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{{Short description|Calendar introduced by Julius Caesar in 45 BC}}
{{about|a calendar used for civil and liturgical purposes|the day-number calendar used for astronomical and historical calculations|Julian day|day of year|Ordinal date|the terms 'Julian date' and 'Julian Period'|Julian day}}
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{| {{Table|class=floatright}}
! Calendar !! Today
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! Gregorian
| {{#time:j F Y|{{JULIANDAY.TIMESTAMP|{{JULIANDAY|{{CURRENTYEAR}}|{{CURRENTMONTH}}|{{CURRENTDAY}}}}}}}}
|-
! Julian
| {{#time:j F Y|{{JULIANDAY.TIMESTAMP|{{JULIANDAY|{{CURRENTYEAR}}|{{CURRENTMONTH}}|{{CURRENTDAY}}}}-13}}}}
|}

The '''Julian calendar''', proposed by [[Julius Caesar]] in {{auc|46|BC}}, was a reform of the [[Roman calendar]].{{sfn|Richards|2013|p = 595}} It took effect on {{nowrap|1 January {{auc|45|BC}}}}, by edict. It was designed with the aid of [[Greek mathematics|Greek mathematicians]] and [[Greek astronomy|astronomers]] such as [[Sosigenes of Alexandria]].

The calendar became the predominant calendar in the [[Roman Empire]] and subsequently most of the [[Western world]] for more than 1,600 years until 1582, when [[Pope Gregory XIII]]  promulgated [[#Replacement by the Gregorian calendar|a minor modification]] to reduce the average length of the year from 365.25 days to 365.2425 days and thus corrected the Julian calendar's drift against the [[solar year]]. [[adoption of the Gregorian calendar|Worldwide adoption]] of this revised calendar, which became known as the [[Gregorian calendar]], took place over the subsequent centuries, first in [[Catholic]] countries, and subsequently in [[Protestant]] countries of the [[Western Christianity|Western Christian world]].

The Julian calendar is still used in parts of the [[Eastern Orthodox Church]] and in parts of [[Oriental Orthodoxy]] as well as by the [[Berbers]].<ref>{{Cite web |url=https://www.dailysabah.com/africa/2018/01/12/berbers-mark-new-year-in-algeria-welcoming-2968 |title=Berbers mark New Year in Algeria, welcoming 2968 |date=12 January 2018 |access-date=25 June 2019 |quote=The Berber calendar is an agrarian system, based around the seasons and agricultural work, that was inspired by the Julian calendar.}}</ref>

The Julian calendar has two types of years: a normal year of 365 days and a leap year of 366 days. They follow a simple cycle of three normal years and one leap year, giving an average year that is 365.25 days long. That is more than the actual [[solar year]] value of 365.24219 days (the current value, which varies) which means the Julian calendar gains a day every 128 years. For any given event during the years from 1901 to 2099 inclusive, its date according to the Julian calendar is 13 days behind its corresponding Gregorian date.

==Table of months==
{| class="wikitable" style="margin:auto;"
|-
! Months (Roman) || Lengths before 45&nbsp;BC || Lengths as of 45&nbsp;BC || Months (English)
|- align="center"
|[[Ianuarius]]<ref name="J">The letter [[J]] was not invented until the 16th century.</ref>|| 29 || 31 ||January
|- align="center"
|[[Februarius]]|| 28 (in common years)<br />In [[Leap year|intercalary years]]:<br />23 if Intercalaris is variable<br />23–24 if Intercalaris is fixed || 28 (leap years: 29) ||February
|- align="center"
|[[Intercalaris]] (Mercedonius) (only in intercalary years)|| 27 (or possibly 27–28) || – || —
|- align="center"
|[[Martius (month)|Martius]]|| 31 || 31 ||March
|- align="center"
|[[Aprilis]]|| 29 || 30 ||April
|- align="center"
|[[Maius]]|| 31 || 31 ||May
|- align="center"
|[[Iunius (month)|Iunius]]<ref name="J" />|| 29 || 30 ||June
|- align="center"
|[[Quintilis]]<ref>The spelling ''Quinctilis'' is also attested; see page 669 of ''The Oxford Companion to the Year''.</ref> (Iulius) || 31 || 31 ||July
|- align="center"
|[[Sextilis]] (Augustus) || 29 || 31 ||August
|- align="center"
|[[September (Roman month)|September]]|| 29 || 30 ||September
|- align="center"
|[[October (Roman month)|October]]|| 31 || 31 ||October
|- align="center"
|[[November (Roman month)|November]]|| 29 || 30 ||November
|- align="center"
|[[December (Roman month)|December]]|| 29 || 31 ||December
|- align="center"
|'''Total'''|| 355 or 377–378 || 365–366 ||| 365–366
|}

=={{anchor|Motivation}}History==
===Motivation===
The ordinary year in the previous Roman calendar consisted of 12 months, for a total of 355 days. In addition, a 27- or 28-day [[intercalary month]], the [[Mercedonius|Mensis Intercalaris]], was sometimes inserted between February and March. This intercalary month was formed by inserting 22 or 23 days after the first 23 days of February; the last five days of February, which counted down toward the start of March, became the last five days of Intercalaris. The net effect was to add 22 or 23 days to the year, forming an intercalary year of 377 or 378 days.<ref>T H Key, "A Dictionary of Greek and Roman Antiquities" (article ''Calendarium''), London, 1875, available at [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Calendarium.html].</ref> Some say the ''mensis intercalaris'' always had 27 days and began on either the first or the second day after the Terminalia (23 February).<ref>Blackburn, B & Holford-Strevens, L ''The Oxford Companion to the Year'', Oxford University Press, 1999, reprinted with corrections, 2003, pp. 669–70.</ref>

According to the later writers [[Censorinus]] and [[Macrobius]], the ideal intercalary cycle consisted of ordinary years of 355 days alternating with intercalary years, alternately 377 and 378 days long. In this system, the average Roman year would have had {{frac|366|1|4}} days over four years, giving it an average drift of one day per year relative to any [[solstice]] or equinox. Macrobius describes a further refinement whereby, in one 8-year period within a 24-year cycle, there were only three intercalary years, each of 377 days (thus 11 intercalary years out of 24). This refinement averages the length of the year to 365.25 days over 24 years.

In practice, intercalations did not occur systematically according to any of these ideal systems, but were determined by the [[Pontifex Maximus|pontifices]]. So far as can be determined from the historical evidence, they were much less regular than these ideal schemes suggest. They usually occurred every second or third year, but were sometimes omitted for much longer, and occasionally occurred in two consecutive years.

If managed correctly this system could have allowed the Roman year to stay roughly aligned to a tropical year. However, since the pontifices were often politicians, and because a Roman magistrate's term of [[official|office]] corresponded with a calendar year, this power was prone to abuse: a pontifex could lengthen a year in which he or one of his political allies was in office, or refuse to lengthen one in which his opponents were in power.<ref>Censorinus, [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Censorinus/text*.html#20.7 ''De die natali'' 20.7] (Latin)</ref>

If too many intercalations were omitted, as happened after the [[Second Punic War]] and during the [[Roman civil wars|Civil Wars]], the calendar would drift out of alignment with the tropical year. Moreover, because intercalations were often determined quite late, the average Roman citizen often did not know the date, particularly if he were some distance from the city. For these reasons, the last years of the pre-Julian calendar were later known as "years of confusion". The problems became particularly acute during the years of Julius Caesar's pontificate before the reform, 63–46&nbsp;BC, when there were only five intercalary months (instead of eight), none of which were during the five Roman years before 46&nbsp;BC.

Caesar's reform was intended to solve this problem permanently, by creating a calendar that remained aligned to the sun without any human intervention. This proved useful very soon after the new calendar came into effect. [[Varro]] used it in 37&nbsp;BC to fix calendar dates for the start of the four seasons, which would have been impossible only 8 years earlier.<ref name="Varro">Varro, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Varro/de_Re_Rustica/1*.html#28 ''On Agriculture'' I.1.28.]</ref> A century later, when [[Pliny the Elder|Pliny]] dated the [[winter solstice]] to 25 December because the sun entered the 8th degree of Capricorn on that date,<ref>Pliny, ''Natural History:'' [https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D18%3Achapter%3D59 ''(Book 18, LIX / LXVI / LXVIII / LXXIV)''.]</ref> this stability had become an ordinary fact of life.

=== Context of the reform ===
Although the approximation of {{frac|365|1|4}} days for the tropical year had been known for a long time,<ref>{{cite journal|first=R. A.|last=Parker|title=Ancient Egyptian Astronomy|journal=Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences|volume=276|issue=1257|date=May 1974|pages=51–65|jstor=74274}}</ref> ancient [[solar calendar]]s had used less precise periods, resulting in gradual misalignment of the calendar with the seasons.

The [[octaeteris]], a cycle of eight [[Lunar calendar|lunar years]] popularised by [[Cleostratus]] (and also commonly attributed to [[Eudoxus of Cnidus|Eudoxus]]) which was used in some early Greek calendars, notably in [[Attic calendar|Athens]], is 1.53 days longer than eight [[Julian year (astronomy)|mean Julian years]]. The length of nineteen years in the [[Metonic cycle|cycle of Meton]] was 6,940 days, six hours longer than the mean Julian year. The mean Julian year was the basis of the [[Callippic cycle|76-year cycle]] devised by [[Callippus]] (a student under Eudoxus) to improve the Metonic cycle.

In Persia (Iran) after the reform in the [[Iranian calendars#Old Persian calendar|Persian calendar]] by introduction of the Persian Zoroastrian (i. e. Young Avestan) calendar in 503&nbsp;BC and afterwards, the first day of the year (1 Farvardin=[[Nowruz]]) slipped against the [[March equinox|vernal equinox]] at the rate of approximately one day every four years.<ref>Hartner, Willy. "The young Avestan and Babylonian calendars and the antecedents of precession." Journal for the History of Astronomy 10 (1979): 1. pp.&nbsp;1–22. [[doi:10.1177/002182867901000102]]</ref><ref>Stern, Sacha. ''Calendars in antiquity: Empires, states, and societies''. Oxford University Press, 2012., p. 178.</ref>

Likewise in the [[Egyptian calendar]], a fixed year of 365 days was in use, drifting by one day against the sun in four years. An unsuccessful attempt to add an extra day every fourth year was made in 238&nbsp;BC ([[Decree of Canopus]]). Caesar probably experienced this "wandering" or "vague" calendar in that country. He landed in the Nile delta in October 48&nbsp;BC and soon became embroiled in the Ptolemaic dynastic war, especially after [[Cleopatra VII|Cleopatra]] managed to be "introduced" to him in [[Alexandria]].

