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 and 2196 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
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January
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01 |
02
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03 |
04 |
05 |
06 |
07 |
08 |
09
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10 |
11 |
12 |
13 |
14 |
15 |
16
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17 |
18 |
19 |
20 |
21 |
22 |
23
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24 |
25 |
26 |
27 |
28 |
29 |
30
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31
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February
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01 |
02 |
03 |
04 |
05 |
06
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07 |
08 |
09 |
10 |
11 |
12 |
13
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14 |
15 |
16 |
17 |
18 |
19 |
20
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21 |
22 |
23 |
24 |
25 |
26 |
27
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28 |
29 |
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March
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01 |
02 |
03 |
04 |
05
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06 |
07 |
08 |
09 |
10 |
11 |
12
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13 |
14 |
15 |
16 |
17 |
18 |
19
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20 |
21 |
22 |
23 |
24 |
25 |
26
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27 |
28 |
29 |
30 |
31
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April
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01 |
02
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03 |
04 |
05 |
06 |
07 |
08 |
09
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10 |
11 |
12 |
13 |
14 |
15 |
16
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17 |
18 |
19 |
20 |
21 |
22 |
23
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24 |
25 |
26 |
27 |
28 |
29 |
30
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May
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01 |
02 |
03 |
04 |
05 |
06 |
07
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08 |
09 |
10 |
11 |
12 |
13 |
14
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15 |
16 |
17 |
18 |
19 |
20 |
21
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22 |
23 |
24 |
25 |
26 |
27 |
28
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29 |
30 |
31
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June
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01 |
02 |
03 |
04
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05 |
06 |
07 |
08 |
09 |
10 |
11
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12 |
13 |
14 |
15 |
16 |
17 |
18
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19 |
20 |
21 |
22 |
23 |
24 |
25
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26 |
27 |
28 |
29 |
30 |
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July
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01 |
02
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03 |
04 |
05 |
06 |
07 |
08 |
09
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10 |
11 |
12 |
13 |
14 |
15 |
16
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17 |
18 |
19 |
20 |
21 |
22 |
23
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24 |
25 |
26 |
27 |
28 |
29 |
30
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31
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August
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01 |
02 |
03 |
04 |
05 |
06
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07 |
08 |
09 |
10 |
11 |
12 |
13
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14 |
15 |
16 |
17 |
18 |
19 |
20
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21 |
22 |
23 |
24 |
25 |
26 |
27
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28 |
29 |
30 |
31
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September
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01 |
02 |
03
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04 |
05 |
06 |
07 |
08 |
09 |
10
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11 |
12 |
13 |
14 |
15 |
16 |
17
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18 |
19 |
20 |
21 |
22 |
23 |
24
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25 |
26 |
27 |
28 |
29 |
30 |
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October
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01
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02 |
03 |
04 |
05 |
06 |
07 |
08
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09 |
10 |
11 |
12 |
13 |
14 |
15
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16 |
17 |
18 |
19 |
20 |
21 |
22
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23 |
24 |
25 |
26 |
27 |
28 |
29
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30 |
31
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November
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01 |
02 |
03 |
04 |
05
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06 |
07 |
08 |
09 |
10 |
11 |
12
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13 |
14 |
15 |
16 |
17 |
18 |
19
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20 |
21 |
22 |
23 |
24 |
25 |
26
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27 |
28 |
29 |
30 |
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December
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01 |
02 |
03
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04 |
05 |
06 |
07 |
08 |
09 |
10
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11 |
12 |
13 |
14 |
15 |
16 |
17
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18 |
19 |
20 |
21 |
22 |
23 |
24
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25 |
26 |
27 |
28 |
29 |
30 |
31
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ISO 8601-conformant calendar with week numbers for any leap year starting on Friday (dominical letter CB)
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January
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53
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01 |
02 |
03
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01
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04 |
05 |
06 |
