View source for Gregorian calendar

{{About||the calendar of religious holidays and periods|Liturgical year|this year's Gregorian calendar|{{Current calendar}}}}
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{{short description|Internationally the most widely accepted civil calendar}}
{{EngvarB|date=May 2014}}
{{Use dmy dates|date=October 2016}}
{{Year in various calendars|year={{CURRENTYEAR}}}}

The '''Gregorian calendar''' is the [[calendar]] used in most of the world.<ref>Dershowitz & Reingold 2008, p. 45. "The calendar in use today in most of the world is the Gregorian or ''new-style'' calendar designed by a commission assembled by Pope Gregory XIII in the sixteenth century."</ref> It is named after [[Pope Gregory XIII]], who introduced it in October 1582. 

The calendar spaces [[leap year]]s to make the average year 365.2425 days long, approximating the 365.2422-day [[tropical year]] that is determined by the Earth's revolution around the Sun. The rule for leap years is:

<blockquote>Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is.<ref>[http://aa.usno.navy.mil/faq/docs/calendars.php Introduction to Calendars]. (15 May 2013). [[United States Naval Observatory]].</ref></blockquote>

The calendar was developed as a correction to the [[Julian calendar]],<ref group=Note>The Julian calendar assumed incorrectly that the average year is exactly 365.25 (365¼) days long.</ref> shortening the average year by 0.0075 days to stop the drift of the calendar with respect to the [[equinox]]es.<ref name=text>See [[:s:Translation:Inter gravissimas|Wikisource English translation]] of the (Latin) 1582 papal bull ''[[Inter gravissimas]]''.</ref> To deal with the 10 days' difference (between calendar and reality) that this drift had already reached, the date was advanced so that 4 October 1582 was followed by 15 October 1582. There was no discontinuity in the cycle of weekdays or of the ''[[Anno Domini]]'' [[calendar era]].{{refn|Two era names occur within the bull ''[[Inter gravissimas]]'' itself, {{lang|la|anno Incarnationis dominicæ}} ("in the year of the Incarnation of the Lord") for the year it was signed, and {{lang|la|anno à Nativitate Domini nostri Jesu Christi}} ("in the year from the Nativity of our Lord [[Jesus]] Christ") for the year it was printed.<ref>[http://henk-reints.nl/cal/audette/calgreg.html#canons Les canons of Les textes fondateurs du calendrier grégorien] {{la icon}} {{fr icon}}</ref>|group=Note}} The reform also altered the lunar cycle used by the Church to calculate the date for Easter ([[computus]]), restoring it to the [[First Council of Nicea#Separation of Easter computation from Jewish calendar|time of the year as originally celebrated]] by the early Church.

The reform was adopted initially by the [[Roman Catholicism|Catholic]] countries of Europe and their overseas possessions. Over the next three centuries, the [[Protestant Reformation|Protestant]] and [[Eastern Orthodoxy|Eastern Orthodox]] countries also moved to what they called the ''Improved calendar'', with Greece being the last European country to adopt the calendar in 1923.<ref>Blegen n.d.</ref> To unambiguously specify a date during the transition period, (or in history texts), [[dual dating]] is sometimes used to specify both [[Old Style and New Style dates]] (abbreviated as O.S and N.S. respectively). Due to [[globalization]] in the 20th century, the calendar has also been adopted by most non-[[Western civilization|Western]] countries for civil purposes. The calendar era carries the alternative secular name of "[[Common Era]]".

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==Description==
{| class="wikitable"
|+A year is divided into twelve [[month]]s
! {{abbr|No.|Number}} !! Name !! Length in days
|-
| 1 || [[January]] || 31
|-
| 2 || [[February]] || 28 (29 in [[leap year]]s)
|-
| 3 || [[March]] || 31
|-
| 4 || [[April]] || 30
|-
| 5 || [[May]] || 31
|-
| 6 || [[June]] || 30
|-
| 7 || [[July]] || 31
|-
| 8 || [[August]] || 31
|-
| 9 || [[September]] || 30
|-
| 10 || [[October]] || 31
|-
| 11 || [[November]] || 30
|-
| 12 || [[December]] || 31
|}

The Gregorian calendar is a [[solar calendar]] with 12 months of 28–31 days each. A regular Gregorian year consists of 365 days, but in certain years known as [[leap year]]s, a [[leap day]] is added to February. Gregorian years are identified by consecutive year numbers.<ref>Clause 3.2.1 [[ISO 8601]]</ref> A calendar date is fully specified by the year (numbered according to a [[calendar era]], in this case ''[[Anno Domini]]'' or [[Common Era]]), the month (identified by name or number), and the day of the month (numbered sequentially starting from 1). Although the calendar year currently runs from 1 January to 31 December, at previous times year numbers were based on a different starting point within the calendar (see the [[#Beginning of the year|"beginning of the year"]] section below).
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In the [[Julian calendar]], a leap year occurred every 4 years, and the leap day was inserted by doubling 24 February. The Gregorian reform omitted a leap day in three of every 400 years and left the leap day unchanged. However, it has become customary in the [[modern period]] to number the days sequentially with no gaps, and 29 February is typically considered as the leap day. Before the [[Mysterii Paschalis|1969 revision of the Roman Calendar]], the Roman Catholic Church delayed February feasts after the 23rd by one day in leap years; Masses celebrated according to the previous calendar still reflect this delay.<ref>Richards 1998, p. 101</ref>

Calendar cycles repeat completely every 400 years, which equals 146,097 days.{{refn|The cycle described applies to the solar, or civil, calendar. If one also considers the ecclesiastical lunar rules, the lunisolar Easter ''computus'' cycle repeats only after 5,700,000 years of 2,081,882,250 days in 70,499,183 lunar months, based on an assumed mean lunar month of 29 days 12 hours 44 minutes {{sfrac|2|49928114|70499183}} seconds. (Seidelmann (1992), p. 582) [To properly function as an Easter ''computus'', this lunisolar cycle must have the same mean year as the Gregorian solar cycle, and indeed that is exactly the case.]|group=Note}}{{refn|The extreme length of the Gregorian Easter ''computus'' is due to its being the product of the 19-year [[Metonic cycle]], the thirty different possible values of the [[epact]], and the least common multiple (10,000) of the 400-year and 2,500-year solar and lunar correction cycles.<ref>Walker (1945), p.218.</ref>|group=Note}} Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A mean calendar year is {{sfrac|365|97|400}} days = 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.<ref group=Note>The same result is obtained by summing the fractional parts implied by the rule: {{nowrap|1= 365 + {{sfrac|1|4}} − {{sfrac|1|100}} + {{sfrac|1|400}} = 365 + 0.25 − 0.01 + 0.0025 = 365.2425}}</ref>

==Gregorian reform==
<gallery>
File:Christopher Clavius.jpg|[[Christopher Clavius]] (1538–1612), one of the main authors of the reform
File:Pope Gregory XIII.jpg|[[Pope Gregory XIII]] in an early 17th-century engraving
File:Inter-grav.jpg|First page of the papal bull ''[[Inter gravissimas]]''
File:Gregorianscher Kalender Petersdom.jpg| Detail of the pope's tomb by [[Camillo Rusconi]] (completed 1723); Antonio Lilio is genuflecting before the pope, presenting his printed calendar.
</gallery>