Caesar imposed a peace, and a banquet was held to celebrate the event.<ref name="Book 10">Lucan, ''[[Pharsalia]]:'' [http://mcllibrary.org/Pharsalia/book10.html ''Book 10''.]</ref> [[Lucan]] depicted Caesar talking to a wise man called [[Acoreus]] during the feast, stating his intention to create a calendar more perfect than that of Eudoxus<ref name="Book 10" /> (Eudoxus was popularly credited with having determined the length of the year to be {{frac|365|1|4}} days).<ref>Émile Biémont, ''Rythmes du temps, astronomie et calendriers'', éd. De Boeck (Bruxelles), 2000 ({{ISBN|2-8041-3287-0}}), p. 224.</ref> But the war soon resumed and Caesar was attacked by the Egyptian army for several months until he achieved victory. He then enjoyed a long cruise on the Nile with Cleopatra before leaving the country in June 47&nbsp;BC.<ref>Suetonius, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Julius*.html#52 ''Caesar'' 52.1.] {{Webarchive|url=https://archive.is/20120530163202/http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Julius*.html#52 |date=2012-05-30 }}</ref>

Caesar returned to Rome in 46&nbsp;BC and, according to [[Plutarch]], called in the best philosophers and mathematicians of his time to solve the problem of the calendar.<ref>Plutarch, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Caesar*.html#59 ''Lives of the Noble Grecians and Romans'': Caesar 59].</ref> Pliny says that Caesar was aided in his reform by the astronomer [[Sosigenes of Alexandria]]<ref>Pliny, ''Natural History:'' [https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D18%3Achapter%3D57 ''(Book 18, LVII)''.]</ref> who is generally considered the principal designer of the reform. Sosigenes may also have been the author of the astronomical almanac published by Caesar to facilitate the reform.<ref>Encyclopædia Britannica [http://www.britannica.com/EBchecked/topic/555018/Sosigenes-of-Alexandria Sosigenes of Alexandria].</ref> Eventually, it was decided to establish a calendar that would be a combination between the old Roman months, the fixed length of the Egyptian calendar, and the {{frac|365|1|4}} days of Greek astronomy. According to Macrobius, Caesar was assisted in this by a certain Marcus Flavius.<ref>Macrobius, [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.2 ''Saturnalia'' I.14.2] (Latin).</ref>

=== Adoption of the Julian calendar ===
{{more citations needed section|date=December 2013}}
Caesar's reform only applied to the [[Roman calendar]]. However, in the following decades many of the local civic and provincial calendars of the empire and neighbouring client kingdoms were aligned to the Julian calendar by transforming them into calendars with years of 365 days with an extra day intercalated every four years.<ref>This section is based on S. Stern, ''Calendars in Antiquity'' (OUP 2012) pp. 259–297.</ref><ref>{{Cite book|url=https://books.google.com/books?id=tiMZAI4oS-MC|title=Calendars in Antiquity: Empires, States, and Societies|last=Stern|first=Sacha|date=2012|publisher=OUP Oxford|isbn=978-0-19-958944-9|pages=259–297|language=en}}</ref> The reformed calendars typically retained many features of the unreformed calendars. In many cases, the New Year was not on 1 January, the leap day was not on the bissextile day, the old month names were retained, the lengths of the reformed months did not match the lengths of Julian months, and, even if they did, their first days did not match the first day of the corresponding Julian month. Nevertheless, since the reformed calendars had fixed relationships to each other and to the Julian calendar, the process of converting dates between them became quite straightforward, through the use of conversion tables known as ''hemerologia''.<ref>Studied in detail in W. Kubitschek, ''Die Kalendarbücher von Florenz, Rom und Leyden'' (Vienna, 1915).</ref> Several of the reformed calendars are only known through surviving hemerologia.

The three most important of these calendars are the [[Coptic calendar|Alexandrian calendar]], the [[Asian calendar]] and the [[Ancient Macedonian calendar|Syro-Macedonian]] calendar. Other reformed calendars are known from Cappadocia, Cyprus and the cities of Syria and Palestine. Most reformed calendars were adopted under Augustus, though the calendar of [[Nabatea]] was reformed after the kingdom became the Roman province of Arabia in AD 106. There is no evidence that local calendars were aligned to the Julian calendar in the western empire. Unreformed calendars continued to be used in [[Coligny calendar|Gaul]], Greece, Macedon, the Balkans and parts of Palestine, most notably in Judea.

The Alexandrian calendar adapted the Egyptian calendar by adding a 6th epagomenal day as the last day of the year in every fourth year, falling on 29 August preceding a Julian bissextile day. It was otherwise identical to the Egyptian calendar. The first leap day was in 22&nbsp;BC, and they occurred every four years from the beginning, even though Roman leap days occurred every three years at this time (see [[#Leap year error|Leap year error]]). This calendar influenced the structure of several other reformed calendars, such as those of the cities of Gaza and Ascalon in Palestine, Salamis in Cyprus, and the province of Arabia. It was adopted by the [[Coptic Orthodox Church of Alexandria|Coptic church]] and remains in use both as the liturgical calendar of the Coptic church and as the civil calendar of [[Ethiopia]].

The Asian calendar was an adaptation of the [[Ancient Macedonian calendar|Macedonian calendar]] used in the province of Asia and, with minor variations, in nearby cities and provinces. It is known in detail through the survival of decrees promulgating it issued in 8 BC by the proconsul [[Paullus Fabius Maximus]]. It renamed the first month Dios as ''Kaisar'', and arranged the months such that each month started on the ninth day before the kalends of the corresponding Roman month; thus the year began on 23 September, Augustus' birthday. Since Greek months typically had 29 or 30 days, the extra day of 31-day months was named ''Sebaste''—the emperor's day—and was the first day of these months. The leap day was a second Sebaste day in the month of Xandikos, i.e., 24 February. This calendar remained in use at least until the middle of the fifth century AD.

The Syro-Macedonian calendar was an adaptation of the Macedonian calendar used in Antioch and other parts of Syria. The months were exactly aligned to the Julian calendar, but they retained their Macedonian names and the year began in Dios = November until the fifth century, when the start of the year was moved to Gorpiaios = September.

These reformed calendars generally remained in use until the fifth or sixth century. Around that time most of them were replaced as civil calendars by the Julian calendar, but with a year starting in September to reflect the year of the [[indiction]] cycle.

The Julian calendar spread beyond the borders of the Roman Empire through its use as the Christian liturgical calendar. When a people or a country was converted to Christianity, they generally also adopted the Christian calendar of the church responsible for conversion. Thus, Christian Nubia and Ethiopia adopted the Alexandrian calendar, while Christian Europe adopted the Julian calendar, in either the Catholic or Orthodox variant. Starting in the 16th century, European settlements in the Americas and elsewhere likewise inherited the Julian calendar of the mother country, until they adopted the Gregorian reform. The last country to adopt the Julian calendar was the Ottoman Empire, which used it for financial purposes for some time under the name [[Rumi calendar]] and dropped the "escape years" which tied it to Muslim chronology in 1840.

== Julian reform ==

=== Realignment of the year ===
The first step of the reform was to realign the start of the calendar year (1 January) to the tropical year by making {{auc|46|BC}} 445 days long, compensating for the intercalations which had been missed during Caesar's pontificate. This year had already been extended from 355 to 378 days by the insertion of a regular [[intercalary month]] in February. When Caesar decreed the reform, probably shortly after his return from the [[Battle of Thapsus|African campaign]] in late Quintilis (July), he added 67 more days by inserting two extraordinary intercalary months between November and December.<ref group="note">It is not known why he decided that 67 was the correct number of days to add, nor whether he intended to align the calendar to a specific astronomical event such as the winter solstice. [[Ideler]] suggested (''Handbuch der mathematischen und technischen Chronologie'' II 123–125) that he intended to align the winter solstice to a supposedly traditional date of 25 December. The number may compensate for three omitted intercalary months (67 = 22+23+22). It also made the distance from 1 March 46&nbsp;BC, the original New Years Day in the Roman calendar, to 1 January 45&nbsp;BC 365 days.</ref>

These months are called ''Intercalaris Prior'' and ''Intercalaris Posterior'' in letters of [[Cicero]] written at the time; there is no basis for the statement sometimes seen that they were called "[[Undecimber]]" and "[[Duodecember|Duodecimber]]", terms that arose in the 18th century over a millennium after the Roman Empire's collapse.<ref group="note">E.g., "... we have a sidelight on what was involved in "the year of confusion" as it was called. According to Dion Cassius, the historian, there was a governor in Gaul who insisted that, in the lengthened year, two months' extra taxes should be paid. The extra months were called Undecimber and Duodecimber." (P. W. Wilson, [https://books.google.com/books?id=9xcbAAAAYAAJ&q=undecimber+duodecimber ''The romance of the calendar''] (New York, 1937), 112). The eponymous dating of the cited passage ([https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/54*.html#21 Dio Cassius 54.21]) shows that it actually refers to an event of 15&nbsp;BC, not 46&nbsp;BC.</ref> Their individual lengths are unknown, as is the position of the [[Nones (calendar)|Nones]] and [[Ides (calendar)|Ides]] within them.<ref>J. Rüpke, ''The Roman Calendar from Numa to Constantine: Time, History and the Fasti'', 117f., suggests, based on the ritual structures of the calendar, that 5 days were added to November and that the two intercalary months each had 31 days, with Nones and Ides on the 7th and 15th.</ref>

Because 46&nbsp;BC was the last of a series of irregular years, this extra-long year was, and is, referred to as the "last year of confusion". The new calendar began operation after the realignment had been completed, in 45&nbsp;BC.<ref>[[William Smith (lexicographer)|William Smith]], ''[[Dictionary of Greek and Roman Antiquities]]:'' [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Calendarium.html#p231 Year of Julius Caesar]), following [[Ideler]], interprets Macrobius, [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.13 ''Saturnalia'' 1.14.13] (Latin) to mean that Caesar decreed that the first day of the new calendar began with the new moon which fell on the night of 1/2 January 45&nbsp;BC. 
<br>
The new moon was on 2 January 45&nbsp;BC (in the [[Proleptic Julian calendar]]) at 00:21 UTC, according to [[Institut de mécanique céleste et de calcul des éphémérides|IMCCE]] (a branch of the [[Paris Observatory]]): [http://bugle.imcce.fr/en/grandpublic/phenomenes/phases_lune/index.php ''Phases of the moon (between −4000 and +2500)''] {{webarchive|url=https://web.archive.org/web/20110720232543/http://bugle.imcce.fr/en/grandpublic/phenomenes/phases_lune/index.php|date=2011-07-20}}. This is in agreement with the [http://astropixels.com/ephemeris/phasescat/phases-0099.html historical moon phase tables by Fred Espenak] in which the new moon was on 2 January 45&nbsp;BC at 00:43 UTC. Espenek's table assumes that the first Julian year of 45 BC was a leap year. If the first year of 45 BC was not a leap year, there would be a day offset, and the new moon would have been on 1 January 45&nbsp;BC at 00:43 UTC.
<br>
Espnek's historical moon phase tables also indicate that there was a new moon on 1 March 45&nbsp;BC at 08:39 UTC ([[Calends|Kalends]] of March), quarter moon on 8 March 45&nbsp;BC at 09:00 UTC (a day after [[Roman calendar#Days|Nones of March]]), and full moon on 15 March 45&nbsp;BC at 07:19 UTC ([[Ides of March]]). Espenak's tables of the phases of the moon are based on computational procedures described in ''Astronomical Algorithms'' by [[Jean Meeus]] (Willmann-Bell, Inc., Richmond, 1998). 
<br>
More recent studies of the Macrobius manuscripts have shown that the word on which Idler's supposition is based, which was read as ''lunam'', should be read as ''linam'', meaning that Macrobius was simply stating that Caesar published an edict giving the revised calendar – see e.g., p.99 in the translation of Macrobius by P. Davies. 
<br>
Smith gives no source or justification for his other speculation that Caesar originally intended to commence the year precisely with the winter solstice.</ref>

=== Months ===

The Julian months were formed by adding ten days to a regular pre-Julian Roman year of 355 days, creating a regular Julian year of 365 days. Two extra days were added to January, Sextilis (August) and December, and one extra day was added to April, June, September, and November. February was not changed in ordinary years, and so continued to be the traditional 28 days. Thus, the ordinary (i.e., non-leap year) lengths of all of the months were set by the Julian calendar to the same values they still hold today. (See [[#Sacrobosco's incorrect theory on month lengths|Sacrobosco's incorrect theory on month lengths (below)]]  for stories purporting otherwise.)

