The Julian calendar was introduced in 46 BC by Julius Caesar and came into force in 45 BC (709 ab urbe condita). It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year, known at least since Hipparchus. It has a regular year of 365 days divided into 12 months, and a leap day is added to February every four years. Hence the Julian year is on average 365.25 days long.
Although the Julian calendar remained in use into the 20th century in some countries and is still used by many national Orthodox churches, it has generally been replaced for civil use by the modern Gregorian calendar. Orthodox Churches no longer using the Julian calendar typically use the Revised Julian calendar rather than the Gregorian calendar.
The notation "Old Style" (OS) is sometimes used to indicate a date in the Julian calendar, as opposed to "New Style" (NS), which either represents the Julian date with the start of the year as 1 January or a full mapping onto the Gregorian calendar.

Julian reform
The ordinary year in the previous Roman calendar consisted of 12 months, for a total of 355 days. In addition, a 27-day intercalary month, the Mensis Intercalaris, was sometimes inserted between February and March. This intercalary month was formed by inserting 22 days after the first 23 or 24 days of February, the last five days of February becoming 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.
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. On this system, the average Roman year would have had 366¼ 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 wherein, for 8 years out of 24, there were only three intercalary years, each of 377 days. This refinement averages the length of the year to 365¼ days over 24 years. In practice, intercalations did not occur schematically according to these ideal systems, but were determined by the 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 allowed the Roman year, on average, to stay roughly aligned to a tropical year. However, if too many intercalations were omitted, as happened after the Second Punic War and during the Civil Wars, the calendar would drift rapidly out of alignment with the tropical year. Moreover, since 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 BC to 46 BC, when there were only five intercalary months, whereas there should have been eight, and none at all during the five Roman years before 46 BC.
The reform was intended to correct this problem permanently. Before it took effect, the missed intercalations during Julius Caesar's pontificate were made up by inserting 67 days (22+23+22) between the last pre-Julian November and December in 46 BC, in the form of two months, in addition to 23 days that had already been added to February. Thus 90 days were added to this last year of the Roman Republican calendar, giving it 445 days. Because it 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 first year of operation of the new calendar was 45 BC.

Leap year error
Immediately after the Julian reform, the twelve months of the Roman calendar were named Ianuarius, Februarius, Martius, Aprilis, Maius, Iunius, Quintilis, Sextilis, September, October, November, and December, just as they were before the reform. The old intercalary month, the Mensis Intercalaris, was abolished and replaced with a single intercalary day at the same point (i.e. five days before the end of Februarius). The first month of the year continued to be Ianuarius, as it had been since 153 BC.
The Romans later renamed months after Julius Caesar and Augustus, renaming Quintilis (originally, "the Fifth month", with March = month 1) as Iulius (July) in 44 BC and Sextilis ("Sixth month") as Augustus (August) in 8 BC. Quintilis was renamed to honour Caesar because it was the month of his birth. 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, fell in that month.
Other months were renamed by other emperors, but apparently none of the later changes survived their deaths. Caligula renamed September ("Seventh month") as Germanicus; Nero renamed Aprilis (April) as Neroneus, Maius (May) as Claudius and Iunius (June) as Germanicus; and Domitian renamed September as Germanicus and October ("Eighth month") as Domitianus. At other times, September was also renamed as Antoninus and Tacitus, and November ("Ninth month") was renamed as Faustina and Romanus. 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.
Much more lasting than the ephemeral month names of the post-Augustan Roman emperors were the names introduced by Charlemagne. He renamed all of the months agriculturally into Old High German. They were used until the 15th century, and with some modifications until the late 18th century in Germany and in the Netherlands (January-December): Wintarmanoth (winter month), Hornung (the month when the male red deer sheds its antlers), Lentzinmanoth (Lent month), Ostarmanoth (Easter month), Wonnemanoth (love making month), Brachmanoth (plowing month), Heuvimanoth (hay month), Aranmanoth (harvest month), Witumanoth (wood month), Windumemanoth (vintage month), Herbistmanoth (autumn/harvest month), and Heilagmanoth (holy month).