The Gregorian calendar was a reform of the Julian calendar. It was instituted by [[papal bull]] ''[[Inter gravissimas]]'' dated 24 February 1582 by Pope Gregory XIII, after whom the calendar is named.<ref name=text /> The motivation for the adjustment was to bring the date for the celebration of Easter to the time of year in which it was celebrated when it was introduced by the early Church. The error in the Julian calendar (its assumption that there are exactly 365.25 days in a year) had led to the date of the equinox according to the calendar drifting from the observed reality, and thus an error had been introduced into the [[Computus|calculation of the date of Easter]]. Although a recommendation of the [[First Council of Nicaea]] in 325 specified that all Christians should celebrate Easter on the same day, it took almost five centuries before virtually all Christians achieved that objective by adopting the rules of the Church of Alexandria (see [[Easter#Controversies over the date|Easter]] for the issues which arose).<ref group=Note>The last major Christian region to accept the Alexandrian rules was the [[Carolingian Empire]] (most of Western Europe) during 780–800. The last monastery in England to accept the Alexandrian rules did so in 931, and a few churches in southwest Asia beyond the eastern border of the [[Byzantine Empire]] continued to use rules that differed slightly, causing four dates for Easter to differ every 532 years.</ref>

===Background===
Because the [[date of Easter]] is a function{{snd}} the ''[[computus]]''{{snd}} of the date of the (northern hemisphere) spring [[equinox]], the [[Catholic Church]] considered the increasing divergence between the [[Canon law of the Catholic Church|canonical date]] of the equinox and observed reality had become unacceptable. Easter is celebrated  on the Sunday after the [[ecclesiastical full moon]] on or after 21 March, which was adopted as approximation to the March equinox.<ref>Richards 2013, p. 599.</ref> European scholars had been well aware of the calendar drift since the early medieval period.

[[Bede]], writing in the 8th century, showed that the accumulated error in his time was more than three days. [[Roger Bacon]] in c. 1200 estimated the error at seven or eight days. [[Dante]], writing c. 1300, was aware of the need of a calendar reform. The first attempt to go forward with such a reform was undertaken by [[Pope Sixtus IV]], who in 1475 invited [[Regiomontanus]] to the Vatican for this purpose. However, the project was interrupted by the death of Regiomontanus shortly after his arrival in Rome.<ref>
Ari Ben-Menahem, ''Historical Encyclopedia of Natural and Mathematical Sciences'' vol. 1 (2009), [https://books.google.ch/books?id=9tUrarQYhKMC&pg=PA863#v=onepage p. 863].</ref>
The increase of astronomical knowledge and the precision of observations towards the end of the 15th century made the question more pressing. Numerous publications over the following decades called for a calendar reform, among them two papers sent to the Vatican by the [[University of Salamanca]] in 1515 and 1578,<ref>Carabias Torres, 2012, p. 241</ref>
but the project was not taken up again until the 1540s, and implemented only under [[Pope Gregory XIII]] (r. 1572–1585).

===Preparation===
In 1545, the [[Council of Trent]] authorized [[Pope Paul III]] to reform the calendar, requiring that the date of the [[vernal equinox]] be restored to that which it held at the time of the [[First Council of Nicaea]] in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of Easter.

In 1577, a ''Compendium'' was sent to expert mathematicians outside the reform commission for comments. Some of these experts, including [[Giambattista Benedetti]] and [[Giuseppe Moletti|Giuseppe Moleto]], believed Easter should be computed from the true motions of the Sun and Moon, rather than using a tabular method, but these recommendations were not adopted.<ref>Ziggelaar (1983), pp. 211, 214.</ref> The reform adopted was a modification of a proposal made by the [[Calabria]]n doctor [[Aloysius Lilius]] (or Lilio).<ref name="Moyer 1983">Moyer 1983.</ref>

Lilius's proposal included reducing the number of leap years in four centuries from 100 to 97, by making three out of four centurial years common instead of leap years. He also produced an original and practical scheme for adjusting the epacts of the Moon when calculating the annual date of Easter, solving a long-standing obstacle to calendar reform.

Ancient tables provided the Sun's mean longitude.<ref>
*See, for example,''Tabule illustrissimi principis regis alfonsii'', Prague 1401−4 (Latin). A full set of Alphonsine Tables (including tables for mean motions, conjunctions of Sun and Moon, equation of time, spherical astronomy, longitudes and latitudes of cities, star tables, eclipse tables).
*For an example of the information provided see Jacques Cassini, ''Tables astronomiques du soleil, de la lune, des planètes, des étoiles fixes, et des satellites de Jupiter et de Saturne'', Paris 1740, available at [https://books.google.com/books?id=fVIVAAAAQAAJ&pg=PA130] (go forward ten pages to Table III on p. 10).</ref> The German mathematician [[Christopher Clavius]], the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the Sun passed through the vernal equinox nor on the length of the mean tropical year. [[Tycho Brahe]] also noticed discrepancies.<ref>
*{{cite book|url=https://books.google.com/books?id=CdzSAgAAQBAJ&pg=PA52|last=Dreyer|first=J L E|title=Tycho Brahe|location=Cambridge|date=2014|page=52|isbn=978-1-108-06871-0|quote=He remarks that both the Alphonsine and the Prutenic Tables are several hours wrong with regard to the time of the equinoxes and solstices.}}
*{{cite book|url=https://books.google.com/books?id=q2xxatst4OQC&pg=PA29|last=North|first=J|title=The Universal frame: historical essays in astronomy, natural philosophy and scientific method|location=London|date=1989|page=29|isbn=978-0-907628-95-8|quote=He noted on one occasion that the ''Alphonsine tables'' differed from the ''Prutenic'' by nineteen hours as to the time of the vernal equinox of 1588.}}</ref> The Gregorian leap year rule (97 leap years in 400 years) was put forward by [[Petrus Pitatus]] of Verona in 1560. He noted that it is consistent with the tropical year of the [[Alfonsine tables]] and with the mean tropical year of Copernicus (''[[De revolutionibus]]'') and [[Erasmus Reinhold]] (''[[Prutenic tables]]''). The three mean tropical years in Babylonian sexagesimals as the excess over 365 days (the way they would have been extracted from the tables of mean longitude) were 14,33,9,57 (Alfonsine), 14,33,11,12 (Copernicus) and 14,33,9,24 (Reinhold). All values are the same to two places (14:33) and this is also the mean length of the Gregorian year. Thus Pitatus' solution would have commended itself to the astronomers.<ref>Swerdlow (1986).</ref>

Lilius's proposals had two components. First, he proposed a correction to the length of the year. The mean [[tropical year]] is 365.24219 days long.<ref>Meeus and Savoie (1992).</ref> A commonly used value in Lilius's time, from the Alfonsine tables, is 365.2425463 days.<ref>Moyer (1983). p.</ref> As the average length of a Julian year is 365.25 days, the Julian year is almost 11 minutes longer than the mean tropical year. The discrepancy results in a drift of about three days every 400 years. Lilius's proposal resulted in an average year of 365.2425 days (see [[#Accuracy|Accuracy]]). At the time of Gregory's reform there had already been a drift of 10 days since the Council of Nicaea, resulting in the vernal equinox falling on 10 or 11 March instead of the ecclesiastically fixed date of 21 March, and if unreformed it would have drifted further. Lilius proposed that the 10-day drift should be corrected by deleting the Julian leap day on each of its ten occurrences over a period of forty years, thereby providing for a gradual return of the equinox to 21 March.