The Julian reform did not change [[Roman calendar#Months|the method used to account days of the month in the pre-Julian calendar]], based on the Kalends, Nones and Ides, nor did it change the positions of these three dates within the months. Macrobius states that the extra days were added immediately before the last day of each month to avoid disturbing the position of the established religious ceremonies relative to the Nones and Ides of the month.<ref>Macrobius, [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.9 ''Saturnalia'' 1.14.9] (Latin). Exceptionally, the extra day in April was inserted as the 26th, a.d. VI Kal. Mai. in the Julian calendar, in order to avoid adding a day to the [[Floralia]], which ran from a.d. IV Kal. Mai. (27 April in the pre-Julian calendar) to a.d. V Non. Mai.</ref> However, since Roman dates after the Ides of the month counted down toward the start of the next month, the extra days had the effect of raising the initial value of the count of the day following the Ides in the lengthened months. Thus, in January, Sextilis and December the 14th day of the month became a.d. XIX Kal. instead of a.d. XVII Kal., while in April, June, September and November it became a.d. XVIII Kal.

Romans of the time born after the Ides of a month responded differently to the effect of this change on their birthdays. [[Mark Antony]] kept his birthday on 14 January, which changed its date from a.d. XVII Kal. Feb to a.d. XIX Kal. Feb, a date that had previously not existed. [[Livia]] kept the date of her birthday unchanged at a.d. III Kal. Feb., which moved it from 28 to 30 January, a day that had previously not existed. [[Augustus]] kept his on 23 September, but both the old date (a.d. VIII Kal. Oct.) and the new (a.d. IX Kal. Oct.) were celebrated in some places.

The inserted days were all initially characterised as ''dies fasti'' ('''F''' – see [[Roman calendar#Character of the day|Roman calendar]]).<ref>Macrobius, [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.12 ''Saturnalia'' 1.14.12] (Latin).</ref> The character of a few festival days was changed. In the early Julio-Claudian period a large number of festivals were decreed to celebrate events of dynastic importance, which caused the character of the associated dates to be changed to '''NP'''. However, this practice was discontinued around the reign of [[Claudius]], and the practice of characterising days fell into disuse around the end of the first century AD: the Antonine jurist [[Gaius (jurist)|Gaius]] speaks of ''dies nefasti'' as a thing of the past.<ref>A. K. Michels, ''The Calendar of the Roman Republic'' Appendix II; J. Rüpke, ''The Roman Calendar from Numa to Constantine'' 113–114, 126–132, 147.</ref>

=== Intercalation ===
The old intercalary month was abolished. The new leap day was dated as ''ante diem bis sextum Kalendas Martias'' ('the sixth doubled day before the Kalends of March'), usually abbreviated as ''a.d. bis VI Kal. Mart.''; hence it is called in English the [[bissextile]] day. The year in which it occurred was termed ''annus bissextus'', in English the bissextile year.

There is debate about the exact position of the bissextile day in the early Julian calendar. The earliest direct evidence is a statement of the 2nd century jurist [[Publius Iuventius Celsus|Celsus]], who states that there were two-halves of a 48-hour day, and that the intercalated day was the "posterior" half. An inscription from AD 168 states that ''a.d. V Kal. Mart.'' was the day after the bissextile day. The 19th century chronologist [[Christian Ludwig Ideler|Ideler]] argued that Celsus used the term "posterior" in a technical fashion to refer to the earlier of the two days, which requires the inscription to refer to the whole 48-hour day as the bissextile. Some later historians share this view. Others, following [[Theodor Mommsen|Mommsen]], take the view that Celsus was using the ordinary Latin (and English) meaning of "posterior". A third view is that neither half of the 48-hour "bis sextum" was originally formally designated as intercalated, but that the need to do so arose as the concept of a 48-hour day became obsolete.<ref>W. Sternkopf, "[https://books.google.com/books?id=MmPMaTG2ukYC&pg=PA718 Das Bissextum]", (JCP 41 (1895) 718–733).</ref>

There is no doubt that the bissextile day eventually became the earlier of the two days for most purposes. In 238 Censorinus stated that it was inserted after the [[Terminus (god)|Terminalia]] (23 February) and was followed by the last five days of February, i.e., a.d. VI, V, IV, III and prid. Kal. Mart. (which would be 24 to 28 February in a common year and the 25th to 29th in a leap year). Hence he regarded the bissextum as the first half of the doubled day. All later writers, including Macrobius about 430, [[Bede]] in 725, and other medieval [[computus|computists]] (calculators of Easter) followed this rule, as does the [[liturgical year|liturgical calendar]] of the Roman Catholic Church. However, Celsus' definition continued to be used for legal purposes. It was incorporated into [[Digest (Roman law)|Justinian's Digest]],<ref>Justinian, [http://webu2.upmf-grenoble.fr/Haiti/Cours/Ak/Anglica/D50_Scott.htm#XVI Digest 50.16.98].</ref> and in the English statute ''De anno et die bissextili'' of 1236,<ref>{{cite book |chapter-url=https://books.google.com/books?id=tKZFAAAAcAAJ&pg=PA20 |chapter=The statute ''De anno et die bissextili'', made at Westminster, Anno 21 Hen. III. and Anno Dom. 1236 |title=The Statutes at Large from Magna Charta to the End of the Reign of King Henry the Sixth |volume=1 |location=London |year=1763}}</ref> which was not formally repealed until 1879.

The effect of the bissextile day on the [[nundinal cycle]] is not discussed in the sources. According to Dio Cassius, a leap day was inserted in 41&nbsp;BC to ensure that the first market day of 40&nbsp;BC did not fall on 1 January, which implies that the old 8-day cycle was not immediately affected by the Julian reform. However, he also reports that in AD 44, and on some previous occasions, the market day was changed to avoid a conflict with a religious festival. This may indicate that a single nundinal letter was assigned to both halves of the 48-hour bissextile day by this time, so that the [[Regifugium]] and the market day might fall on the same date but on different days. In any case, the 8-day nundinal cycle began to be displaced by the 7-day [[Seven-day week|week]] in the first century AD, and [[dominical letter]]s began to appear alongside nundinal letters in the fasti.<ref>[https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/48*.html#33.4 Dio Cassius 48.33.4], [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/60*.html#24.7 60.24.7]; C. J. Bennett, "The Imperial Nundinal Cycle", ''Zeitschrift für Papyrologie und Epigraphik'' 147 (2004) 175–179.</ref>

During the late [[Middle Ages]] days in the month came to be numbered in consecutive day order. Consequently, the leap day was considered to be the last day in February in leap years, i.e., 29 February, which is its current position.

=== Sacrobosco's incorrect theory on month lengths ===
The Julian reform set the lengths of the months to their modern values. However, a different explanation for the lengths of Julian months, usually alleged to the 13th&nbsp;century scholar [[Sacrobosco]],<ref>{{cite magazine |first=Roscoe |last=Lamont |year=1919 |title=The Roman calendar and its reformation by Julius Caesar |magazine=[[Popular Astronomy (US magazine) |Popular Astronomy]] |volume=27 |pages=583–595, esp.&nbsp;585–587 |url=http://articles.adsabs.harvard.edu//full/1919PA.....27..579P/0000583.000.html}} Sacrobosco's theory is discussed on pages&nbsp;585–587.</ref> but also attested in 12th&nbsp;century works,<ref>{{cite book |last=Nothaft |first=C. Philipp E. |date=2018 |title=Scandalous Error: Calendar Reform and Calendrical Astronomy in Medieval Europe |publisher=Oxford University Press |page=122 |isbn=9780198799559 |doi=10.1093/oso/9780198799559.001.0001}}</ref> is still widely repeated, but is certainly wrong.

Allegedly according to Sacrobosco, the month lengths for ordinary years in the Roman Republican calendar were a standard lunar calendar, similar the Greek city calendars. From Ianuarius to December, the month lengths were:

:{| style="text-align:center;"
|-
| Ian || Feb || Mar || Apr || Mai || Iun || Qun || Sex || Sep || Oct || Nov || Dec || –
|-
| 30 || 29 || 30 || 29 || 30 || 29 || 30 || 29 || 30 || 29 || 30 || 29 || 11
|}

Sacrobosco then thought that Julius Caesar added one day to every month except Februarius, a total of 11&nbsp;more days to regular months, giving the ordinary Julian year of 365&nbsp;days. A single leap day could now be added to this extra-short Februarius:

:{| style="text-align:center;"
|-
| Ian || Feb || Mar || Apr || Mai || Iun || Qun || Sex || Sep || Oct || Nov || Dec 
|-
| 31 || 29<br>30 || 31 || 30 || 31 || 30 || 31 || 30 || 31 || 30 || 31 || 30
|}

He then said Augustus changed this, by taking one day from Februarius to add it to Sextilis, and then modifying the alternation of the following months, to:

:{| style="text-align:center;"
|-
| Ian || Feb || Mar || Apr || Mai || Iun || Qun<br>'''Iul''' || Sex<br>'''Aug''' || Sep || Oct || Nov || Dec 
|-
| 31 || '''28'''<br>29 || 31 || 30 || 31 || 30 || 31 || '''31''' || '''30''' || '''31''' || '''30''' || '''31''' 
|}

so that the length of ''Augustus'' (August) would not be shorter than (and therefore inferior to) the length of ''Iulius'' (July), giving us the irregular month lengths which are still in use.

Although plausible and filled with ingenious arithmetical organization, there is abundant evidence disproving this theory.