07 |
08 |
09 |
10
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02
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
03
|
18 |
19 |
20 |
21 |
22 |
23 |
24
|
04
|
25 |
26 |
27 |
28 |
29 |
30 |
31
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|
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February
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05
|
01 |
02 |
03 |
04 |
05 |
06 |
07
|
06
|
08 |
09 |
10 |
11 |
12 |
13 |
14
|
07
|
15 |
16 |
17 |
18 |
19 |
20 |
21
|
08
|
22 |
23 |
24 |
25 |
26 |
27 |
28
|
09
|
29 |
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March
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|
09
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|
01 |
02 |
03 |
04 |
05 |
06
|
10
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07 |
08 |
09 |
10 |
11 |
12 |
13
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11
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14 |
15 |
16 |
17 |
18 |
19 |
20
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12
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21 |
22 |
23 |
24 |
25 |
26 |
27
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13
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28 |
29 |
30 |
31
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April
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|
13
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01 |
02 |
03
|
14
|
04 |
05 |
06 |
07 |
08 |
09 |
10
|
15
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
16
|
18 |
19 |
20 |
21 |
22 |
23 |
24
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17
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25 |
26 |
27 |
28 |
29 |
30 |
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May
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|
17
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01
|
18
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02 |
03 |
04 |
05 |
06 |
07 |
08
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19
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09 |
10 |
11 |
12 |
13 |
14 |
15
|
20
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16 |
17 |
18 |
19 |
20 |
21 |
22
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21
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23 |
24 |
25 |
26 |
27 |
28 |
29
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22
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30 |
31
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June
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|
22
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01 |
02 |
03 |
04 |
05
|
23
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06 |
07 |
08 |
09 |
10 |
11 |
12
|
24
|
13 |
14 |
15 |
16 |
17 |
18 |
19
|
25
|
20 |
21 |
22 |
23 |
24 |
25 |
26
|
26
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27 |
28 |
29 |
30 |
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July
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|
26
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|
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01 |
02 |
03
|
27
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04 |
05 |
06 |
07 |
08 |
09 |
10
|
28
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
29
|
18 |
19 |
20 |
21 |
22 |
23 |
24
|
30
|
25 |
26 |
27 |
28 |
29 |
30 |
31
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August
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31
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01 |
02 |
03 |
04 |
05 |
06 |
07
|
32
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08 |
09 |
10 |
11 |
12 |
13 |
14
|
33
|
15 |
16 |
17 |
18 |
19 |
20 |
21
|
34
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22 |
23 |
24 |
25 |
26 |
27 |
28
|
35
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29 |
30 |
31
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September
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35
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01 |
02 |
03 |
04
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36
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05 |
06 |
07 |
08 |
09 |
10 |
11
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37
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12 |
13 |
14 |
15 |
16 |
17 |
18
|
38
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19 |
20 |
21 |
22 |
23 |
24 |
25
|
39
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26 |
27 |
28 |
29 |
30 |
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October
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|
39
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01 |
02
|
40
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03 |
04 |
05 |
06 |
07 |
08 |
09
|
41
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10 |
11 |
12 |
13 |
14 |
15 |
16
|
42
|
17 |
18 |
19 |
20 |
21 |
22 |
23
|
43
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24 |
25 |
26 |
27 |
28 |
29 |
30
|
44
|
31
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November
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|
44
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01 |
02 |
03 |
04 |
05 |
06
|
45
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07 |
08 |
09 |
10 |
11 |
12 |
13
|
46
|
14 |
15 |
16 |
17 |
18 |
19 |
20
|
47
|
21 |
22 |
23 |
24 |
25 |
26 |
27
|
48
|
28 |
29 |
30 |
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December
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|
48
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|
01 |
02 |
03 |
04
|
49
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05 |
06 |
07 |
08 |
09 |
10 |
11
|
50
|
12 |
13 |
14 |
15 |
16 |
17 |
18
|
51
|
19 |
20 |
21 |
22 |
23 |
24 |
25
|
52
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26 |
27 |
28 |
29 |
30 |
31
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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 (≈ 15.5%) 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 year types per leap cycle by Dominical letter (DL)[1] and Doomsday (DD)
Year starts
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Common years
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Leap years
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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).
References