Lilius's work was expanded upon by Christopher Clavius in a closely argued, 800-page volume. He would later defend his and Lilius's work against detractors. Clavius's opinion was that the correction should take place in one move, and it was this advice which prevailed with Gregory.

The second component consisted of an approximation which would provide an accurate yet simple, rule-based calendar. Lilius's formula was a 10-day correction to revert the drift since the Council of Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. The proposed rule was that ''years divisible by 100 would be leap years only if they were divisible by 400 as well''.

The 19-year cycle used for the lunar calendar was also to be corrected by one day every 300 or 400 years (8 times in 2500 years) along with corrections for the years that are no longer leap years (i.e. 1700, 1800, 1900, 2100, etc.) In fact, a new method for computing the date of Easter was introduced.

When the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of 10 days. The Julian calendar day Thursday, 4 October 1582 was followed by the first day of the Gregorian calendar, Friday, 15 October 1582 (the cycle of weekdays was not affected).
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====First printed Gregorian calendar====
[[File:Reforma Gregoriana del Calendario Juliano.jpg|thumb|
''Lunario Novo, Secondo la Nuova Riforma della Correttione del l'Anno Riformato da N.S. Gregorio XIII'', printed in [[Rome]] by Vincenzo Accolti in 1582, one of the first printed editions of the new calendar.]]
A month after having decreed the reform, the pope (with a brief of 3 April 1582) granted to one Antoni Lilio the exclusive right to publish the calendar for a period of ten years. The ''Lunario Novo secondo la nuova riforma''{{efn|"New Almanac according to the new reform".}} was printed by Vincenzo Accolti, one of the first calendars printed in Rome after the reform, notes at the bottom that it was signed with papal authorization and by Lilio (''Con licentia delli Superiori... et permissu Ant(onii) Lilij''). The papal brief was revoked on 20 September 1582, because Antonio Lilio proved unable to keep up with the demand for copies.<ref>Mezzi, E., and Vizza, F., ''Luigi Lilio Medico Astronomo e Matematico di Cirò'', Laruffa Editore, Reggio Calabria, 2010, p. 14; p. 52, citing as primary references: Biblioteca Nazionale Centrale die Firenze, Magl. 5.10.5/a, [[Vatican Secret Archives|ASV]] A.A., Arm. I‑XVIII, 5506, f. 362r.</ref>

===Adoption {{anchor|Timeline}}===
{{main|Adoption of the Gregorian calendar}}
Although Gregory's reform was enacted in the most solemn of forms available to the Church, the bull had no authority beyond the Catholic Church and the [[Papal States]]. The changes that he was proposing were changes to the civil calendar, over which he had no authority. They required adoption by the civil authorities in each country to have legal effect.

The bull ''Inter gravissimas'' became the law of the Catholic Church in 1582, but it was not recognised by [[Protestantism|Protestant Churches]], [[Eastern Orthodox Churches]], [[Oriental Orthodox Churches]], and a few others. Consequently, the days on which Easter and related holidays were celebrated by different Christian Churches again diverged.

On 29 September 1582, [[Philip II of Spain]] decreed the change from the Julian to the Gregorian calendar.<ref>{{cite book |last=Kamen |first=Henry |date=1998 |title=Philip of Spain |url= https://books.google.co.uk/books?id=wyWourPR5S8C&printsec=frontcover&q=gregorian%20calendar|publisher=Yale University Press |page=248 |isbn=978-0300078008}}</ref> This affected much of Roman Catholic Europe, as Philip was at the time ruler over [[Iberian Union|Spain and Portugal]] as well as [[History of Italy (1559–1814)|much of Italy]]. In these territories, as well as in the [[Polish–Lithuanian Commonwealth]]{{citation needed|date=December 2016}} (ruled by [[Anna Jagiellon]]) and in the Papal States, the new calendar was implemented on the date specified by the bull, with Julian Thursday, 4 October 1582, being followed by Gregorian Friday, 15 October 1582. The [[Spanish Empire|Spanish]] and [[Portuguese Empire|Portuguese colonies]] followed somewhat later ''de facto'' because of delay in communication.<ref>[http://hdl.loc.gov/loc.wdl/wdl.2837 ''"Pragmatica" on the Ten Days of the Year''] [[World Digital Library]], the first known South American imprint, produced in 1584 by Antonio Ricardo, of a four-page edict issued by King Philip II of Spain in 1582, decreeing the change from the Julian to the Gregorian calendar.</ref>

Many [[Protestant]] countries initially objected to adopting a Catholic innovation; some Protestants feared the new calendar was part of a plot to return them to the Catholic fold. For example, the British could not bring themselves to adopt the Catholic system explicitly: the Annexe to their [[Calendar (New Style) Act 1750]] established a computation for the date of Easter that achieved the same result as Gregory's rules, without actually referring to him.<ref>24 Geo. II Ch. 23, § 3.</ref>

[[Kingdom of Great Britain|Britain]] and the [[British Empire]] (including the eastern part of what is now the United States) adopted the Gregorian calendar in 1752.<!-- NOTE SUSPENDED AS SOURCE DOES NOT APPEAR TO BE RELIABLE: SEE TALK {{refn|The twentieth century historian T.S.Pattie reports that mobs rioted at the time of adoption, crying "Give us back our eleven days". He attributes this to irrational resentment of "black magic".<ref>Pattie (1976), pp.27-28.</ref> However, the mobs were not irrational. Many contracts, such as for rents, ran on a quarterly basis and the law shortened a quarter, in effect depriving renters of 11 days of lodging that they had paid for.|group=Note}} --> [[Swedish calendar|Sweden]] followed in 1753.

Prior to 1917, Turkey used the lunar [[Islamic calendar]] with the [[Hijri year|Hegira era]] for general purposes and the Julian calendar for fiscal purposes. The start of the fiscal year was eventually fixed at 1 March and the year number was roughly equivalent to the Hegira year (see [[Rumi calendar]]). As the solar year is longer than the lunar year this originally entailed the use of "escape years" every so often when the number of the fiscal year would jump. From 1 March 1917 the fiscal year became Gregorian, rather than Julian. On 1 January 1926 the use of the Gregorian calendar was extended to include use for general purposes and the number of the year became the same as in most other countries.

====Adoption of the Gregorian Calendar====

{| class="wikitable"
! Year
! Country/-ies/Areas 
|-
| 1582
| Spain, Portugal, France, Poland, Italy, Catholic Low Countries, Luxemburg, and colonies
|-
| 1584
| Kingdom of Bohemia
|-
| 1610
| Prussia
|-
| 1648
| Alsace
|-
| 1682
| Strasbourg
|-
| 1700
| 'Germany',{{refn |name=Germany1700 |group=Note}} Swiss Cantons, Protestant Low Countries, Norway, Denmark
|-
| 1752
| Great Britain and colonies
|-
| 1753
| Sweden and Finland
|-
| 1873
| Japan
|-
| 1875
| Egypt
|-
| 1896
| Korea
|-
| 1912
| China, Albania
|-
| 1915
| Latvia, Lithuania
|-
| 1916
| Bulgaria
|-
| 1918
| Russia, Estonia
|-
| 1919
| Romania, Yugoslavia<ref group=Note>1919 in the regions comprising the former Kingdoms of Serbia and Montenegro (present-day Kosovo, Montenegro, Serbia and Macedonia). The western and northern regions of what became Yugoslavia were already using the Gregorian calendar. For example, most of Slovenia adopted the Gregorian calendar at the same time as Austria in 1583. Coastal Croatia, which was at the time ruled by Venice, adopted the Gregorian calendar in 1582. Inland Croatia, ruled by the Habsburgs, adopted it in 1587 along with Hungary. The Gregorian calendar was used in Bosnia and Herzegovina since the 16th century by the Catholic population and was formally adopted for government use in 1878 following occupation by Austria-Hungary.</ref>
|-
| 1923
| Greece
|-
| 1926
| Turkey
|-
| 2016
| Saudi Arabia
|}