Month names
The Julian reform set the lengths of the months to their modern values. However, a 13th century scholar, Sacrobosco, proposed a different explanation for the lengths of Julian months which is still widely repeated but is certainly wrong. According to Sacrobosco, the original scheme for the months in the Julian Calendar was very regular, alternately long and short. From January through December, the month lengths according to Sacrobosco for the Roman Republican calendar were:
He then thought that Julius Caesar added one day to every month except February, a total of 11 more days, giving the year 365 days. A leap day could now be added to the extra short February:
He then said Augustus changed this to:
so that the length of Augustus would not be shorter than (and therefore inferior to) the length of Iulius, giving us the irregular month lengths which are still in use.
There is abundant evidence disproving this theory. First, a wall painting of a Roman calendar predating the Julian reform has survived, which confirms the literary accounts that the months were already irregular before Julius Caesar reformed them:
Also, the Julian reform did not change the dates of the Nones and 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 days in the Roman calendar, whereas Sacrobosco's theory requires that March, May and July were originally 30 days long and that the length of October was changed from 29 to 30 days by Caesar and to 31 days by Augustus. Further, Sacrobosco's theory is explicitly contradicted by the third and fifth century authors Censorinus and Macrobius, and it is inconsistent with seasonal lengths given by Varro, writing in 37 BC, before the Augustan reform, with the 31-day Sextilis given by the new Egyptian papyrus from 24 BC, and with the 28-day February shown in the Fasti Caeretani, which is dated before 12 BC.

Month lengths
The dominant method that the Romans used to identify a year for dating purposes was to name it after the two consuls who took office in it. Since 153 BC, they had taken office on 1 January, and Julius Caesar did not change the beginning of the year. Thus this consular year was an eponymous or named year. In addition to consular years, the Romans sometimes used the regnal year of the emperor, and by the late fourth century documents were also being dated according to the 15-year cycle of the indiction. In 537, 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 eras. After 541, however, only the reigning emperor held the consulate, typically for only one year in his reign. As a result, the consular date was often a count of years since the last consul (so-called "post-consular" dating). Similar post-consular dates are also known in the West in the early sixth century. The last known post-consular date is year 22 after the consulate of Heraclius.
While the Julian reform applied originally to the Roman calendar, many of the other calendars then used in the Roman Empire were aligned with the reformed calendar under Augustus. This led to the adoption of several local eras for the Julian calendar, such as the Era of Actium and the Spanish Era, some of which were used for a considerable time. Perhaps the best known is the Era of Martyrs, sometimes also called Anno Diocletiani (after Diocletian), which was often used by the Alexandrian Christians to number their Easters during the fourth and fifth centuries and continued to be used by the Coptic and Abyssinian 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. The most important of these was the Aetos Kosmou, used throughout the Byzantine world from the 10th century and in Russia till 1700. In the West, 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.

Year numbering
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 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 Russia 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.
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 sixteenth 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 Orthodox Church, began the year on 1 September from about 988.
Note that as a consequence of change of New Year, 1 January 1751 to 24 March 1751 were non-existent dates in England.

New Year's Day
The Julian calendar was in general use in Europe and Northern Africa from the times of the Roman Empire until 1582, when Pope Gregory XIII promulgated the Gregorian Calendar. Reform was required because too many leap days are added with respect to the astronomical seasons on the Julian scheme. On average, the astronomical solstices and the equinoxes advance by about 11 minutes per year against the Julian year, causing the calendar to gain a day about every 134 years. While Hipparchus and presumably Sosigenes were aware of the discrepancy, although not of its correct value, it was evidently felt to be of little importance at the time of the Julian reform. However, it accumulated significantly over time.
The Gregorian Calendar was soon adopted by most Catholic countries (e.g. Spain, Portugal, Poland, most of Italy). Protestant countries followed later, and the countries of Eastern Europe even later. In the British Empire (including the American colonies), Wednesday 2 September 1752 was followed by Thursday 14 September 1752. For 12 years from 1700 Sweden used a modified Julian Calendar, and adopted the new-style calendar in 1753, but Russia remained on the Julian calendar until 1917, after the Russian Revolution (which is thus called the 'October Revolution' though it occurred in Gregorian November), while Greece continued to use it until 1923.
Although all Eastern Orthodox countries (most of them in Eastern or Southeastern Europe) had adopted the Gregorian calendar by 1927, their national churches had not. A revised Julian calendar was proposed during 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 almost all Orthodox churches continue to celebrate Easter according to the Julian calendar (the Finnish Orthodox Church uses the Gregorian Easter).
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 Alexandria, Antioch, the Orthodox Churches of Greece, Cyprus, Romania, Poland, Bulgaria (the last 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 on the same day that Western Christians do, 25 December Gregorian until 2800. The Orthodox Churches of Jerusalem, Russia, Macedonia, Serbia, Georgia, Ukraine, and the Greek Old Calendarists continue to use the Julian calendar for their fixed dates, thus they celebrate the Nativity on 25 December Julian (which is 7 January Gregorian until 2100).
In Northern Africa, the Julian calendar (the Berber calendar) is still in use for agricultural purposes, and is called فلاحي fellāhī "peasant" or sاﻋﺠﻤﻲ ajamī "not Arabic". Since it did not follow the Gregorian reform, its beginning slowly shifted and now the first of yennayer corresponds to January 14.

See also