040506
45 07080910111213
46 14151617181920
47 21222324252627
48 282930  
   
March
Wk Mo Tu We Th Fr Sa Su
09 010203040506
10 07080910111213
11 14151617181920
12 21222324252627
13 28293031  
   
June
Wk Mo Tu We Th Fr Sa Su
22 0102030405
23 06070809101112
24 13141516171819
25 20212223242526
26 27282930  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01020304
36 05060708091011
37 12131415161718
38 19202122232425
39 2627282930  
   
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 starting on a Friday, along with leap years that start on Sunday, occur most frequently of all the leap years (15 times out of the 97 total leap years) in a 400-year cycle (20871 weeks) in the Gregorian calendar. Thus, the overall frequency is 3.75% (15 out of 400) or approximately 15.5% (15 out of 97) if just leap years are taken into consideration.

Gregorian leap years starting on Friday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1616 1644 1672
18th century 1712 1740 1768 1796
19th century 1808 1836 1864 1892
20th century 1904 1932 1960 1988
21st century 2016 2044 2072
22nd century 2112 2140 2168 2196
Gregorian year types per leap cycle by Dominical letter (DL)[1] and Doomsday (DD)
Year starts Common years Leap years
1 Jan Count Ratio 31 Dec DL DD Count Ratio 31 Dec DL DD Count Ratio
Sun 58 14.50 % Sun A Tue 43 10.75 % Mon AG Wed 15 03.75 %
Sat 56 14.00 % Sat B Mon 43 10.75 % Sun BA Tue 13 03.25 %
Fri 58 14.50 % Fri C Sun 43 10.75 % Sat CB Mon 15 03.75 %
Thu 57 14.25 % Thu D Sat 44 11.00 % Fri DC Sun 13 03.25 %
Wed 57 14.25 % Wed E Fri 43 10.75 % Thu ED Sat 14 03.50 %
Tue 58 14.50 % Tue F Thu 44 11.00 % Wed FE Fri 14 03.50 %
Mon 56 14.00 % Mon G Wed 43 10.75 % Tue GF Thu 13 03.25 %
∑ 400 100.0 % 303 75.75 % 97 24.25 %

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 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1412 1440 1468 1496
16th century 1524 1552 1580
17th century 1608 1636 1664 1692
18th century 1720 1748 1776
19th century 1804 1832 1860 1888
20th century 1916 1944 1972 2000
21st century 2028 2056 2084
22nd century 2112 2140 2168 2196

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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