==Difference between Gregorian and Julian calendar dates==
{| class="wikitable floatright"
|+Conversion from Julian to Gregorian dates.<ref>A more extensive list is available at [[Conversion between Julian and Gregorian calendars]]</ref>
! Gregorian range || Julian range || Difference
|- align=right
|From 15 October 1582<br>to 28 February 1700
|From 5 October 1582<br>to 18 February 1700
| align=center |10 days
|- align=right
|From 1 March 1700<br>to 28 February 1800
|From 19 February 1700<br>to 17 February 1800
| align=center |11 days
|- align=right
|From 1 March 1800<br>to 28 February 1900
|From 18 February 1800<br>to 16 February 1900
| align=center |12 days
|- align=right
|From 1 March 1900<br>to 28 February 2100
|From 17 February 1900<br>to 15 February 2100
| align=center |13 days
|- align=right
|From 1 March 2100<br>to 28 February 2200
|From 16 February 2100<br>to 14 February 2200
| align=center |14 days<!--
|When converting a date in a year which is leap in one calendar but not the other include 29 February in the calculation when the conversion crosses the border between February and March.-->
|}

This section always places the intercalary day on {{nowrap|29 February}} even though it was always obtained by doubling {{nowrap|24 February}} (the ''bissextum'' (twice sixth) or bissextile day) until the late [[Middle Ages]]. The Gregorian calendar is [[Proleptic calendar|proleptic]] before 1582 (assumed to exist before 1582), and the difference between Gregorian and Julian calendar dates increases by three days every four centuries (all date ranges are inclusive).

The following equation gives the number of days (actually, dates) that the Gregorian calendar is ahead of the Julian calendar, called the ''secular difference'' between the two calendars. A negative difference means the Julian calendar is ahead of the Gregorian calendar.<ref>Blackburn & Holford-Strevens (1999), p. 788.</ref>
:<math>D = \left\lfloor{Y/100}\right\rfloor - \left\lfloor{Y/400}\right\rfloor - 2</math>
where <math>D</math> is the secular difference and <math>Y</math> is the year using [[astronomical year numbering]], that is, use {{nowrap|(year BC) − 1}} for BC years. <math>\left\lfloor{x}\right\rfloor</math> means that if the result of the division is not an integer it is rounded down to the nearest integer. Thus during the 1900s, 1900/400 = 4, while during the −500s, −500/400 = −2.

The general rule, in years which are leap years in the Julian calendar but not the Gregorian, is:

Up to 28 February in the calendar being converted {{em|from}}, add one day less or subtract one day more than the calculated value. Give February the appropriate number of days for the calendar being converted {{em|into}}. When subtracting days to calculate the Gregorian equivalent of 29 February (Julian), 29 February is discounted. Thus if the calculated value is −4 the Gregorian equivalent of this date is 24 February.<ref>
*James Evans, ''[https://books.google.com/books?id=nS51_7qbEWsC&pg=PA169 The history and practice of ancient astronomy]'' (Oxford: Oxford University Press, 1998) 169. {{ISBN|0-19-509539-1}}.
*''Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac'' (London: Her Majesty's Stationery Office, 1961) 417.</ref>
{{clear}}

==Beginning of the year==
{| class="sortable wikitable floatright"
|-
! Country || Start numbered year<br>on 1 January || Adoption of<br>Gregorian calendar
|-
| Denmark || Gradual change from<br>13th to 16th centuries<ref>Herluf Nielsen: ''Kronologi'' (2nd ed., Dansk Historisk Fællesforening, Copenhagen 1967), pp. 48–50.</ref> || 1700
|-
| [[Holy Roman Empire]] (Catholic states) || 1544 || 1583
|-
| Spain, Poland, Portugal || 1556 || 1582
|-
| [[Holy Roman Empire]] (Protestant states) || 1559 || 1700{{refn|Protestant states in Germany used an astronomical Easter from 1700 to 1774, based on [[Kepler]]'s [[Rudolphine Tables]], differing from the Gregorian Easter twice, one week early in 1724 and 1744.<ref>{{citation |last=Lamont |first=Roscoe |year=1920 |title=The reform of the Julian calendar |url=http://adsbit.harvard.edu//full/1920PA.....28...18L/0000018.000.html |journal=Popular Astronomy |volume=28 |pages=18–32}}</ref> |name=Germany1700 |group=Note}}
|-
| Sweden || 1559 || 1753
|-
| France || 1564<ref>[http://www.henk-reints.nl/cal/audette/cgfrance.html Le calendrier grégorien en France] {{fr icon}}</ref> || 1582{{refn|In 1793 France abandoned the Gregorian calendar in favour of the [[French Republican Calendar]]. This change was reverted in 1805.|group=n}}
|-
| [[Southern Netherlands]] || 1576<ref>Per decree of 16 June 1575. Hermann Grotefend, "[http://www.manuscripta-mediaevalia.de/gaeste/grotefend/g_o.htm#Osteranfang Osteranfang]" (Easter beginning), ''[http://www.manuscripta-mediaevalia.de/gaeste/grotefend/grotefend.htm Zeitrechnung de Deutschen Mittelalters und der Neuzeit]'' (Chronology of the German Middle Ages and modern times) (1891–1898)</ref> || 1582
|-
| [[Lorraine (province)|Lorraine]] || 1579 || 1582<ref group=Note>Lorraine reverted to Julian in 1735 and adopted Gregorian again in 1760</ref>
|-
| [[Dutch Republic]] || 1583 || 1582
|-
| Scotland || 1600<ref name=Blackburn>Blackburn & Holford-Strevens (1999), p. 784.</ref><ref>[[John James Bond]], ''[https://books.google.com/books?id=bzAWAAAAYAAJ Handy-book of rules and tables for verifying dates with the Christian era]'' Scottish decree on pp. xvii–xviii.</ref> || 1752
|-
| Russia || 1700<ref>Roscoe Lamont, [http://articles.adsabs.harvard.edu/full/1920PA.....28...18L The reform of the Julian calendar], ''Popular Astronomy'' '''28''' (1920) 18–32. Decree of Peter the Great is on pp. 23–24.</ref>||1918 
|-
| [[Tuscany]] || 1750<ref>
*Alexandre Dumas, [https://books.google.com/books?id=EfVfmMYXxD4C&pg=PA201&lpg=PA201&dq=toscana+1750+calendario+gregoriano&source=bl&ots=fJsAtGgRlh&sig=1_cfVkGayydjz424WACFZ0aXBJM&hl=en&sa=X&ved=2ahUKEwj-yIngva7eAhVvwIsKHeXjChg4ChDoATADegQIAhAB#v=onepage&q=toscana%201750%20calendario%20gregoriano&f=false Storia del governo della Toscana: sotto La casa de'Medici].
*[https://www.florencewithguide.com/it/blog-it/il-calendario-fiorentino/ Il calendario fiorentino].</ref> || 1582<ref>Lorenzo Cattini, [https://books.google.com/books?id=v--l2PRjuJQC&printsec=frontcover&hl=en&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Legislazione toscana raccolta e illustrata], vol. 10, p. 208.</ref>
|-
| [[Kingdom of Great Britain|Great Britain]] and the [[British Empire]]<br>except Scotland || 1752<ref name=Blackburn/> || 1752
|-
| [[Republic of Venice|Venice]] || 1797<ref>[https://www.sporting04.it/modules.php?name=News&file=article&sid=554 Fora Febraro].</ref> || 1582
|}
The year used in dates during the [[Roman Republic]] and the [[Roman Empire]] was the consular year, which began on the day when consuls first entered office—probably 1 May before 222 BC, 15 March from 222 BC and 1 January from 153 BC.<ref>{{cite web|url=http://www.tyndalehouse.com/Egypt/ptolemies/chron/roman/chron_rom_cal.htm#eponymous |title=Roman Dates: Eponymous Years |publisher=Tyndalehouse.com |date= |accessdate=14 September 2010}}</ref> The Julian calendar, which began in 45 BC, continued to use 1 January as the first day of the [[new year]]. Even though the year used for dates changed, the civil year always displayed its months in the order January to December from the Roman Republican period until the present.

