Common year starting on Friday explained

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,[1] 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 begin 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

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.

Decade! 1st !!colspan=2
2nd !3rd 4th 5th 6th 7th 8th 9th 10th
16th centuryprior to first adoption (proleptic) 1599
17th century1700
18th century
19th century1897
20th century1999
21st century2100
22nd century
23rd century2297
24th century2399
400-year cycle
0–9910 21 27 38 49 55 66 77 83 94
100–199100 106 117 123 134 145 151 162 173 179 190
200–299202 213 219 230 241 247 258 269 275 286 297
300–399309 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.

Decade!colspan=2
1st !2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century
16th century1585 1591
17th century1602 1613 1619 1630 1641 1647 1658 1669 1675 1686 1697
18th century1703 1714 1725 1731 1742 1753 1759 1770 1781 1787 1798
19th century1809 1815 1826 1837 1843 1854 1865 1871 1882 1893 1899
20th century1910 1921 1927 1938 1949 1955 1966 1977 1983 1994
21st century2005 2011 2022 2033 2039 2050 2061 2067 2078 2089 2095

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

Notes and References

  1. Web site: The Mathematics of the ISO 8601 Calendar . Robert van Gent . Utrecht University, Department of Mathematics . 2017 . 20 July 2017.