Common year starting on Friday (calendar type)

Key characteristics and Doomsday

For a common year beginning on Friday the Doomsday weekday — the anchor weekday used in Conway's Doomsday algorithm and related mappings — is Sunday. In a common year the Doomsday dates include January 3 and February 28, and the repeating month anchors are 4/4, 6/6, 8/8, 10/10, 12/12 and the paired dates 5/9, 9/5, 7/11 and 11/7. Because Doomsday is Sunday in this year type, each of those reference dates falls on a Sunday. Knowing Doomsday allows one to quickly compute the weekday of any date in the year.

Month start weekdays

Once January 1 is known to be a Friday, the weekday that begins each month in that year type is fixed. For a common year that begins on Friday the months begin on these weekdays:

• January — Friday
• February — Monday
• March — Monday
• April — Thursday
• May — Saturday
• June — Tuesday
• July — Thursday
• August — Sunday
• September — Wednesday
• October — Friday
• November — Monday
• December — Wednesday

These starts determine, for example, which months will contain particular weekday/date combinations and explain why certain holidays fall on the weekdays they do in this year type.

Holidays and notable dates (typical US examples)

When January 1 is a Friday, many widely observed holidays fall on predictable weekdays. Typical placements in such a year include:

• Martin Luther King Jr. Day — Monday, January 18
• Valentine’s Day — Sunday, February 14
• Presidents Day (third Monday of February) — February 15
• St. Patrick’s Day — Wednesday, March 17
• Mother’s Day (second Sunday in May) — May 9
• Memorial Day (last Monday in May) — May 31
• Father’s Day (third Sunday in June) — June 20
• Independence Day — Sunday, July 4
• Labor Day (first Monday in September) — September 6
• Columbus Day (second Monday in October) — October 11
• Halloween — Sunday, October 31
• Veterans Day — Thursday, November 11
• Thanksgiving (fourth Thursday in November) — November 25
• Christmas Day — Saturday, December 25

These are illustrative examples using common U.S. conventions for federal and widely observed holidays; local or religious calendars will follow their own rules but still follow the same weekday arithmetic.

Friday the 13th and month patterns

One notable feature of this year type is that it contains exactly one Friday the 13th, and that occurrence is in August. With August beginning on Sunday, the 13th of August falls on Friday (Sunday + 12 days = Friday). Only a few year types have a single Friday the 13th; this common-year pattern is shared in some ways with certain leap-year patterns but differs in the number and placement of such dates.

Occurrence, cycles and century behavior

In the Gregorian calendar the full sequence of year types repeats every 400 years because of the leap-year rules (years divisible by 4 are leap years, except that century years are leap years only if divisible by 400). Within that cycle shorter repetitions may be observed. Examples of recent and near-future Gregorian common years that begin on Friday include 1971, 1982, 1993, 1999, 2010, 2021 and 2027. The same weekday pattern can also be identified under the Julian calendar's simpler leap rules for appropriately chosen years.

Century years (years ending in 00) are governed by the Gregorian exception: many century years are common years because they are not divisible by 400. Historically, 1700 is often cited as a century example that behaved as a common year starting on Friday, and under the Gregorian scheme 2100 will be the next century year of that kind. Century behavior highlights how the 400-year cycle modifies simple four-year repetition.

ISO week numbering quirk

The ISO week date system numbers weeks so that week 1 is the week containing January 4 and weeks start on Monday. In a common year beginning on Friday the Doomsday date of January 3 is a Sunday and therefore falls in the ISO week that precedes ISO week 1. This makes this year type the only common-year pattern in which the nth occurrence of the Doomsday weekday in the calendar falls in ISO week n−1 rather than ISO week n, a subtle consequence of the interaction between ISO conventions and the year's weekday layout.

Computation and practical use

Knowing that a year is a common year starting on Friday lets one determine weekdays for any date quickly using simple modular arithmetic or the Doomsday method. That property is useful for historical research, planning recurring events, software date handling, and calendar layout production. For printable diagrams, calculators and tables, standard calendar resources list examples, diagrams and algorithms to convert between dates, weekdays and week numbers.

Further reading and links

See these resources for diagrams, definitions and example years: calendar layout, common year definition, weekday mapping, 1971 example, 1982 example, 1993 example, 1999 example, 2010 example, 2021 example, 2027 example, Gregorian calendar, Julian example 2011, Julian example 2022, Julian calendar, 1700 century example, 2100 century example, common year starting on Wednesday, common year starting on Saturday, leap year starting on Thursday, leap year definition.