During the Middle Ages, under the influence of the Catholic Church, many Western European countries moved the start of the year to one of several important Christian festivals—25 December (supposed [[Nativity of Jesus]]), 25 March ([[Annunciation]]), or Easter (France),<ref name=MS>Mike Spathaky ''[http://www.cree.name/genuki/dates.htm Old Style and New Style Dates and the change to the Gregorian Calendar: A summary for genealogists]''</ref> while the Byzantine Empire began its year on 1 September and Russia did so on 1 March until 1492 when the new year was moved to 1 September.<ref>S. I. Seleschnikow: ''Wieviel Monde hat ein Jahr?'' (Aulis-Verlag, Leipzig/Jena/Berlin 1981, p. 149), which is a German translation of С. И. Селешников: ''История календаря и хронология'' (Издательство "Наука", Moscow 1977). The relevant chapter is available online here: [http://grigam.narod.ru/kalend/kalen19.htm История календаря в России и в СССР (Calendar history in Russia and the USSR)]. Anno Mundi 7000 lasted from {{nowrap|1 March 1492}} to {{nowrap|31 August 1492}}. {{ru icon}}</ref>

In common usage, 1 January was regarded as New Year's Day and celebrated as such,<ref>[http://www.pepysdiary.com/archive/1661/12/31/index.php Tuesday 31 December 1661], [http://www.pepysdiary.com The Diary of Samuel Pepys] "I sat down to end my journell for this year, ..."</ref> but from the 12th century until 1751 the legal year in England began on 25 March ([[Lady Day]]).<ref>Nørby, Toke. [http://www.norbyhus.dk/calendar.html#England The Perpetual Calendar: What about England] Version 29 February 2000</ref> So, for example, the Parliamentary record lists the execution of [[Charles I of England|Charles I]] on 30 January as occurring in 1648 (as the year did not end until 24 March),<ref>{{cite web|url= http://www.british-history.ac.uk/report.asp?compid=26211#s5|title= House of Commons Journal Volume 8, 9 June 1660 (Regicides)|publisher=British History Online|accessdate=18 March 2007}}</ref> although later histories adjust the start of the year to 1 January and record the execution as occurring in 1649.<ref name="EC-NA"/>

Most Western European countries changed the start of the year to 1 January before they adopted the Gregorian calendar. For example, Scotland changed the start of the Scottish New Year to 1 January in 1600 (this means that 1599 was a short year). England, Ireland and the British colonies changed the start of the year to 1 January in 1752 (so 1751 was a short year with only 282 days) though in England the start of the tax year remained at 25 March (O.S.), 5 April (N.S.) until 1800, when it moved to 6 April. Later in 1752 in September the Gregorian calendar was introduced throughout Britain and the British colonies (see the section [[#Adoption|Adoption]]). These two reforms were implemented by the [[Calendar (New Style) Act 1750]].<ref name="NT-Perpetual-Calendar">Nørby, Toke. [http://www.norbyhus.dk/calendar.php The Perpetual Calendar]</ref>

In some countries, an official decree or law specified that the start of the year should be 1 January. For such countries a specific year when a 1 January-year became the norm can be identified. In other countries the customs varied, and the start of the year moved back and forth as fashion and influence from other countries dictated various customs.

Neither the papal bull nor its attached canons explicitly fix such a date, though it is implied by two tables of [[saint]]'s days, one labelled 1582 which ends on 31 December, and another for any full year that begins on 1 January. It also specifies its epact relative to 1 January, in contrast with the Julian calendar, which specified it relative to 22 March. The old date was derived from the Greek system: the earlier ''Supputatio Romana'' specified it relative to 1 January.

{{Reflist|group=n}}
{{clear}}

==Dual dating==
{{Main|Dual dating}}

During the period between 1582, when the first countries adopted the Gregorian calendar, and 1923, when the last European country adopted it, it was often necessary to indicate the date of some event in both the Julian calendar and in the Gregorian calendar, for example, "10/21 February 1750/51", where the dual year accounts for some countries already beginning their numbered year on 1 January while others were still using some other date. Even before 1582, the year sometimes had to be double dated because of the different beginnings of the year in various countries. Woolley, writing in his biography of [[John Dee (mathematician)|John Dee]] (1527–1608/9), notes that immediately after 1582 English letter writers "customarily" used "two dates" on their letters, one OS and one NS.<ref>Benjamin Woolley, ''The Queen's Conjurer: The science and magic of Dr. John Dee, adviser to Queen Elizabeth I'' (New York: Henry Holt, 2001) p. 173</ref>

===Old Style and New Style dates===
{{Main|Old Style and New Style dates|Dual dating}}

"Old Style" (OS) and "New Style" (NS) are sometimes added to dates to identify which calendar reference system is used for the date given. In Britain and its colonies, where the [[Calendar (New Style) Act 1750|Calendar Act of 1750]] altered the start of the year,<ref group=Note>In Scotland the legal start of year had been moved to 1 January in 1600 (Mike Spathaky. [http://www.cree.name/genuki/dates.htm Old Style New Style dates and the change to the Gregorian calendar]).</ref> and also aligned the British calendar with the Gregorian calendar, there is some confusion as to what these terms mean. They can indicate that the start of the [[Julian year (calendar)|Julian year]] has been adjusted to start on 1 January (NS) even though contemporary documents use a different start of year (OS); or to indicate that a date conforms to the Julian calendar (OS), formerly in use in many countries, rather than the Gregorian calendar (NS).<ref name="EC-NA">[http://www.nationalarchives.gov.uk/pathways/citizenship/rise_parliament/docs/charles_warrant.htm Death warrant of Charles I] web page of the [http://www.nationalarchives.gov.uk/ UK National Archives]. A demonstration of New Style meaning Julian calendar with a start of year adjustment.</ref><ref>
*Spathaky, Mike [http://www.cree.name/genuki/dates.htm Old Style New Style dates and the change to the Gregorian calendar]. "increasingly parish registers, in addition to a new year heading after 24th March showing, for example '1733', had another heading at the end of the following December indicating '1733/4'. This showed where the New Style 1734 started even though the Old Style 1733 continued until 24th March. ... We as historians have no excuse for creating ambiguity and must keep to the notation described above in one of its forms. It is no good writing simply 20th January 1745, for a reader is left wondering whether we have used the Old or the New Style reckoning. The date should either be written 20th January 1745 OS (if indeed it was Old Style) or as 20th January 1745/6. The hyphen (1745-6) is best avoided as it can be interpreted as indicating a period of time."
*[http://www.britannica.com/eb/article-38556/Russia: The October (November) Revolution] Britannica encyclopaedia, A demonstration of New Style meaning the Gregorian calendar.
*Stockton, J.R. [http://www.merlyn.demon.co.uk/miscdate.htm#Styles Date Miscellany I: The Old and New Styles] "The terms 'Old Style' and 'New Style' are now commonly used for both the 'Start of Year' and 'Leap Year' [(Gregorian calendar)] changes (England & Wales: both in 1752; Scotland: 1600, 1752). I believe that, properly and historically, the 'Styles' really refer only to the 'Start of Year' change (from March&nbsp;25th to January&nbsp;1st); and that the 'Leap Year' change should be described as the change from Julian to Gregorian."</ref>