First, the ''[[Fasti Antiates Maiores]]'', a wall painting of a pre-Julian Roman calendar has survived.<ref>{{cite book |last=Grout |first=James |title=Fasti Antiates |publisher=penelope.uchicago.edu |url=http://penelope.uchicago.edu/~grout/encyclopaedia_romana/calendar/antiates.html}}</ref><ref>[[:c:File:Museo del Teatro Romano de Caesaraugusta.43.jpg|Reproduction of pre-Julian Roman calendar]]. Month lengths at bottom.</ref> That pre-Julian calendar confirms the literary accounts that the months were already irregular before Julius Caesar reformed them, with an ordinary year of 355&nbsp;days (not evenly divisible into Roman weeks), not 354, with month lengths arranged as:

:{| style="text-align:center;"
|-
| Ian || Feb || Mar || Apr || Mai || Iun || Qun || Sex || Sep || Oct || Nov || Dec || – 
|-
| 29 || 28 || 31 || 29 || 31 || 29 || 31 || 29 || 29 || 31 || 29 || 29 || 10 
|}

Also, the Julian reform did not change the dates of the [[Nones (calendar)|Nones]] and [[Ides (calendar)|Ides]]. In particular, the Ides were late (on the 15th rather than 13th) in March, May, July, and October, showing that these months always had 31&nbsp;days in the Roman calendar,<ref>{{cite book |author=Macrobius |url=https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#13.7 |title=Saturnalia'', 1.13.7'' |postscript=,}} {{cite book |url=https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.7 |title=1.14.7–8 |lang=Latin}}</ref><ref>{{cite book |author=Censorinus |url=https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Censorinus/text*.html#20.10 |title=De Die Natali |at=20.10 |lang=Latin |postscript=,}} {{cite web |url=http://elfinspell.com/ClassicalTexts/Maude/Censorinus/DeDieNatale-Part2.html#chap9 |title=(in English)}}</ref> whereas Sacrobosco's theory requires that March, May, and July were originally 30&nbsp;days long and that the length of October was changed from 29 to 30&nbsp;days by Caesar and to 31&nbsp;days by Augustus.

Further, Sacrobosco's theory is explicitly contradicted by the 3rd and 5th&nbsp;century authors Censorinus<ref>{{cite book |author=Censorinus |url=https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Censorinus/text*.html#20.9 |title=De Die Natali |at=20.9 |lang=Latin |postscript=,}} {{cite web |url=http://elfinspell.com/ClassicalTexts/Maude/Censorinus/DeDieNatale-Part2.html#chap9 |title=(in English)}}</ref> and Macrobius,<ref>{{cite book |author=Macrobius |url=https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.7 |title=Saturnalia |at=1.14.7 |lang=Latin}}</ref> and it is inconsistent with seasonal lengths given by Varro, writing in 37&nbsp;BCE,<ref name="Varro"/> before Sextilis was [[#Month names|renamed]] for Augustus in 8&nbsp;BCE, with the 31&nbsp;day Sextilis given by an Egyptian papyrus from 24&nbsp;BCE,<ref name="papyrus"/> and with the 28&nbsp;day Februarius shown in the ''Fasti Caeretani'', which is dated before 12&nbsp;BCE.<ref>{{cite book |first=A. |last=Degrassi |series=Inscriptiones Italiae |volume=XIII |title=Fasti et Elogia 2: Fasti Anni Numani et Iuliani; Accedunt Feralia, Menologia Rustica, Parapegmata |place=Rome |year=1963 |page=66 |lang=Latin}}</ref>

===Year length; leap years===
The Julian calendar has two types of year: "normal" years of 365 days and [[leap year|"leap" years]] of 366 days. There is a simple cycle of three "normal" years followed by a leap year and this pattern repeats forever without exception. The Julian year is, therefore, on average 365.25 days long. Consequently, the Julian year drifts over time with respect to the [[tropical year|tropical (solar) year]] (365.24217 days).<ref name="Richards">Using value from Richards (2013, p. 587) for tropical year in mean solar days, the calculation is {{nowrap|1/(365.2425-365.24217)}}</ref>

Although Greek astronomers had known, at least since [[Hipparchus]],<ref name=":0">[[Ptolemy|Claudius Ptolemy]], tr. [[G. J. Toomer]], ''[[Almagest|Ptolemy's Almagest]]'', 1998, Princeton University Press, p. 139. Hipparchus stated that the "solar year ... contains 365 days, plus a fraction which is less than {{sfrac|1|4}} by about {{sfrac|1|300}}th of the sum of one day and night".</ref> a century before the Julian reform, that the tropical year was slightly shorter than 365.25 days, the calendar did not compensate for this difference. As a result, the calendar year gains about three days every four centuries compared to observed [[equinox]] times and the seasons. This discrepancy was largely corrected by the [[Gregorian calendar|Gregorian reform]] of 1582. The Gregorian calendar has the same months and month lengths as the Julian calendar, but, in the Gregorian calendar, year numbers evenly divisible by 100 are not leap years, except that those evenly divisible by 400 remain leap years.<ref name=":1">[http://aa.usno.navy.mil/faq/docs/calendars.php Introduction to Calendars]. (15 May 2013). [[United States Naval Observatory]].</ref> (Even then, the Gregorian calendar diverges from astronomical observations by one day in 3,030 years.)<ref name=Richards />

The difference in the average length of the year between Julian (365.25 days) and Gregorian (365.2425 days) is 0.002%, making the Julian 10.8 minutes longer. The accumulated effect of this difference over some 1600 years since the basis for [[Computus|calculation of the date of Easter]] was [[First Council of Nicea#Separation of Easter computation from Jewish calendar|determined at the First Council of Nicea]] means for example that, from 29 February ''Julian'' (13 March ''Gregorian'') 1900 and until 28 February ''Julian'' (13 March ''Gregorian'') 2100, the ''Julian'' calendar is 13 days behind the ''Gregorian'' calendar; one day after (i.e. on 29 February ''Julian'' or 14 March ''Gregorian''), the difference will be 14 days.

== Leap year error ==
<!-- Linked from Roman calendar: Later reforms -->
Although the new calendar was much simpler than the pre-Julian calendar, the pontifices initially added a leap day every three years, instead of every four. There are accounts of this in Solinus,<ref>Gaius Julius Solinus, ''De mirabilibus mundi'', c.3, available at [https://books.google.com/books?id=ABxNAAAAcAAJ].</ref> Pliny,<ref>Gaius Plinius Secundus, ''Natural History'', Vol. 2, 18.57, tr. J Bostock and H T Riley, London 1855, available at [https://www.perseus.tufts.edu/hopper/text?doc=Plin.+Nat.+18.57&fromdoc=Perseus%3Atext%3A1999.02.0137].</ref> Ammianus,<ref>''The Roman History of Ammianus Marcellinus'', 26.10, Loeb Classical Library vol. II, Harvard 1940, available at [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Ammian/26*.html].</ref> Suetonius,<ref>Gaius Suetonius Tranquillus, ''Life of Julius Caesar'', 40.1, Loeb Classical Library, Harvard 1913, available at [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Julius*.html#ref38] {{Webarchive|url=https://archive.is/20120530163202/http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Julius*.html#ref38 |date=2012-05-30 }}.</ref> and Censorinus.<ref>Censorinus, ''The Natal Day'', 20.30, tr. William Maude, New York 1900 available at [http://elfinspell.com/ClassicalTexts/Maude/Censorinus/DeDieNatale-Part2.html#chap9].</ref>

Macrobius<ref>Macrobius Ambrosius Theodosius, ''Saturnalia'', 1.14.13–1.14.14, tr. Percival Vaughan Davies, New York 1969, Latin text at [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#14.13.]</ref> gives the following account of the introduction of the Julian calendar:
{{quote|text=Caesar's regulation of the civil year to accord with his revised measurement was proclaimed publicly by edict, and the arrangement might have continued to stand had not the correction itself of the calendar led the priests to introduce a new error of their own; for they proceeded to insert the intercalary day, which represented the four quarter-days, at the beginning of each fourth year instead of at its end, although the intercalation ought to have been made at the end of each fourth year and before the beginning of the fifth.

This error continued for thirty-six years by which time twelve intercalary days had been inserted instead of the number actually due, namely nine. But when this error was at length recognised, it too was corrected, by an order of Augustus, that twelve years should be allowed to pass without an intercalary day, since the sequence of twelve such years would account for the three days which, in the course of thirty-six years, had been introduced by the premature actions of the priests.}}
So, according to Macrobius,
# the year was considered to begin after the Terminalia (23 February),<ref>Marcus Terentius Varro, ''On the Latin Language'', 6.13, tr. Roland Kent, London 1938 available at [https://ryanfb.github.io/loebolus-data/L333.pdf].</ref>
# the calendar was operated correctly from its introduction on 1 January 45&nbsp;BC until the beginning of the fourth year (February 42&nbsp;BC) at which point the priests inserted the first intercalation,
# Caesar's intention was to make the first intercalation at the beginning of the fifth year (February 41&nbsp;BC),
# the priests made a further eleven intercalations after 42&nbsp;BC at three-year intervals so that the twelfth intercalation fell in 9&nbsp;BC,
# had Caesar's intention been followed there would have been intercalations every four years after 41&nbsp;BC, so that the ninth intercalation would have been in 9&nbsp;BC,
# after 9&nbsp;BC, there were twelve years without [[leap year]]s, so that the leap days Caesar would have had in 5&nbsp;BC, 1&nbsp;BC and AD&nbsp;4 were omitted and
# after AD&nbsp;4 the calendar was operated as Caesar intended, so that the next leap year was AD&nbsp;8 and then leap years followed every fourth year thereafter.<ref>Nautical Almanac Offices of the United Kingdom and the United States. (1961). ''Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac'', London: Her Majesty's Stationery Office. p. 410–11.</ref>

Some people have had different ideas as to how the leap years went. The above scheme is that of Scaliger (1583) in the table below. He established that the Augustan reform was instituted in AUC 746 (8&nbsp;BC). The table shows for each reconstruction the implied proleptic Julian date for the first day of Caesar's reformed calendar (Kal. Ian. AUC 709) and the first Julian date on which the Roman calendar date matches the Julian calendar after the completion of Augustus' reform.

Alexander Jones says that the correct Julian calendar was in use in Egypt in 24&nbsp;BC,<ref name="papyrus" /> implying that the first day of the reform in both Egypt and Rome, {{nowrap|1 January 45 BC}}, was the Julian date 1&nbsp;January if 45&nbsp;BC was a leap year and 2&nbsp;January if it was not. This necessitates fourteen leap days up to and including AD&nbsp;8 if 45&nbsp;BC was a leap year and thirteen if it was not.

