(Redirected from Common years starting on Friday)
Type of solar year
A common year starting on Friday is any non-leap year (i.e. a year with 365 days) that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2021 and the next one will be 2027 in the Gregorian calendar, or, likewise, 2022 and 2033 in the obsolete Julian calendar; see below for more. This common year is one of the three possible common years in which a century year can end on, and occurs in century years that yield a remainder of 100 when divided by 400. The most recent such year was 1700 and the next one will be 2100.
Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th: the only one in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.
From July of the year that precedes this type of year until September in this type of year is the longest period (14 months) that occurs without a Friday the 17th. Leap years starting on Tuesday share this characteristic, from August of the common year that precedes it to October in that type of year, (e.g. 2007-08 and 2035-36). This type of year also has the longest period (also 14 months) without a Tuesday the 13th, from July of this year until September of the next common year (that being on Saturday), unless the next year is a leap year (which is also a Saturday), then the period is reduced to only 11 months (e.g. 1999-2000 and 2027-28).
This is the one of two types of years overall where a rectangular February is possible, in places where Monday is considered to be the first day of the week. Common years starting on Thursday share this characteristic, but only in places where Sunday is considered to be the first day of the week.
Additionally, this type of year has three months (February, March and November) beginning exactly on the first day of the week, in areas which Monday is considered the first day of the week. Leap years starting on Monday share this characteristic on the months of January, April and July.
Calendars
Calendar for any common year starting on Friday, presented as common in many English-speaking areas |
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|
January
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
|
|
01 |
02
|
03 |
04 |
05 |
06 |
07 |
08 |
09
|
10 |
11 |
12 |
13 |
14 |
15 |
16
|
17 |
18 |
19 |
20 |
21 |
22 |
23
|
24 |
25 |
26 |
27 |
28 |
29 |
30
|
31
|
|
|
|
February
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
01 |
02 |
03 |
04 |
05 |
06
|
07 |
08 |
09 |
10 |
11 |
12 |
13
|
14 |
15 |
16 |
17 |
18 |
19 |
20
|
21 |
22 |
23 |
24 |
25 |
26 |
27
|
28 |
|
|
|
|
|
|
|
March
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
01 |
02 |
03 |
04 |
05 |
06
|
07 |
08 |
09 |
10 |
11 |
12 |
13
|
14 |
15 |
16 |
17 |
18 |
19 |
20
|
21 |
22 |
23 |
24 |
25 |
26 |
27
|
28 |
29 |
30 |
31
|
|
|
|
|
April
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
|
01 |
02 |
03
|
04 |
05 |
06 |
07 |
08 |
09 |
10
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
18 |
19 |
20 |
21 |
22 |
23 |
24
|
25 |
26 |
27 |
28 |
29 |
30 |
|
|
|
|
May
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
|
|
|
01
|
02 |
03 |
04 |
05 |
06 |
07 |
08
|
09 |
10 |
11 |
12 |
13 |
14 |
15
|
16 |
17 |
18 |
19 |
20 |
21 |
22
|
23 |
24 |
25 |
26 |
27 |
28 |
29
|
30 |
31
|
|
|
|
June
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
01 |
02 |
03 |
04 |
05
|
06 |
07 |
08 |
09 |
10 |
11 |
12
|
13 |
14 |
15 |
16 |
17 |
18 |
19
|
20 |
21 |
22 |
23 |
24 |
25 |
26
|
27 |
28 |
29 |
30 |
|
|
|
|
|
July