==Proleptic Gregorian calendar==
{{Main|Proleptic Gregorian calendar}}
Extending the Gregorian calendar backwards to dates preceding its official introduction produces [[proleptic Gregorian calendar|a proleptic calendar]], which should be used with some caution. For ordinary purposes, the dates of events occurring prior to 15 October 1582 are generally shown as they appeared in the Julian calendar, with the year starting on 1 January, and no conversion to their Gregorian equivalents. For example, the [[Battle of Agincourt]] is universally considered to have been fought on 25 October 1415 which is [[Crispin|Saint Crispin]]'s Day.

Usually, the mapping of new dates onto old dates with a start of year adjustment works well with little confusion for events that happened before the introduction of the Gregorian calendar. But for the period between the first introduction of the Gregorian calendar on 15 October 1582 and its introduction in Britain on 14 September 1752, there can be considerable confusion between events in continental western Europe and in British domains in English language histories.

Events in continental western Europe are usually reported in English language histories as happening under the Gregorian calendar. For example, the [[Battle of Blenheim]] is always given as 13 August 1704. Confusion occurs when an event affects both. For example, [[William III of England]] set sail from the Netherlands on 11 November 1688 (Gregorian calendar) and arrived at [[Brixham]] in England on 5 November 1688 (Julian calendar).

[[William Shakespeare|Shakespeare]] and [[Miguel de Cervantes|Cervantes]] seemingly died on exactly the same date (23 April 1616), but Cervantes predeceased Shakespeare by ten days in real time (as Spain used the Gregorian calendar, but Britain used the Julian calendar). This coincidence encouraged [[UNESCO]] to make 23 April the [[World Book and Copyright Day]].

Astronomers avoid this ambiguity by the use of the [[Julian day number]].

For dates before the year 1, unlike the proleptic Gregorian calendar used in the [[international standard]] [[ISO 8601]], the traditional proleptic Gregorian calendar (like the Julian calendar) does not have a [[year zero|year 0]] and instead uses the ordinal numbers 1, 2, ... both for years AD and BC. Thus the traditional time line is 2 BC, 1 BC, AD 1, and AD 2. ISO 8601 uses astronomical year numbering which includes a year 0 and negative numbers before it. Thus the ISO 8601 time line is {{nowrap|−0001}}, 0000, 0001, and 0002.

{{anchor|Month|Months of the year}}

==Months==
The Gregorian calendar continued to employ the [[Julian calendar|Julian]] months, which have Latinate names and irregular numbers of [[day]]s:

* [[January]] (31 days), from Latin ''{{lang|la|mēnsis Iānuārius}}'', "Month of [[Janus (mythology)|Janus]]",<ref name=janoed>{{citation |contribution=January, ''n.'' |contribution-url=http://www.oed.com/view/Entry/100755 |title=Oxford English Dictionary |url=http://www.oed.com/ |location=Oxford |publisher=Oxford University Press }}.</ref> the [[Roman mythology|Roman god]] of gates, doorways, beginnings and endings
* [[February]] (28 days in [[common year|common]] and 29 in [[leap year]]s), from Latin ''{{lang|la|mēnsis Februārius}}'', "Month of the [[Februa]]", the [[Roman festivals|Roman festival]] of purgation and purification,<ref name=foed>{{citation |contribution=February, ''n.'' |contribution-url=http://www.oed.com/view/Entry/68878 |title=Oxford English Dictionary }}.</ref><ref name=oe>{{citation |last=Liberman |first=Anatoly |date=7 March 2007 |contribution=On a Self-Congratulatory Note |contribution-url=http://blog.oup.com/2007/03/on_a_self_congr |title=Oxford Etymologist Archives |url=https://blog.oup.com/category/series-columns/oxford_etymologist/ |publisher=Oxford University Press |location=Oxford }}.</ref> [[cognate word|cognate]] with [[fever]],<ref name=foed/> the [[Etruscan mythology|Etruscan]] [[death god]] [[Februus]] ("Purifier"),{{citation needed|date=February 2017}} and the [[Proto-Indo-European language|PIE]] word for [[sulfur]]<ref name=foed/>
* [[March (month)|March]] (31 days), from Latin ''{{lang|la|mēnsis Mārtius}}'', "Month of [[Mars (mythology)|Mars]]",<ref name=maroed>{{citation |contribution=March, ''n.'' |contribution-url=http://www.oed.com/view/Entry/113951 |title=Oxford English Dictionary }}.</ref> the Roman [[war god]]<ref name=oe/>
* [[April (month)|April]] (30 days), from Latin ''{{lang|la|mēnsis Aprīlis}}'', of uncertain meaning<ref name=aproed>{{citation |contribution=April, ''n.'' |contribution-url=http://www.oed.com/view/Entry/9939 |title=Oxford English Dictionary }}.</ref> but usually derived from some form of the verb ''{{lang|la|aperire}}'' ("to open"){{refn|It's not unusual for month names to be based on natural descriptions but this etymology is sometimes doubted since no other ''Roman'' months have such names.<ref name=oe/>}} or the name of the goddess [[Aphrodite]]<ref name=oe/>{{refn|This derivation was apparently a popular one in ancient Rome, given by [[Plutarch]]<ref>{{citation |author=[[Plutarch]] |url=http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Numa*.html#Romulan_year |title=Life of Numa |at=Ch. xix }}.</ref> but rejected by [[Varro]] and [[Cincius]].{{where?|date=February 2017}}<ref>
*{{citation |last=Scullard |title=Festivals and Ceremonies of the Roman Republic |p=96}}.
*{{citation |last=Forsythe |title=Time in Roman Religion |p=10}}.</ref>}}
* [[May (month)|May]] (31 days), from Latin ''{{lang|la|mēnsis Māius}}'', "Month of [[Maia Maiestas|Maia]]",<ref name=mayoed>{{citation |contribution=May, ''n.'' |contribution-url=http://www.oed.com/view/Entry/115285 |title=Oxford English Dictionary }}.</ref> a Roman [[vegetation goddess]]<ref name=oe/> whose name is cognate with Latin ''{{lang|la|magnus}}'' ("great")<ref name=mayoed/> and English ''major''
* [[June (month)|June]] (30 days), from Latin ''{{lang|la|mēnsis Iūnius}}'', "Month of [[Juno (mythology)|Juno]]",<ref name=junoed>{{citation |contribution=June, ''n.'' |contribution-url=http://www.oed.com/view/Entry/102068 |title=Oxford English Dictionary }}.</ref> the Roman goddess of [[marriage in ancient Rome|marriage]], [[childbirth goddess|childbirth]], and rule<ref name=oe/>
* [[July]] (31 days), from Latin ''{{lang|la|mēnsis Iūlius}}'', "Month of [[Julius Caesar]]", the month of Caesar's birth, instituted in 44{{nbsp}}{{sc|bc}}<ref name=juloed>{{citation |contribution=July, ''n.'' |contribution-url=http://www.oed.com/view/Entry/102005 |title=Oxford English Dictionary }}.</ref> as part of [[Julian calendar|his calendrical reforms]]<ref name=oe/>
* [[August (month)|August]] (31 days), from Latin ''{{lang|la|mēnsis Augustus}}'', "Month of [[Augustus]]", instituted by Augustus in 8{{nbsp}}{{sc|bc}} in agreement with July and from the occurrence during the month of several important events during his rise to power<ref name=augoed>{{citation |contribution=August, ''n.'' |contribution-url=http://www.oed.com/view/Entry/13110 |title=Oxford English Dictionary }}.</ref> 
* [[September]] (30 days), from Latin ''{{lang|la|mēnsis september}}'', "seventh month", of the ten-month Roman year of [[Romulus]] {{circa|750}}{{nbsp}}{{sc|bc}}<ref name=septoed>{{citation |contribution=September, ''n.'' |contribution-url=http://www.oed.com/view/Entry/176171 |title=Oxford English Dictionary }}.</ref>
* [[October]] (31 days), from Latin ''{{lang|la|mēnsis octōber}}'', "eighth month", of the ten-month Roman year of Romulus {{circa|750}}{{nbsp}}{{sc|bc}}<ref name=ooed>{{citation |contribution=October, ''n.'' |contribution-url=http://www.oed.com/view/Entry/130330 |title=Oxford English Dictionary }}.</ref>
* [[November]] (30 days), from Latin ''{{lang|la|mēnsis november}}'', "ninth month", of the ten-month Roman year of Romulus {{circa|750}}{{nbsp}}{{sc|bc}}<ref name=noed>{{citation |contribution=November, ''n.'' |contribution-url=http://www.oed.com/view/Entry/130330 |title=Oxford English Dictionary }}.</ref>
* [[December]] (31 days), from Latin ''{{lang|la|mēnsis december}}'', "tenth month", of the ten-month Roman year of Romulus {{circa|750}}{{nbsp}}{{sc|bc}}<ref name=doed>{{citation |contribution=December, ''n.'' |contribution-url=http://www.oed.com/view/Entry/48106 |title=Oxford English Dictionary }}.</ref>