Pierre Brind'Amour<ref>Pierre Brind'Amour, ''Le calendrier romain'', Ottawa 1983, pp. 45–46.</ref> argued that "only one day was intercalated between 1/1/45 and 1/1/40 (disregarding a momentary 'fiddling' in December of 41)<ref>Dio Cassius 48.33.4, tr. Earnest Cary, Loeb Classical Library, 9 vol., Harvard 1914–1927, available at [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Cassius_Dio/48*.html#33.4].</ref> to avoid the nundinum falling on Kal. Ian."<ref>Refutation of Brind'Amour's theory by John Ward, ''Re: Intercalation in 45BC to 8AD'', East Carolina University Calendar discussion List CALNDR-L, April 1998.</ref>

{|class="wikitable" style="margin:1em auto;text-align:center"
|-
! Scholar !! Date !! Triennial leap years (BC) !! First Julian day !! First aligned day !! Quadriennial leap year resumes
|-
|style="text-align:left"| Bennett<ref>C. J. Bennett, "The Early Augustan Calendars in Rome and Egypt", Zeitschrift fűr Papyrologie und Epigraphik 142 (2003) 221–240 and "The Early Augustan Calendars in Rome and Egypt: Addenda et Corrigenda", Zeitschrift fűr Papyrologie und Epigraphik 147 (2004) 165–168; see also Chris Bennett, [http://www.tyndalehouse.com/Egypt/ptolemies/chron/roman/024bc.htm A.U.C. 730 = 24 B.C. (Egyptian papyrus)].</ref>
| 2003
|style="text-align:left"| 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8 || 31 Dec 46 BC || 25 Feb 1 BC || AD 4
|-
|style="text-align:left"| Soltau<ref>W. Soltau, [https://books.google.com/books?id=dVs-AAAAYAAJ&pg=PA170#v=onepage&q&f=false ''Römische Chronologie''] (Freiburg, 1889) 170–173. He accepted Matzat's phase of the triennial cycle but argued that it was absurd to suppose that Caesar would have made the second Julian year a leap year and that the 36 years had to be accounted from 45&nbsp;BC.</ref>
| 1889
|style="text-align:left"| 45, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11 || 2 Jan 45 BC || 25 Feb AD 4 || AD 8
|-
|style="text-align:left"| Matzat<ref>H. Matzat, [https://archive.org/details/rmischechronolo02matzgoog/page/n197 <!-- pg=13 --> ''Römische Chronologie'' I] (Berlin, 1883), 13–18. His argument rested on [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/48*.html#33.4 Dio Cassius 48.33.4] which mentions a leap day inserted in 41&nbsp;BC, "contrary to the (i.e., Caesar's) rule", in order to avoid having a market day on the first day of 40&nbsp;BC. Dio stated that this leap day was compensated for "later". Matzat proposed this was done by omitting a scheduled leap day in 40&nbsp;BC, rather than by omitting a day from an ordinary year.</ref>
| 1883
|style="text-align:left"| 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11 || 1 Jan 45 BC || 25 Feb 1 BC || AD 4
|-
|style="text-align:left"| [[Ludwig Ideler|Ideler]]<ref>C. L. Ideler, [https://books.google.com/books?id=ql56SzvCeJMC&pg=PA130#v=onepage&q&f=false ''Handbuch der mathematischen und technischen Chronologie''] (Berlin, 1825) II 130–131. He argued that Caesar would have enforced the bissextile day by introducing it in his first reformed year. T. E. Mommsen, [https://archive.org/details/bub_gb_qsspAAAAYAAJ/page/n281 <!-- pg=282 --> ''Die Römische Chronologie bis auf Caesar''] (Berlin, 1859) 282–299, provided additional circumstantial arguments.</ref>
| 1825
|style="text-align:left"| 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9 || 1 Jan 45 BC || 25 Feb AD 4 || AD 8
|-
|style="text-align:left"| [[Johannes Kepler|Kepler]]<ref>J. Kepler, ''De Vero Anno Quo Æternus Dei Filius Humanan Naturam in Utero Benedictæ Virginis Mariæ Assumpsit'' (Frankfurt, 1614) Cap. V, repub. in F. Hammer (ed.), ''Johannes Keplers Gesammelte Werke'' (Berlin, 1938) V 28.</ref>
| 1614
|style="text-align:left"| 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10 || 2 Jan 45 BC || 25 Feb AD 4 || AD 8
|-
|style="text-align:left"| [[Thomas Harriot|Harriot]]<ref name="Harriot" />
| After 1610
|style="text-align:left"| 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10 || 1 Jan 45 BC || 25 Feb 1 BC || AD 4
|-
|style="text-align:left"| [[Heinrich Bünting|Bünting]]<ref name="Harriot">For the list of triennial leap years proposed by Bünting, Christmann and Harriot, see [http://www.hermetic.ch/cal_stud/cassidy/shspk1zc.pdf Harriot's comparative table reproduced by Simon Cassidy] (Fig. 6). The table numbers years as Julian years, where Julian year 1 = 45&nbsp;BC. Thus, Scaliger and Clavius (col. 7) resume intercalation in Julian year 53 = AD 8, while Bünting (col. 8) and Harriot (col. 3) resume it in Julian year 49 = AD 4 and Christmann (col. 9) in year 52 = AD 7.</ref>
| 1590
|style="text-align:left"| 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12 || 1 Jan 45 BC || 25 Feb 1 BC || AD 4
|-
|style="text-align:left"| [[Jakob Christmann|Christmann]]<ref name="Harriot" /><ref>J. Christmann [https://books.google.com/books?id=NTc6AAAAcAAJ&pg=PA173 ''Muhamedis Alfragani arabis chronologica et astronomica elementa''] (Frankfurt, 1590), 173. His argument assumed that the triennial cycle started in the third Julian year.</ref>
| 1590
|style="text-align:left"| 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10 || 2 Jan 45 BC || 25 Feb AD 4 || AD 7<ref name="Harriot" />
|-
|style="text-align:left"| [[Joseph Scaliger|Scaliger]]<ref>J. J. Scaliger, ''De emendatione temporum'' (Paris, 1583), 159, 238.</ref>
| 1583
|style="text-align:left"| 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9 || 2 Jan 45 BC || 25 Feb AD 4 || AD 8
|}

By the systems of Scaliger, Ideler and Bünting, the leap years prior to the suspension happen to be BC years that are divisible by 3, just as, after leap year resumption, they are the AD years divisible by 4.

In 1999, a papyrus was discovered which gives the dates of astronomical phenomena in 24&nbsp;BC in both the Egyptian and Roman calendars. From {{nowrap|30 August 26 BC (Julian)}}, Egypt had two calendars: the old Egyptian in which every year had 365 days and the new Alexandrian in which every fourth year had 366 days. Up to {{nowrap|28 August 22 BC (Julian)}} the date in both calendars was the same. The dates in the Alexandrian and Julian calendars are in one-to-one correspondence except for the period from 29 August in the year preceding a Julian leap year to the following 24 February.<ref>Dieter Hagedorn, ''Zum aegyptischen Kalender unter Augustus'', Zeitschrift fűr Papyrologie und Epigraphik 100 (1994) 211–222, available at [http://www.uni-koeln.de/phil-fak/ifa/zpe/downloads/1994/100pdf/100211.pdf].</ref> From a comparison of the astronomical data with the Egyptian and Roman dates, Alexander Jones<ref name="papyrus">Alexander Jones, ''Calendrica II: Date Equations from the Reign of Augustus'', Zeitschrift fűr Papyrologie und Epigraphik 129 (2000) 159–166, available at [http://www.uni-koeln.de/phil-fak/ifa/zpe/downloads/2000/129pdf/129159.pdf].</ref> concluded that the Egyptian astronomers (as opposed to travellers from Rome) used the correct Julian calendar.

An inscription has been discovered which orders a [[Paullus Fabius Maximus#A New Calendar in the Province of Asia|new calendar]] to be used in  the [[Province of Asia]] to replace the previous Greek lunar calendar.<ref>[http://epigraphy.packhum.org/inscriptions/main?url=oi%3Fikey%3D252886%26region%3D8%26subregion%3D29%26bookid%3D520%26caller%3Dsearch%26start%3D1193%26end%3D1202 OGIS 458] (Greek).</ref> According to one translation
{{quote|text=Intercalation shall commence on the day after 14 Peritius [a.d. IX Kal. Feb, which would have been 15 Peritius] as it is currently constituted in the third year following promulgation of the decree. Xanthicus shall have 32 days in this intercalary year.<ref>B A Buxton and R Hannah in ''Studies in Latin Literature and Roman History'' (ed. C Deroux), XII 290.</ref> }}

This is historically correct. It was decreed by [[Paullus Fabius Maximus|the proconsul]] that the first day of the year in the new calendar shall be Augustus' birthday, a.d. IX Kal. Oct. Every month begins on the ninth day before the kalends. The date of introduction, the day after 14 Peritius, was 1 Dystrus, the next month. The month after that was Xanthicus. Thus Xanthicus began on a.d. IX Kal. Mart., and normally contained 31 days. In leap year, however, it contained an extra "Sebaste day", the Roman leap day, and thus had 32 days. From the lunar nature of the old calendar we can fix the starting date of the new one as 24&nbsp;January, {{nowrap|a.d. IX Kal. Feb 5 BC}} in the Julian calendar, which was a leap year. Thus from inception the dates of the reformed Asian calendar are in one-to-one correspondence with the Julian.

Another translation of this inscription is
{{quote|Intercalation shall commence on the day after the fourteenth day in the current month of Peritius [a.d. IX Kal. Feb], occurring every third year. Xanthicus shall have 32 days in this intercalary year.<ref>U. Laffi, "Le iscrizioni relative all'introduzione nel 9 a.c. del nuovo calendario della provincia d'Asia", Studi Classici e Orientali 16 (1967) 5–99.</ref>}}

This would move the starting date back three years to 8&nbsp;BC, and from the lunar synchronism back to 26 January (Julian). But since the corresponding Roman date in the inscription is 24 January, this must be according to the incorrect calendar which in 8&nbsp;BC Augustus had ordered to be corrected by the omission of leap days. As the authors of the previous{{which|date=October 2019}} paper point out, with the correct four-year cycle being used in Egypt and the three-year cycle abolished in Rome, it is unlikely that Augustus would have ordered the three-year cycle to be introduced in Asia.

==Month names==
The Julian reform did not immediately cause the names of any months to be changed. The old [[Mercedonius|intercalary month]] was abolished and replaced with a single intercalary day at the same point (i.e., five days before the end of February). January continued to be the first month of the year.

The Romans later renamed months after Julius Caesar and Augustus, renaming Quintilis as "Iulius" (July)<ref name=J /> in 44&nbsp;BC and Sextilis as "Augustus" (August) in 8&nbsp;BC. Quintilis was renamed to honour Caesar because it was the month of his birth.<ref>Suetonius, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Julius*.html#76 ''Caesar''] {{Webarchive|url=https://archive.is/20120530163202/http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Julius*.html#76 |date=2012-05-30 }} 76.1.</ref> According to a ''[[senatus consultum]]'' quoted by Macrobius, Sextilis was renamed to honour Augustus because several of the most significant events in his rise to power, culminating in the fall of Alexandria, occurred in that month.<ref>Suetonius, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Augustus*.html#31.2 ''Augustus'' 31.2]; Macrobius, [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Macrobius/Saturnalia/1*.html#12.35  ''Saturnalia'' 1.12.35] (Latin)</ref>

Other months were renamed by other emperors, but apparently none of the later changes survived their deaths. In AD 37, [[Caligula]] renamed September as "Germanicus" after his [[Germanicus|father]];<ref>Suetonius, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Caligula*.html#15.2 ''Caligula'' 15.2].</ref> in AD 65, [[Nero]] renamed April as "Neroneus", May as "Claudius" and June as "Germanicus";<ref>Tacitus, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Tacitus/Annals/15C*.html#74 ''Annals'' 15.74], [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Tacitus/Annals/16*.html#12 16.12].</ref> and in AD 84 [[Domitian]] renamed September as "Germanicus" and October as "Domitianus".<ref>Suetonius, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Domitian*.html#13.3 ''Domitian'' 13.3].</ref> [[Commodus]] was unique in renaming all twelve months after his own adopted names (January to December): "Amazonius", "Invictus", "Felix", "Pius", "Lucius", "Aelius", "Aurelius", "Commodus", "Augustus", "Herculeus", "Romanus", and "Exsuperatorius".<ref>[https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/73*.html#72-15.3 Dio Cassius 73.15.3].</ref> The emperor [[Marcus Claudius Tacitus|Tacitus]] is said to have ordered that September, the month of his birth and accession, be renamed after him, but the story is doubtful since he did not become emperor before November 275.<ref>Historia Augusta, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Historia_Augusta/Tacitus*.html#13.6 ''Tacitus'' 13.6]. On the chronology see [http://www.roman-emperors.org/tacitus.htm R. McMahon, ''Tacitus''.]</ref> Similar honorific month names were implemented in many of the provincial calendars that were aligned to the Julian calendar.<ref>Surveyed in K. Scott, ''Honorific Months'', Yale Classical Studies 2 (1931) 201–278.</ref>

