The Gregorian calendar is the calendar that is used nearly everywhere in the world. A modification of the Julian calendar, it was first proposed by the Calabrian doctor Aloysius Lilius, and was decreed by Pope Gregory XIII, for whom it was named, on 24 February 1582 via the papal bull Inter gravissimas. Its years are numbered per the perceived birth year of Jesus Christ, which is labeled the "anno Domini" era. This era was created in the 6th century by Roman monk Dionysius Exiguus.

The Gregorian Calendar was devised both because the mean year in the Julian Calendar was slightly too long, causing the vernal equinox to slowly drift backwards in the calendar year, and because the lunar calendar used to compute the date of Easter had grown conspicuously in error as well.

The Gregorian solar calendar is an arithmetical calendar. It counts days as the basic unit of time, grouping them into years of 365 or 366 days. The calendar repeats completely every 146,097 days, the cycle consisting of 400 years, of which 303, the "common years", have 365 days, and 97, the leap years, have 366 days. This gives an average year length of exactly 365.2425 days.

A Gregorian year is divided into twelve "months". Despite the name these are not synchronized with the phases of the Moon; the terminology derives from the Roman calendar that preceded the Julian calendar. The twelve months are of irregular lengths.

A calendar date is fully specified by the year (numbered by some scheme beyond the scope of the calendar itself), the month (identified by name or number), and the day of the month (numbered sequentially starting at 1).The leap years are all years divisible by 4, with the exception that those divisible by 100, but not by 400, are common years. These 366-day years add a 29th day to February, which normally has 28 days.

The intercalary day in a leap year is known as a leap day. Since Roman times 24 February (bissextile) was counted as the leap day, but nowadays 29 February is regarded as the leap day in most countries.

Although the calendar year runs from 1 January to 31 December, sometimes year numbers are based on a different starting point within the calendar. Confusingly, the term "Anno Domini" is not specific on this point, and actually refers to a family of year numbering systems with different starting points for the years.

The motivation of the Catholic Church in adjusting the calendar was to have Easter celebrated at the time that they thought had been agreed to at the First Council of Nicaea in 325. Although a canon of the council implies that all churches used the same Easter, they did not.

The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the Moon that falls on or after the vernal equinox, which they placed on 21 March.

However, the Church of Rome still regarded 25 March as the equinox and used a different day of the moon. By the tenth century all churches (except for some on the eastern border of the Byzantine Empire) had adopted the Alexandrian Easter, which still placed the vernal equinox on 21 March, although Bede had already noted its drift in 725 - it had drifted even further by the sixteenth century.

Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by a 19 year cycle. However, that is an approximation that built up an error of one day every 310 years. So by the sixteenth century the lunar calendar was out of phase with the real Moon by four days.

The Council of Trent approved a plan in 1563 for correcting the calendrical errors, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of Easter.

The fix was to come in two stages.

First, it was necessary to approximate the correct length of a solar year. The value chosen was 365.2425 days in decimal notation. This is 365;14,33 days in sexagesimal notation - the length of the tropical year, rounded to two sexagesimal positions; this was the value used in the major astronomical tables of the day.

Although close to the mean tropical year of 365.24219 days, it is even closer to the vernal equinox year of 365.2424 days; this fact made the choice of approximation particularly appropriate as the purpose of creating the calendar was to ensure that the vernal equinox would be near a specific date (21 March).

The second stage was to devise a model based on the approximation which would provide an accurate yet simple, rule-based calendar.

The formula designed by Aloysius Lilius was ultimately successful. It proposed a 10 day correction to revert the drift since Nicaea and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4.

He is primarily known as the creator of the Gregorian Calendar after writing a manuscript titled Compendiuem novae rationis restituendi kalendarium (Compendium of the New Plan for the Restitution of the Calendar). However, the reform to the calendar did not occur until after his death, when his brother Antonio presented the manuscript to Pope Gregory XIII. The manuscript was then given to the reform commission, and was adopted in 1582, after some modification by Christopher Clavius.

To implement the model, it was provided that years divisible by 100 would be leap years only if they were divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300 and 2500 will not be leap years, but 2400 will be. This theory was expanded upon by Christopher Clavius in a closely argued, 800 page volume. He would later defend his and Lilius's work against detractors.

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

Lilius originally proposed that the 10 day correction should be implemented by deleting the Julian leap day on each of its ten occurrences during a period of 40 years, thereby providing for a gradual return of the equinox to 21 March. However, Clavius's opinion was that the correction should take place in one move and it was this advice which prevailed with Gregory.

Accordingly, when the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of ten days. The last day of the Julian calendar was Thursday 4 October 1582 and this was followed by the first day of the Gregorian calendar, Friday 15 October 1582 (the cycle of weekdays was not affected).

Nevertheless, the dates "5 October 1582" to "14 October 1582" (inclusive) are still valid in virtually all countries because even most Roman Catholic countries did not adopt the new calendar on the date specified by the bull, but months or even years later (the last in 1587).

During the Middle Ages 1 January was given the name New Year's Day (or an equivalent name) in all Western European countries (those with predominantly Catholic populations), even while most of those countries began their numbered year on 25 December (the Nativity of Jesus), then 25 March (the Incarnation of Jesus), and even Easter, as in France.