Europeans sometimes attempt to remember the number of days in each month by memorizing some form of the traditional verse "[[Thirty Days Hath September]]". It appears in Latin,<ref>
*{{citation |last=Ballew |first=Pat |contribution=On This Day in Math |contribution-url=http://pballew.blogspot.com/2015/09/on-this-day-in-math-september-1.html |url=http://pballew.blogspot.com/ |title=Pat's Blog |date=1 September 2015 }}.
*{{citation |author=Anianus |title=Computus Metricus Manualis |location=Strasbourg }}. {{la icon}}</ref> Italian,<ref name=i4d>{{citation |url=https://books.google.com/books?id=Ek2LCwAAQBAJ&printsec=frontcover |pp=[https://books.google.com/books?id=Ek2LCwAAQBAJ&pg=PT101 101–2] |title=Italian for Dummies |last=Onofri |first=Francesca Romana |author2=Karen Antje Moller |author3=Teresa L. Picarazzi |display-authors=1 |publisher=Berlitz |date=2012 |isbn=9781118258767 }}.</ref> and French,<ref>{{citation |p=[https://books.google.com/books?id=jWtIAAAAYAAJ&pg=PA11 11] |last=Bond |first=Otto Ferdinand |author2=Hilda Laura Norman |display-authors=1 |title=Military Manual of Elementary French |date=1918 |publisher=E.L. Steck |location=[[Austin, Texas|Austin]] }}.</ref> and belongs to a broad [[oral tradition]] but the earliest currently attested form of the poem is the English [[marginalia]] inserted into a [[calendar of saints]] {{c.|1425}}:<ref name=tto>{{citation |last=Bryan |first=Roger |date=30 October 2011 |contribution=The Oldest Rhyme in the Book |contribution-url=http://www.thetimes.co.uk/tto/life/article3209766.ece |title=The Times |publisher=Times Newspapers |location=London |url=http://www.thetimes.co.uk/ |ref={{harvid|Bryan|2011b}} }}.</ref><ref>
*{{citation |last=Misstear |first=Rachael |contribution=Welsh Author Digs Deep to Find Medieval Origins of Thirty Days Hath Verse |contribution-url=https://web.archive.org/web/20120206080222/http://www.walesonline.co.uk/news/need-to-read/2012/01/16/welsh-author-digs-deep-to-find-medieval-origins-of-thirty-days-hath-verse-91466-30128447 |date=16 January 2012 |title=Wales Online |location= |publisher=Media Wales }}.
*{{citation |title=Today |publisher=BBC Radio 4 |location=London |contribution=Memorable Mnemonics |contribution-url=http://news.bbc.co.uk/today/hi/today/newsid_9651000/9651594.stm |date=30 November 2011 }}.</ref>

{|
|-
| <blockquote>{{nowrap|Thirti dayes hath novembir}}<br>{{nowrap|April june and Septembir.}}<br>{{nowrap|Of xxviij is but oon}}<br>{{nowrap|And alle the remenaunt xxx and j<ref name=tto/>}}</blockquote>
| {{gaps|{{nbsp}}|{{nbsp}}|gap=8em}}
| <blockquote>{{nowrap|Thirty days have November,}}<br>{{nowrap|April, June, and September.}}<br>{{nowrap|Of 28 is but one}}<br>{{nowrap|And all the remnant 30 and 1.}}</blockquote>
|-
|}

[[File:Month - Knuckles (en).svg|thumb|The [[knuckle mnemonic]] for the days of the months of the year]]
Variations appeared in ''[[Mother Goose]]'' and continue to be taught at schools. The unhelpfulness of such involved [[mnemonic]]s has been parodied as "Thirty days hath September{{nbsp}}/ But all the rest I can't remember"<ref>{{citation |title=The Cincinnati Enquirer |date=20 September 1924 |location=Cincinnati |p=6 }}.</ref> but it has also been called "probably the only sixteenth-century poem most ordinary citizens know by heart".<ref name=holly>{{citation |last=Holland |first=Norman N. |location=New York |publisher=Columbia University Press |title=The Critical I |url=https://books.google.com/books?id=7uOdAwAAQBAJ&printsec=frontcover |date=1992 |p=[https://books.google.com/books?id=7uOdAwAAQBAJ&pg=PA64 64–5] |isbn=9780231076517 }}.</ref> A common nonverbal alternative is the [[knuckle mnemonic]], considering the [[knuckle]]s of one's [[hand]]s as months with 31 days and the lower spaces between them as the months with fewer days. Using two hands, one may start from either [[pinkie finger|pinkie]] knuckle as January and count across, omitting the space between the [[index finger|index]] knuckles (July and August). The same procedure can be done using the knuckles of a single hand, returning from the last (July) to the first (August) and continuing through. A similar mnemonic is to move up a [[musical keyboard|piano keyboard]] in [[semitone]]s from an F key, taking the white keys as the longer months and the black keys as the shorter ones.