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
|
01 |
02 |
03
|
04 |
05 |
06 |
07 |
08 |
09 |
10
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
18 |
19 |
20 |
21 |
22 |
23 |
24
|
25 |
26 |
27 |
28 |
29 |
30 |
31
|
|
|
|
August
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
01 |
02 |
03 |
04 |
05 |
06 |
07
|
08 |
09 |
10 |
11 |
12 |
13 |
14
|
15 |
16 |
17 |
18 |
19 |
20 |
21
|
22 |
23 |
24 |
25 |
26 |
27 |
28
|
29 |
30 |
31
|
|
|
|
|
September
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
01 |
02 |
03 |
04
|
05 |
06 |
07 |
08 |
09 |
10 |
11
|
12 |
13 |
14 |
15 |
16 |
17 |
18
|
19 |
20 |
21 |
22 |
23 |
24 |
25
|
26 |
27 |
28 |
29 |
30 |
|
|
|
|
|
October
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
|
|
01 |
02
|
03 |
04 |
05 |
06 |
07 |
08 |
09
|
10 |
11 |
12 |
13 |
14 |
15 |
16
|
17 |
18 |
19 |
20 |
21 |
22 |
23
|
24 |
25 |
26 |
27 |
28 |
29 |
30
|
31
|
|
|
|
November
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
01 |
02 |
03 |
04 |
05 |
06
|
07 |
08 |
09 |
10 |
11 |
12 |
13
|
14 |
15 |
16 |
17 |
18 |
19 |
20
|
21 |
22 |
23 |
24 |
25 |
26 |
27
|
28 |
29 |
30 |
|
|
|
|
|
December
|
|
Su
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
|
|
|
01 |
02 |
03 |
04
|
05 |
06 |
07 |
08 |
09 |
10 |
11
|
12 |
13 |
14 |
15 |
16 |
17 |
18
|
19 |
20 |
21 |
22 |
23 |
24 |
25
|
26 |
27 |
28 |
29 |
30 |
31
|
|
|
|
ISO 8601-conformant calendar with week numbers for any common year starting on Friday (dominical letter C) |
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|
January
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
53
|
|
|
|
|
01 |
02 |
03
|
01
|
04 |
05 |
06 |
07 |
08 |
09 |
10
|
02
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
03
|
18 |
19 |
20 |
21 |
22 |
23 |
24
|
04
|
25 |
26 |
27 |
28 |
29 |
30 |
31
|
|
|
|
|
February
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
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
|
|
|
|
|
|
March
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
09
|
01 |
02 |
03 |
04 |
05 |
06 |
07
|
10
|
08 |
09 |
10 |
11 |
12 |
13 |
14
|
11
|
15 |
16 |
17 |
18 |
19 |
20 |
21
|
12
|
22 |
23 |
24 |
25 |
26 |
27 |
28
|
13
|
29 |
30 |
31
|
|
|
|
|
|
April
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
13
|
|
|
|
01 |
02 |
03 |
04
|
14
|
05 |
06 |
07 |
08 |
09 |
10 |
11
|
15
|
12 |
13 |
14 |
15 |
16 |
17 |
18
|
16
|
19 |
20 |
21 |
22 |
23 |
24 |
25
|
17
|
26 |
27 |
28 |
29 |
30 |
|
|
|
|
|
|
May
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
17
|
|
|
|
|
|
01 |
02
|
18
|
03 |
04 |
05 |
06 |
07 |
08 |
09
|
19
|
10 |
11 |
12 |
13 |
14 |
15 |
16
|
20
|
17 |
18 |
19 |
20 |
21 |
22 |
23
|
21
|
24 |
25 |
26 |
27 |
28 |
29 |
30
|
22
|
31
|
|
|
|
June
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
22
|
|
01 |
02 |
03 |
04 |
05 |
06
|
23
|
07 |
08 |
09 |
10 |
11 |
12 |
13
|
24
|
14 |
15 |
16 |
17 |
18 |
19 |
20
|
25
|
21 |
22 |
23 |
24 |
25 |
26 |
27
|
26
|
28 |
29 |
30 |
|
|
|
|
|
|
July
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
26
|
|
|
|
01 |
02 |
03 |
04
|
27
|
05 |
06 |
07 |
08 |
09 |
10 |
11
|
28
|
12 |
13 |
14 |
15 |
16 |
17 |
18
|
29
|
19 |
20 |
21 |
22 |
23 |
24 |
25
|
30
|
26 |
27 |
28 |
29 |
30 |
31
|
|
|
|
|
|
August
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
30
|
|
|
|
|
|
|
01
|
31
|
02 |
03 |
04 |
05 |
06 |
07 |
08
|
32
|
09 |
10 |
11 |
12 |
13 |
14 |
15
|
33
|
16 |
17 |
18 |
19 |
20 |
21 |
22
|
34
|
23 |
24 |
25 |
26 |
27 |
28 |
29
|
35
|
30 |
31
|
|
|
|
September
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