Other name changes were proposed but were never implemented. [[Tiberius]] rejected a senatorial proposal to rename September as "Tiberius" and October as "Livius", after his mother Livia.<ref>Suetonius, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Tiberius*.html#26.2 ''Tiberius'' 26.2].</ref> [[Antoninus Pius]] rejected a senatorial decree renaming September as "Antoninus" and November as "Faustina", after [[Faustina the Elder|his empress]].<ref>Historia Augusta, [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Historia_Augusta/Antoninus_Pius*.html#10 ''Antoninus Pius'' 10.1].</ref>

Much more lasting than the ephemeral month names of the post-Augustan Roman emperors were the [[Germanic calendar|Old High German names]] introduced by [[Charlemagne]]. According to his biographer, Charlemagne renamed all of the months agriculturally into German.<ref>Einhard, [http://www.fordham.edu/halsall/basis/einhard.asp#Reforms ''Life of Charlemagne'', 29].</ref> These names were used until the 15th century, over 700 years after his rule, and continued, with some modifications, to see some use as "traditional" month names until the late 18th century. The names (January to December) were: ''Wintarmanoth'' ("winter month"), ''Hornung'',<ref group=note>This name of February, the only name in the list without the "month" suffix, is explained by König, ''Festschrift Bergmann'' (1997), pp. 425 ff. as a collective of ''[[:wikt:horn|horn]]'', taken to refer to the antlers shed by [[red deer]] during this time. Older explanations compare the name with Old Frisian ''horning'' (Anglo-Saxon ''hornung-sunu'', Old Norse ''hornungr'') meaning "bastard, illegitimate son", taken to imply a meaning of "disinherited" in reference to February being the shortest of months.</ref> ''Lentzinmanoth'' ("spring month", "[[:wikt:Lent|Lent]] month"), ''Ostarmanoth'' ("[[:wikt:Easter|Easter]] month"), ''Wonnemanoth'' ("[[:wikt:Appendix:Proto-Germanic/wunjō|joy]]-month", a corruption of ''Winnimanoth'' "pasture-month"), ''Brachmanoth'' ("[[:wikt:Brache|fallow]]-month"), ''Heuuimanoth'' ("hay month"), ''Aranmanoth'' ("[[:wikt:earnian|reaping]] month"), ''Witumanoth'' ("wood month"), ''Windumemanoth'' ("vintage month"), ''Herbistmanoth'' ("harvest month"), and ''Heilagmanoth'' ("holy month").

The calendar month names used in western and northern Europe, in Byzantium, and by the [[Berber calendar#The months|Berbers]], were derived from the Latin names. However, in eastern Europe older seasonal month names continued to be used into the 19th century, and in some cases are still in use, in many languages, including: [[Belarusian months|Belarusian]], [[Bulgarian months|Bulgarian]], [[Croatian months|Croatian]], [[Czech months|Czech]], Finnish,<ref>{{cite web |url=http://wordinfo.info/unit/3236/ip:23 |title=Calendar, Finnish |website=English-Word Information}}</ref> [[Georgian calendar|Georgian]], [[Lithuanian calendar#Names of the months|Lithuanian]], [[Macedonian months|Macedonian]], [[Polish months|Polish]], [[Romanian calendar#Traditional month names|Romanian]], [[Slovene months|Slovene]], [[Ukrainian months|Ukrainian]]. When the Ottoman Empire adopted the Julian calendar, in the form of the Rumi calendar, the [[Rumi calendar#History|month names]] reflected Ottoman tradition.

== Year numbering ==
The principal method used by the Romans to identify a year for dating purposes was to name it after the two consuls who took office in it, the eponymous period in question being the consular year. Beginning in 153&nbsp;BC, consuls began to take office on 1&nbsp;January, thus synchronizing the commencement of the consular and calendar years. The calendar year has begun in January and ended in December since about 450&nbsp;BC according to Ovid or since about 713&nbsp;BC according to Macrobius and Plutarch (see [[Roman calendar]]). Julius Caesar did not change the beginning of either the consular year or the calendar year. In addition to consular years, the Romans sometimes used the regnal year of the emperor, and by the late 4th&nbsp;century documents were also being dated according to the 15&nbsp;year cycle of the [[indiction]]. In 537, [[Justinian I|Justinian]] required that henceforth the date must include the name of the emperor and his regnal year, in addition to the indiction and the consul, while also allowing the use of local [[Calendar era|eras]].

In 309 and 310, and from time to time thereafter, no consuls were appointed.<ref>[http://www.tertullian.org/fathers/chronography_of_354_08_fasti.htm Chronography of AD&nbsp;354.]</ref> When this happened, the consular date was given a count of years since the last consul (called "post-consular" dating). After 541, only the reigning emperor held the consulate, typically for only one year in his reign, and so post-consular dating became the norm. Similar post-consular dates were also known in the west in the early 6th&nbsp;century. <!-- Commented out pending further research. [[User:Dojarca]] is up to 4th&nbsp;year of the consulate of [[Justinian II]] with no assurance he is the latest. --~~~~ The last known post-consular date is year&nbsp;22 after the consulate of [[Heraclius]].{{Verify source|date=August 2007}} The last emperor to hold the consulate was [[Constans II]]. --> The system of consular dating, long obsolete, was formally abolished in the law code of [[Leo VI the Wise|Leo&nbsp;VI]], issued in 888.

Only rarely did the Romans number the year from the [[founding of Rome|founding of the city (of Rome)]], ''[[ab urbe condita]]'' (AUC). This method was used by Roman historians to determine the number of years from one event to another, not to date a year. Different historians had several different dates for the founding. The ''[[Fasti]] Capitolini'', an inscription containing an official list of the consuls which was published by Augustus, used an [[epoch (reference date)|epoch]] of 752&nbsp;BC. The epoch used by [[Marcus Terentius Varro|Varro]], 753&nbsp;BC, has been adopted by modern historians. Indeed, [[Renaissance]] editors often added it to the manuscripts that they published, giving the false impression that the Romans numbered their years. Most modern historians tacitly assume that it began on the day the consuls took office, and ancient documents such as the ''Fasti Capitolini'' which use other [[ab urbe condita|AUC]] systems do so in the same way. However, Censorinus, writing in the 3rd&nbsp;century&nbsp;AD, states that, in his time, the [[ab urbe condita|AUC]] year began with the [[Parilia]], celebrated on 21&nbsp;April, which was regarded as the actual anniversary of the foundation of Rome.<ref>{{cite book |author=[[Censorinus]] |title=De Die Natali |at=21.6 |lang=Latin |url=https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Censorinus/text*.html#21.6}} Because the lively festivities associated with the [[Parilia]] conflicted with the solemnity of [[Lent]], which was observed until the Saturday before Easter Sunday, the early Roman church did not celebrate Easter after 21&nbsp;April.{{cite book |author=[[Bede]] |editor-first=Charles W. |editor-last=Jones |chapter=Development of the Latin ecclesiastical calendar |title=Bedae Opera de Temporibus |year=1943 |pages=1–122, esp.&nbsp;28}}</ref>

Many local eras, such as the Era of Actium and the [[Spanish Era]], were adopted for the Julian calendar or its local equivalent in the provinces and cities of the Roman Empire. Some of these were used for a considerable time.<ref>For a partial survey see {{cite book |first=A.E. |last=Samuel |year=1972 |title=Greek and Roman Chronology: Calendars and years in classical antiquity |place=Munich, DE |pages=245&nbsp;ff}} Samuel introduces his survey by saying: "The number of eras which came into use and then expired to be replaced by yet other eras during Hellenistic and Roman times is probably not infinite, but I have not been able to find the end of them." Anatolian eras are exhaustively surveyed in {{cite book |first=W. |last=Leschhorn |year=1993 |title=Antike Ären: Zeitrechnung, Politik und Geschichte im Schwarzmeerraum und in Kleinasien nördlich des Tauros |place=Stuttgart, DE |lang=DE}}</ref> Perhaps the best known is the [[Era of Martyrs]], sometimes also called ''Anno Diocletiani'' (after [[Diocletian]]), which was associated with the Alexandrian calendar and often used by the [[Alexandria]]n Christians to number their Easters during the 4th and 5th&nbsp;centuries, and continues to be used by the Coptic and [[Ethiopian Orthodox Church|Ethiopian]] churches.

In the eastern Mediterranean, the efforts of Christian chronographers such as [[Annianus of Alexandria]] to date the Biblical creation of the world led to the introduction of [[Anno Mundi]] eras based on this event.<ref>{{cite book |first=A.A. |last=Mosshammer |year=2008 |title=The Easter Computus and the Origins of the Christian Era |place=Oxford, UK |pages=27–29}}</ref> The most important of these was the [[Etos Kosmou]], used throughout the Byzantine world from the 10th century and in Russia until 1700. In the west, the kingdoms succeeding the empire initially used indictions and [[regnal year]]s, alone or in combination. The chronicler [[Prosper of Aquitaine]], in the fifth century, used an era dated from the [[Passion (Christianity)|Passion of Christ]], but this era was not widely adopted. [[Dionysius Exiguus]] proposed the system of [[Anno Domini]] in 525. This era gradually spread through the western Christian world, once the system was adopted by [[Bede]] in the eighth century.

The Julian calendar was also used in some Muslim countries. The [[Rumi calendar]], the Julian calendar used in the later years of the [[Ottoman Empire]], adopted an era derived from the lunar [[Islamic calendar|AH]] year equivalent to AD&nbsp;1840, i.e., the effective [[Rumi calendar|Rumi epoch]] was AD&nbsp;585. In recent years, some users of the [[Berber calendar#The computation of the years|Berber calendar]] have adopted an era starting in 950&nbsp;BC, the approximate date that the Libyan pharaoh {{nowrap|[[Sheshonq I]]}} came to power in Egypt.

== New Year's Day ==
The Roman calendar began the year on 1 January, and this remained the start of the year after the Julian reform. However, even after local calendars were aligned to the Julian calendar, they started the new year on different dates. The Alexandrian calendar in Egypt started on 29 August (30 August after an Alexandrian leap year). Several local provincial calendars were aligned to start on the birthday of Augustus, 23 September. The indiction caused the [[Byzantine Empire|Byzantine]] year, which used the Julian calendar, to begin on 1 September; this date is still used in the [[Eastern Orthodox Church]] for the beginning of the liturgical year. When the Julian calendar was adopted in AD 988 by [[Vladimir I of Kiev]], the year was numbered Anno Mundi 6496, beginning on 1 March, six months after the start of the Byzantine Anno Mundi year with the same number. In 1492 (AM 7000), [[Ivan III]], according to church tradition, realigned the start of the year to 1 September, so that AM 7000 only lasted for six months in Russia, from 1 March to 31 August 1492.<ref>[https://translate.google.com/translate?hl=en&sl=ru&u=http://grigam.narod.ru/kalend/kalen19.htm История календаря в России и в СССР (Calendar history in Russia and in the USSR).]</ref>

During the Middle Ages 1 January retained the name ''New Year's Day'' (or an equivalent name) in all western European countries (affiliated with the [[Roman Catholic Church]]), since the medieval calendar continued to display the months from January to December (in twelve columns containing 28 to 31 days each), just as the Romans had. However, most of those countries began their numbered year on 25 December (the Nativity of Jesus), 25 March (the [[Annunciation|Incarnation of Jesus]]), or even Easter, as in France (see the [[Liturgical year]] article for more details).