{{anchor|Week}}

==Weeks==
{{Main|Seven-day week}}
In conjunction with the system of months there is a system of [[week]]s. A physical or electronic calendar provides conversion from a given date to the [[weekday]], and shows multiple dates for a given weekday and month. [[Calculating the day of the week]] is not very simple, because of the irregularities in the Gregorian system. When the Gregorian calendar was adopted by each country, the weekly cycle continued uninterrupted. For example, in the case of the few countries that adopted the reformed calendar on the date proposed by Gregory XIII for the calendar's adoption, Friday, 15 October 1582, the preceding date was Thursday, 4 October 1582 (Julian calendar).

Opinions vary about the numbering of the days of the week. [[ISO 8601]], in common use worldwide, starts with Monday=1; printed monthly calendar grids often list Mondays in the first (left) column of dates and Sundays in the last. In North America, the week typically begins on Sunday and ends on Saturday.

==Accuracy==
The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 [[solar time|mean solar days]] long.<ref>Seidelmann (1992), pp. 580–581.</ref> This approximation has an error of about one day per 3,030 years<ref>Using value from Richards (2013, p. 587) for tropical year in mean solar days, the calculation is {{nowrap|1/(365.2425-365.24217)}}</ref> with respect to the current value of the [[mean tropical year]]. However, because of the [[Axial precession (astronomy)|precession of the equinoxes]], which is not constant, and the movement of the [[perihelion]] (which affects the Earth's orbital speed) the error with respect to the ''astronomical'' vernal equinox is variable; using the average interval between vernal equinoxes near 2000 of 365.24237 days<ref>Meeus and Savoie (1992), p. 42</ref> implies an error closer to 1 day every 7,700 years. By any criterion, the Gregorian calendar is substantially more accurate than the 1 day in 128 years error of the Julian calendar (average year 365.25 days).

In the 19th century, Sir [[John Herschel]] proposed a modification to the Gregorian calendar with 969 leap days every 4000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period.<ref>John Herschel, [http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-94926 ''Outlines of Astronomy''], 1849, p. 629.</ref> This would reduce the average year to 365.24225 days. Herschel's proposal would make the year 4000, and multiples thereof, common instead of leap. While this modification has often been proposed since, it has never been officially adopted.<ref>{{cite book|author=Steel, Duncan|title=Marking Time: The Epic Quest to Invent the Perfect Calendar|year=2000|publisher=John Wiley & Sons|isbn=978-0-471-29827-4|page=185|url=https://books.google.com/books?id=rxvVdXyr_hMC&lpg=PA152&pg=PA185#v=onepage}}</ref>

On time scales of thousands of years, the Gregorian calendar falls behind the astronomical seasons. This is because [[Earth's rotation#Changes|the Earth's speed of rotation is gradually slowing down]], which makes each day slightly longer over time (see [[tidal acceleration]] and [[leap second]]) while the year maintains a more uniform duration.

===Calendar seasonal error===
[[File:Gregoriancalendarleap solstice.svg|frameless|upright=3.65|Gregorian calendar seasons difference]]

This image shows the difference between the Gregorian calendar and the astronomical seasons.

The ''y''-axis is the date in June and the ''x''-axis is Gregorian calendar years.

Each point is the date and time of the [[Solstice|June solstice]] in that particular year. The error shifts by about a quarter of a day per year. Centurial years are ordinary years, unless they are divisible by 400, in which case they are leap years. This causes a correction in the years 1700, 1800, 1900, 2100, 2200, and 2300.

For instance, these corrections cause 23 December 1903 to be the latest December solstice, and 20 December 2096 to be the earliest solstice—about 2.35 days of variation compared with the seasonal event.

==Proposed reforms==
The following are [[Calendar reform|proposed reforms]] of the Gregorian calendar:
* [[Holocene calendar]]
* [[International Fixed Calendar]] (also called the ''International Perpetual calendar'')
* [[World Calendar]]
* [[World Season Calendar]]
* [[Leap week calendar]]s
** [[Pax Calendar]]
** [[Symmetry454]]
** [[Hanke–Henry Permanent Calendar]]

==See also==
{{Portal|Christianity}}
*[[Calendar (New Style) Act 1750]]
*[[Calendar reform]]
*[[Conversion between Julian and Gregorian calendars]]
*[[Doomsday rule]]
*[[French revolutionary calendar]]
*[[Hebrew calendar]]
*[[Islamic calendar]]
*[[s:Translation:Inter gravissimas|Inter gravissimas in English]] – Wikisource
*[[Julian day]]
*[[History of calendars]]
* [[ISO 8601]], an international standard for the representation of dates and times, which uses the Gregorian calendar (see Section 3.2.1).
*[[List of adoption dates of the Gregorian calendar per country]]
*[[List of calendars]]
*[[Old Calendarists]]
**[[Greek Old Calendarists]]
*[[Revised Julian calendar]] (Milanković) – used in Eastern Orthodoxy
'''Precursors of the Gregorian reform'''
* [[Johannes de Sacrobosco]], ''De Anni Ratione'' ("On reckoning the years"), c. 1235
* [[Roger Bacon]], ''[[Opus Majus]]'' ("Greater Work"), c. 1267

==Notes==
{{notelist}}
{{reflist|group=Note}}

==Citations==
{{Reflist|30em}}

==References==
*Barsoum, Ignatius A. (2003). ''The Scattered Pearls''. Piscataway: Georgias Press.
*Blackburn, B. & Holford-Strevens, L. (1999). ''The Oxford Companion to the Year''. Oxford University Press. {{ISBN|0-19-214231-3}}.
*Blackburn, B. & Holford-Strevens, L. (2003). ''The Oxford Companion to the Year: An exploration of calendar customs and time-reckoning'', Oxford University Press.
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==External links==
* {{In Our Time|Gregorian calendar|p00548m9|Gregorian_calendar}}
* [http://www.fourmilab.ch/documents/calendar/ Calendar Converter]
* [http://www.bluewaterarts.com/calendar/NewInterGravissimas.htm Inter Gravissimas (Latin and French plus English)]
* [http://webexhibits.org/calendars/year-history.html History of Gregorian Calendar]
* [http://www.norbyhus.dk/calendar.php The Perpetual Calendar Gregorian Calendar adoption dates for many countries. ]
* [http://www.recordholders.org/en/records/dates.html World records for mentally calculating the day of the week in the Gregorian Calendar ]
* [http://www.tondering.dk/claus/calendar.html The Calendar FAQ] – Frequently Asked Questions about Calendars
* [http://curiousnotions.com/todays-date Today's date (Gregorian) in over 800 more-or-less obscure foreign languages]

{{calendars}}
{{Time Topics}}
{{Time measurement and standards}}
{{Chronology}}
{{Time in religion and mythology}}

{{Authority control}}

{{DEFAULTSORT:Gregorian Calendar}}
[[Category:Gregorian calendar| ]]
[[Category:1582 establishments]]
[[Category:Articles which contain graphical timelines]]
[[Category:1582 establishments in Europe]]