35
|
|
|
01 |
02 |
03 |
04 |
05
|
36
|
06 |
07 |
08 |
09 |
10 |
11 |
12
|
37
|
13 |
14 |
15 |
16 |
17 |
18 |
19
|
38
|
20 |
21 |
22 |
23 |
24 |
25 |
26
|
39
|
27 |
28 |
29 |
30 |
|
|
|
|
|
|
October
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
39
|
|
|
|
|
01 |
02 |
03
|
40
|
04 |
05 |
06 |
07 |
08 |
09 |
10
|
41
|
11 |
12 |
13 |
14 |
15 |
16 |
17
|
42
|
18 |
19 |
20 |
21 |
22 |
23 |
24
|
43
|
25 |
26 |
27 |
28 |
29 |
30 |
31
|
|
|
|
|
November
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
44
|
01 |
02 |
03 |
04 |
05 |
06 |
07
|
45
|
08 |
09 |
10 |
11 |
12 |
13 |
14
|
46
|
15 |
16 |
17 |
18 |
19 |
20 |
21
|
47
|
22 |
23 |
24 |
25 |
26 |
27 |
28
|
48
|
29 |
30 |
|
|
|
|
|
|
December
|
|
Wk
|
Mo
|
Tu
|
We
|
Th
|
Fr
|
Sa
|
Su
|
48
|
|
|
01 |
02 |
03 |
04 |
05
|
49
|
06 |
07 |
08 |
09 |
10 |
11 |
12
|
50
|
13 |
14 |
15 |
16 |
17 |
18 |
19
|
51
|
20 |
21 |
22 |
23 |
24 |
25 |
26
|
52
|
27 |
28 |
29 |
30 |
31
|
|
|
|
|
This is the only year type where the nth "Doomsday" (this year Sunday) is not in ISO week n; it is in ISO week n-1.
Applicable years
Gregorian calendar
In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Saturday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Friday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.
For this kind of year, the ISO week 10 (which begins March 8) and all subsequent ISO weeks occur later than in all other years, and exactly one week later than Leap years starting on Thursday. Also, the ISO weeks in January and February occur later than all other common years, but leap years starting on Friday share this characteristic in January and February, until ISO week 8.
400-year cycle
0–99
|
10 |
21 |
27 |
38 |
49 |
55 |
66 |
77 |
83 |
94 |
|
100–199
|
100 |
106 |
117 |
123 |
134 |
145 |
151 |
162 |
173 |
179 |
190
|
200–299
|
202 |
213 |
219 |
230 |
241 |
247 |
258 |
269 |
275 |
286 |
297
|
300–399
|
309 |
315 |
326 |
337 |
343 |
354 |
365 |
371 |
382 |
393 |
399
|
Julian calendar
In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). This sequence occurs exactly once within a cycle, and every common letter thrice.
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). Years 4, 15 and 26 of the cycle are common years beginning on Friday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Friday.
Julian common years starting on Friday
Decade
|
1st |
2nd |
3rd |
4th |
5th |
6th |
7th |
8th |
9th |
10th
|
15th century
|
1406 |
1417 |
1423 |
1434 |
1445 |
1451 |
1462 |
1473 |
1479 |
1490 |
—
|
16th century
|
1501 |
1507 |
1518 |
1529 |
1535 |
1546 |
1557 |
1563 |
1574 |
1585 |
1591
|
17th century
|
1602 |
1613 |
1619 |
1630 |
— |
1641 |
1647 |
1658 |
1669 |
1675 |
1686 |
1697
|
18th century
|
1703 |
1714 |
1725 |
1731 |
1742 |
1753 |
1759 |
1770 |
— |
1781 |
1787 |
1798
|
19th century
|
1809 |
1815 |
1826 |
1837 |
1843 |
1854 |
1865 |
1871 |
1882 |
1893 |
1899
|
20th century
|
1910 |
— |
1921 |
1927 |
1938 |
1949 |
1955 |
1966 |
1977 |
1983 |
1994
|
21st century
|
2005 |
2011 |
2022 |
2033 |
2039 |
2050 |
— |
2061 |
2067 |
2078 |
2089 |
2095
|
Holidays
International
Roman Catholic Solemnities
Australia and New Zealand
British Isles
Canada
United States
References
- ^ Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
Gregorian year types per leap cycle by Dominical letter (DL) 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 %
|
|
Source: Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017. |
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