In Anglo-Saxon England, the year most commonly began on 25 December, which, as (approximately) the [[winter solstice]], had marked the start of the year in pagan times, though 25 March (the [[equinox]]) is occasionally documented in the 11th century. Sometimes the start of the year was reckoned as 24 September, the start of the so-called "western indiction" introduced by Bede.<ref>M. L. R. Beaven, "The Regnal Dates of Alfred, Edward the Elder, and Athelstan", English Historical Review 32 (1917) 517–531; idem, "The Beginning of the Year in the Alfredian Chronicle (866–87)", English Historical Review 33 (1918) 328–342.</ref> These practices changed after the Norman conquest. From 1087 to 1155 the English year began on 1 January, and from 1155 to 1751 it began on 25 March.<ref>Catholic Encyclopedia, [http://www.newadvent.org/cathen/03738a.htm#beginning General Chronology (Beginning of the Year)].</ref> In 1752 it was moved back to 1 January. (See [[Calendar (New Style) Act 1750]]).

Even before 1752, 1 January was sometimes treated as the start of the new year – for example by Pepys<ref>[http://www.pepysdiary.com/archive/1661/12/31/index.php Pepys Diary], "I sat down to end my journell for this year, ..."</ref> – while the "year starting 25th March was called the Civil or Legal Year".<ref name=MS>Spathaky, Mike [http://www.cree.name/genuki/dates.htm Old Style and New Style dates and the change to the Gregorian calendar].</ref> To reduce misunderstandings on the date, it was not uncommon for a date between 1 January and 24 March to be written as "1661/62". This was to explain to the reader that the year was 1661 counting from March and 1662 counting from January as the start of the year.<ref name=MS-oblique-stroke>Spathaky, Mike [http://www.cree.name/genuki/dates.htm Old Style and New Style dates and the change to the Gregorian calendar]. "An oblique stroke is by far the most usual indicator, but sometimes the alternative final figures of the year are written above and below a horizontal line, as in a fraction (a form which cannot easily be reproduced here in ASCII text). Very occasionally a hyphen is used, as 1733{{hyphen}}34."</ref> (For more detail, see [[Dual dating]]).

Most western European countries shifted the first day of their numbered year to 1 January while they were still using the Julian calendar, ''before'' they adopted the Gregorian calendar, many during the 16th century. The following table shows the years in which various countries adopted 1 January as the start of the year. Eastern European countries, with populations showing allegiance to the [[orthodoxy|Orthodox Church]], began the year on 1 September from about 988. The Rumi calendar used in the Ottoman Empire began the civil year on 1 March until 1918.

{| class="wikitable sortable" style="margin:auto;"
|-
! Country !! Year starting<br />1 January<ref>[[John James Bond]], [https://archive.org/details/handybookrulesa01bondgoog "Commencement of the Year"], ''Handy-book of rules and tables for verifying dates with the Christian era'', (London: 1875), 91–101.</ref><ref>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> !!Adoption of<br /> new calendar
|-
| [[Holy Roman Empire]]<ref group=note>The source has Germany, whose current area during the sixteenth century was a major part of the Holy Roman Empire, a religiously divided confederation. The source is unclear as to whether all or only parts of the country made the change. In general, Roman Catholic countries made the change a few decades before Protestant countries did.</ref>|| 1544 || 1582
|-
| Spain, [[Portugal]] || 1556 || 1582
|-
| [[Prussia]], [[Denmark–Norway]]|| 1559 || 1700
|-
| Sweden || 1559 || 1753<ref group=note>Sweden started a conversion process in 1700, which was abandoned later that year due to the [[Great Northern War]], and in 1712 returned to the Julian calendar. In 1753 Sweden switched to the Gregorian calendar. See [[Swedish calendar]].</ref>
|-
|France||[[Edict of Roussillon|1567]] || 1582
|-
|[[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 || 1760
|-
| [[Holland]], [[Zeeland]] || 1583 || 1582
|-
| [[Dutch Republic]] except<br /> [[Holland]] and [[Zeeland]] || 1583 || 1700
|-
| [[Kingdom of Scotland|Scotland]] || 1600 || 1752
|-
| Russia || 1700 || 1918
|-
| [[Grand Duchy of Tuscany|Tuscany]] || 1750<ref>Alexandre Dumas, [https://archive.org/details/storiadelgoverno00duma/page/201 <!-- quote=toscana 1750 calendario gregoriano. --> Storia del governo della Toscana: sotto La casa de'Medici].</ref><ref>[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>
|-
| [[British Empire]] excluding [[Scotland]]|| 1752 || 1752<ref group=note>1751 in England only lasted from 25 March to 31 December. The dates 1 January to 24 March which would have concluded 1751 under the old calendar became part of 1752 when the beginning of the numbered year was changed from 25 March to 1 January.</ref>
|-
| [[Republic of Venice]] || 1522 || 1582
|-
| [[Serbia]] || 1804{{Citation needed|date=January 2008}} || 1918
|-
| [[Ottoman Empire]] ([[Turkey]]) || 1918 || 1917<ref group=note>See [[Rumi calendar]] for details. It is often stated that Turkey adopted the Gregorian calendar in 1926 or 1927: in fact this is when it adopted the AD/CE [[epoch]].</ref>
|}

== Replacement by the Gregorian calendar ==
{{Main|Adoption of the Gregorian calendar}}
The Julian calendar [[Adoption of the Gregorian calendar|has been replaced]] as the [[civil calendar]] by the [[Gregorian calendar]] in all countries which officially used it. Turkey switched (for fiscal purposes) on [[Dual Dating|16 February/1 March 1917]]. Russia changed on 1/14 February 1918.<ref>{{cite web|url=https://secure.ssa.gov/poms.nsf/lnx/0200307180|last=Social Security Administration|title=GN 00307.180 Gregorian/Julian calendar|date=26 August 2005|access-date=27 July 2016|quote=Although the Russian authorities officially changed calendars in 1918, individual registrars particularly in remote areas continued to use the old calendar for as long as ten years.}}</ref> Greece made the change for civil purposes on 16 February/1 March 1923, but the national day (25 March), was to remain on the old calendar. Most [[Christian denomination]]s in the west and areas evangelised by western churches have made the change to Gregorian for their [[liturgical calendar]]s to align with the civil calendar.

A calendar similar to the Julian one, the [[Alexandrian calendar]], is the basis for the [[Ethiopian calendar]], which is still the civil calendar of Ethiopia. Egypt converted from the Alexandrian calendar to Gregorian on 1 Thaut 1592/11 September 1875.<ref>[https://books.google.com/books?id=4llHAQAAIAAJ&pg=PA1348&dq=Beardsley+Fish+1875+1348&hl=en&sa=X&ved=0ahUKEwiv-_z805reAhVCkSwKHaKmDQoQ6AEIRDAE#v=onepage&q=Beardsley%20Fish%201875%201348&f=false Papers Relating to the Foreign Relations of the United States, vol. 2, pp. 1348–1349].</ref>

During the changeover between calendars and for some time afterwards, [[dual dating]] was used in documents and gave the date according to both systems. In contemporary as well as modern texts that describe events during the period of change, it is customary to clarify to which calendar a given date refers by using an [[Old Style and New Style dates|O.S. or N.S. suffix]] (denoting Old Style, Julian or New Style, Gregorian).

=== Transition history ===
{{See also|Gregorian calendar|Old Style and New Style dates}}
The Julian calendar was in general use in Europe and northern Africa until 1582, when [[Pope Gregory XIII]] promulgated the Gregorian calendar. Reform was required because too many leap days were added with respect to the astronomical seasons under the Julian scheme. On average, the astronomical solstices and the equinoxes advance by 10.8 minutes per year against the Julian year. As a result, 21 March (which is the base date for the [[Computus|calculating the date of Easter]]) gradually moved out of alignment with the March equinox.
[[File:Julian to Gregorian Date Change.png|thumb|This is a visual example of the official date change from the Julian calendar to the Gregorian.]]
While Hipparchus and presumably [[Sosigenes of Alexandria|Sosigenes]] were aware of the discrepancy, although not of its correct value,{{sfn|Richards|1998|page=216}} it was evidently felt to be of little importance at the time of the Julian reform (46 BC). However, it accumulated significantly over time: the Julian calendar gained a day every 128 years. By 1582, 21 March was ten days out of alignment with the March equinox, the date where it supposedly had been in 325, the year of the [[First Council of Nicaea|Council of Nicaea]].

The Gregorian calendar was soon adopted by most Catholic countries (e.g., Spain, Portugal, Poland, most of Italy). Protestant countries followed later, and some countries of eastern Europe even later. In the British Empire (including the [[United States|American colonies]]), Wednesday {{nowrap|2 September 1752}} was followed by Thursday {{nowrap|14 September 1752}}. For 12 years from 1700 Sweden used a [[Swedish calendar|modified Julian calendar]], and adopted the Gregorian calendar in 1753.

Since the Julian and Gregorian calendars were long used simultaneously, although in different places, calendar dates in the transition period are often ambiguous, unless it is specified which calendar was being used. In some circumstances, double dates might be used, one in each calendar. The notation [[Old Style and New Style dates|"Old Style" (O.S.)]] is sometimes used to indicate a date in the Julian calendar, as opposed to [[Old Style and New Style dates|"New Style" (N.S.)]], which either represents the Julian date with the start of the year as 1 January or a full mapping onto the Gregorian calendar. This notation is used to clarify dates from countries that continued to use the Julian calendar after the Gregorian reform, such as Great Britain, which did not switch to the reformed calendar until 1752, or Russia, which did not switch until 1918 (see [[Soviet calendar]]). This is why the Russian Revolution of 7 November 1917 N.S. is known as the [[October Revolution]], because it began on 25 October O.S.

Throughout the long transition period, the Julian calendar has continued to diverge from the Gregorian. This has happened in whole-day steps, as leap days that were dropped in certain centennial years in the Gregorian calendar continued to be present in the Julian calendar. Thus, in the year 1700 the difference increased to 11 days; in 1800, 12; and in 1900, 13. Since 2000 was a leap year according to both the Julian and Gregorian calendars, the difference of 13 days did not change in that year: {{nowrap|29 February 2000}} (Gregorian) fell on {{nowrap|16 February 2000}} (Julian). This difference of 13 days will persist until Saturday 28 February 2100 (Julian), i.e. 13 March 2100 (Gregorian), since 2100 is ''not'' a Gregorian leap year, but ''is'' a Julian leap year; the next day the difference will be of 14 days:  Sunday 29 February (Julian) will be Sunday 14 March (Gregorian); the next day Monday {{nowrap|1 March 2100}} (Julian) falls on Monday {{nowrap|15 March 2100}} (Gregorian).{{sfn|Walker|2009}}

== Modern usage ==
=== Eastern Orthodox ===
[[File:Bogojavlenie.jpg|thumb|250px|[[Russian icon]] of the [[Epiphany (feast)|Theophany]] (the baptism of Jesus by [[John the Baptist]]) (6 January), the highest-ranked feast which occurs on the fixed cycle of the [[Eastern Orthodox liturgical calendar]].]]

Although most [[Eastern Orthodox Church|Eastern Orthodox]] countries (most of them in [[Eastern Europe|eastern]] or southeastern Europe) had adopted the Gregorian calendar by 1924, their national churches had not. The "[[Revised Julian calendar]]" was endorsed by a [[synod]] in [[Constantinople]] in May 1923, consisting of a solar part which was and will be identical to the Gregorian calendar until the year 2800, and a lunar part which calculated Easter astronomically at [[Jerusalem]]. All Orthodox churches refused to accept the lunar part, so all Orthodox churches continue to celebrate Easter according to the Julian calendar, with the exception of the [[Finnish Orthodox Church]].<ref>Bishop Photius of Triaditsa, [http://orthodoxinfo.com/ecumenism/photii_2.aspx "The 70th Anniversary of the Pan-Orthodox Congress, Part II of II"]; {{cite web
|url=http://www.hs.fi/english/article/Moscow-affiliated+Russian+Orthodox+church+grows+in+Helsinki/1135230488329
|date=21 September 2007
|title=HELSINGIN SANOMAT (International edition)
}}</ref> (The [[Estonian Apostolic Orthodox Church|Estonian Orthodox Church]] was also an exception from 1923 to 1945.<ref>[http://antimodern.files.wordpress.com/2011/06/communique-de-presse.pdf Communiqué du Bureau de Presse de l’Eglise Orthodoxe d’Estonie]</ref>)

The solar part of the Revised Julian calendar was accepted by only some Orthodox churches. Those that did accept it, with hope for improved dialogue and negotiations with the western denominations, were the [[Ecumenical Patriarchate of Constantinople]], the Patriarchates of [[Greek Church of Alexandria|Alexandria]], [[Eastern Orthodox Church of Antioch|Antioch]], the Orthodox Churches of [[Church of Greece|Greece]], [[Orthodox Church of Cyprus|Cyprus]], [[Romanian Orthodox Church|Romania]], [[Polish Orthodox Church|Poland]] (from 1924 to 2014; it is still permitted to use the Revised Julian calendar in parishes that want it), [[Bulgarian Orthodox Church|Bulgaria]] (in 1963), and the [[Orthodox Church in America]] (although some OCA parishes are permitted to use the Julian calendar). Thus these churches celebrate the [[Nativity of Jesus|Nativity]] on the same day that western Christians do, 25 December Gregorian until 2799.

The Orthodox Churches of [[Eastern Orthodox Patriarchate of Jerusalem|Jerusalem]], [[Russian Orthodox Church|Russia]], [[Serbian Orthodox Church|Serbia]], [[Montenegrin Orthodox Church|Montenegro]], Poland (from 15 June 2014), [[Macedonian Orthodox Church – Ohrid Archbishopric|North Macedonia]], [[Georgian Orthodox and Apostolic Church|Georgia]], [[History of Christianity in Ukraine|Ukraine]], and the [[Greek Old Calendarists]] and other groups continue to use the Julian calendar, thus they celebrate the Nativity on 25 December ''Julian'' (which is 7 January ''Gregorian'' until 2100). The [[Russian Orthodox Church]] has some parishes in the West that celebrate the Nativity on 25 December ''Gregorian'' until 2799. 

Parishes of the [[Orthodox Church in America Bulgarian Diocese]], both before and after the 1976 transfer of that diocese from the [[Russian Orthodox Church Outside Russia]] to the Orthodox Church in America, were permitted to use this date. Some [[Old Calendarist]] groups which stand in opposition to the [[state church]]es of their homelands will use the [[Great Feast]] of the [[Epiphany (feast)|Theophany]] ([[January 6 (Eastern Orthodox liturgics)|6 January]] ''Julian''/19 January ''Gregorian'') as a day for [[Crucession|religious processions]] and the [[Great Blessing of Waters]], to publicise their cause.{{Citation needed|date=January 2010}}

==== Date of Easter ====
Most branches of the [[Eastern Orthodox Church]] use the Julian calendar for [[Computus|calculating the date of Easter]], upon which the timing of all the other [[moveable feast]]s depends. Some such churches have adopted the [[Revised Julian calendar]] for the observance of [[fixed feast]]s, while such Orthodox churches retain the Julian calendar for all purposes.<ref>[http://www.oikoumene.org/en/resources/documents/commissions/faith-and-order/i-unity-the-church-and-its-mission/towards-a-common-date-for-easter/index Towards a Common Date of Easter.] (5–10 March). World Council of Churches/Middle East Council of Churches Consultation, Aleppo, Syria.</ref>

===Syriac Christianity===
The [[Ancient Assyrian Church of the East]], an [[East Syriac]] rite that is commonly miscategorised under "eastern Orthodox", uses the Julian calendar, where its participants celebrate Christmas on 7 January ''Gregorian'' (which is  25 December ''Julian''). The [[Assyrian Church of the East]], the church it split from in 1968 (the replacement of traditional Julian calendar with Gregorian calendar being among the reasons), uses the Gregorian calendar ever since the year of the [[schism]].<ref>[https://theorthodoxchurch.info/blog/news/the-quest-for-orthodox-assyrian-alliance/ The Quest for Orthodox–Assyrian Alliance] Orthodoxy Cognate PAGE</ref> The [[Syriac Orthodox Church]] uses both Julian calendar and Gregorian calendar based on their regions and traditions they adapted.

=== Oriental Orthodox ===
The [[Oriental Orthodox]] Churches generally use the local calendar of their homelands. However, when calculating the Nativity Feast, most observe the Julian calendar. This was traditionally for the sake of unity throughout Christendom. In the west, some Oriental Orthodox Churches either use the Gregorian calendar or are permitted to observe the Nativity according to it.

The [[Armenian Patriarchate of Jerusalem]] of [[Armenian Apostolic Orthodox Church]] uses Julian calendar, while the rest of Armenian Church uses Gregorian calendar. Both celebrate the Nativity as part of the Feast of [[Epiphany (holiday)|Theophany]] according to their respective calendar.<ref>{{Cite web|url=https://www.peopleofar.com/2015/01/07/armenians-celebrate-christmas-january-6th/|title=Armenian Christmas on January 6th|last=Reply|first=hairabed|date=2015-01-07|website=PeopleOfAr|language=en-US|access-date=2018-12-21}}</ref>

=== Berbers ===
The Julian calendar is still used by the [[Berbers]] of the Maghreb in the form of the [[Berber calendar]].<ref>{{cite journal|title=The manipulation of time: Calendars and power in the Sahara|first=Clare|last=Oxby|journal=Nomadic Peoples |series=New Series|volume=2|issue=1/2|year=1998|pages=137–149|doi=10.3167/082279498782384522|jstor=43123542}}</ref>

== See also ==
* [[Byzantine calendar]]
* [[Conversion between Julian and Gregorian calendars]]
* [[Julian day]]
* [[Julian year (astronomy)]]
* [[List of adoption dates of the Gregorian calendar per country]]
* [[Mixed-style date]]
* [[Old New Year]]
* [[Proleptic Gregorian calendar]]
* [[Proleptic Julian calendar]]
* [[Revised Julian calendar]]
* [[Roman timekeeping]]
* [[Week]]

== Footnotes ==
{{notelist}}
{{reflist|group=note}}

==References==
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{{reflist|25em}}

== Bibliography ==
* Bonnie Blackburn and Leofranc Holford-Strevens, ''The Oxford Companion to the Year'', Oxford University Press, reprinted with corrections 2003.
* {{cite book
|title=Le Calendrier romain: Recherches chronologiques
|date=1983
|publisher=Ottawa University Press
|last1=Brind'Amour
|first1=Pierre
}}
* {{cite web | date = 2008 | url = https://ethiopianembassy.org/ethiopian-time/ | title = Ethiopian Time | publisher = Embassy of Ethiopia | location = Washington D.C.}}
* {{cite book
|title=Caesar's Calendar: Ancient Time and the Beginnings of History
|url=https://archive.org/details/caesarscalendara0000feen
|url-access=registration
|date=2007
|publisher=University of California Press
|location=Berkeley
|last1=Feeney
|first1=Dennis}}
* {{cite book
|title=The Roman Calendar from Numa to Constantine: Time, History and the Fasti
|date=2011
|publisher=Wiley
|last1=Rüpke
|first1=Jörg}}
* {{cite book
|title=Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac
|author=Nautical Almanac Offices of the United Kingdom and the United States of America
|publisher=Her Majesty's Stationery Office
|date=1961
|location=London}}
* {{cite book
| publisher = Oxford University Press
| isbn = 978-0-19-286205-1
| last = Richards
| first = E. G
| title = Mapping time: the calendar and its history
| url = https://archive.org/details/mappingtimecalen00rich
| url-access = registration
| date = 1998
}}
* {{cite book
| last1 = Richards | first1 = E. G.
| editor-last1 = Urban | editor-first1 = Sean E.
| editor-last2 = Seidelmann | editor-first2 = P. Kenneth
| edition = 3rd
| publisher = University Science Books
| isbn = 978-1-891389-85-6
| title = Explanatory Supplement to the Astronomical Almanac
| location = Mill Valley, Calif
| date = 2013
}}
* {{cite book
|last1=Stern
|first1=Sacha
|title=Calendars in Antiquity: Empires, States and Societies
|date=2012
|publisher=Oxford University Press}}
* {{cite web
|last = Walker
|first = John
|title= Calendar Converter
|url = https://www.fourmilab.ch/documents/calendar/
|date = 2009
}}

== External links ==
{{Wiktionary|evenly divisible}}
{{Commons|Julian calendar}}
* [http://webexhibits.org/calendars/index.html Calendars through the ages] on WebExhibits.
* [https://web.archive.org/web/20051228123115/http://www.tondering.dk/claus/calendar.html Calendar FAQ]
* [http://www.tyndalehouse.com/Egypt/ptolemies/chron/roman/chron_rom_cal.htm Roman Dates]
* [http://penelope.uchicago.edu/~grout/encyclopaedia_romana/calendar/romancalendar.html The Roman Calendar]
* [http://www.fourmilab.ch/documents/calendar/#juliancalendar Calendar Converter] – converts between several calendars, for example Gregorian, Julian, Mayan, Persian, Hebrew

{{Calendars}}
{{Ancient Rome topics}}
{{Time Topics}}
{{Time measurement and standards}}
{{Chronology}}
{{Authority control}}

[[Category:Julian calendar| ]]
[[Category:Roman calendar]]
[[Category:Eastern Orthodox liturgy]]
[[Category:Liturgical calendars]]