This name was the result of always displaying the months of the medieval calendar from January to December (in twelve columns containing 28 to 31 days each), just like the Romans did. Furthermore, all Western European countries (except for a few Italian states) 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.

Eastern European countries (most of them with populations showing allegiance to the Orthodox Church) began their numbered year on 1 September (since about 988).

Neither the papal bull nor its attached canons explicitly state that the year of the Gregorian calendar is to begin on 1 January, contrary to popular opinion. However, it does imply such a year by including two tables of saint's days, one labeled 1582 which ends on 31 December, and another for any full year that begins on 1 January. It also specifies its epact relative to 1 January, in contrast with the Julian calendar, which specified it relative to 22 March. These would have been the inevitable result of the above shift in the beginning of the Julian year.

During the period between 1582, when the first countries adopted the Gregorian calendar, and 1923, when the last European country adopted it, it was often necessary to indicate the date of some event in both the Julian calendar and in the Gregorian calendar, for example, "10/21 February 1751/52", where the dual year accounts for some countries already beginning their numbered year on 1 January while others were still using some other date.

Even before 1582, the year sometimes had to be double dated because of the different beginnings of the year in various countries. Woolley, writing in his biography of John Dee (1527-1608/9), notes that immediately after 1582 English letter writers "customarily" used "two dates" on their letters, one OS and one NS.

Though Gregory's reform was "enacted" in the most solemn of forms available to the Church, in fact the bull had no authority of its own. The changes which he was "proposing" were changes to the civil calendar over which he had no authority. The changes required "adoption" by the civil authorities in each country to have legal effect.

Only four (Catholic) countries adopted the new calendar on the date specified by the bull. Other Catholic countries experienced some delay before adopting the reform; and non-Catholic countries, not being subject to the decrees of the Pope, initially rejected or simply ignored the reform altogether, although they all eventually adopted it. Hence, the dates "October 5, 1582" to "14 October 1582" (inclusive) are still valid dates in many countries.

Spain, Portugal, the Polish-Lithuanian Commonwealth, and most of Italy implemented the new calendar on Friday, 15 October 1582, following Julian Thursday, October 4, 1582.

The Spanish and Portuguese colonies adopted the calendar later due to the slowness of communication in those days. France adopted the new calendar on Monday, 20 December 1582, following Sunday, December 9, 1582.

October 5-14 1582: The Ten Days That Didn't Happen   IFL Science - October 18, 2023

The Protestant Dutch provinces of Holland and Zeeland also adopted it in December of that year. Most non-Catholic countries initially objected to adopting a Catholic invention, especially during the Counter-Reformation (of which Gregory was a leading proponent); some Protestants feared the new calendar was part of a plot to return them to the Catholic fold.

In the Czech lands, Protestants resisted the calendar imposed by the Hapsburg Monarchy. In parts of Ireland, Catholic rebels till their defeat in the Nine Years' War kept the "new" Easter in defiance of the English-loyal authorities; later Catholics practising in secret petitioned the Propaganda Fide for dispensation from observing the new calendar, as it signaled their disloyalty.

Denmark, Norway and the Protestant states of Germany adopted the solar portion of the new calendar on Monday, 1 March 1700, following Sunday, 18 February 1700, due to the influence of Ole R¿mer, but did not adopt the lunar portion. Instead, they decided to calculate the date of Easter astronomically using the instant of the vernal equinox and the full moon according to Kepler's Rudolphine Tables of 1627. They finally adopted the lunar portion of the Gregorian calendar in 1776.

The remaining provinces of the Dutch Republic also adopted the Gregorian calendar in 1700. Sweden's relationship with the Gregorian Calendar had a difficult birth. Sweden started to make the change from the OS calendar and towards the NS calendar in 1700, but it was decided to make the (then 11 day) adjustment gradually, by excluding the leap days (29 February) from each of 11 successive leap years, 1700 to 1740. In the meantime, not only would the Swedish calendar be out of step with both the Julian calendar and the Gregorian calendar for 40 years, but also the difference would not be static but would change every 4 years.

This strange system clearly had great potential for endless confusion when working out the dates of Swedish events in this 40 year period. To make matters worse, the system was poorly administered and the leap days that should have been excluded from 1704 and 1708 were not excluded. The Swedish calendar should by now have been 8 days behind the Gregorian, but it was still in fact 10 days behind. King Charles XII wisely recognized that the gradual change to the new system was not working and he abandoned it. However, rather than now proceeding directly to the Gregorian calendar (as in hindsight seems to have been the sensible and obvious thing to do), it was decided to revert to the Julian calendar.

This was achieved by introducing the unique date 30 February in the year 1712, adjusting the discrepancy in the calendars from 10 back to 11 days. Sweden finally adopted the Gregorian calendar in 1753, when Wednesday, 17 February was followed by Thursday, 1 March. Since Finland was under Swedish rule at that time, it did the same.

Britain and the British Empire (including the eastern part of what is now the United States) adopted the Gregorian calendar in 1752 (see the Calendar (New Style) Act 1750) by which time it was necessary to correct by 11 days. Wednesday, September 2, 1752 was followed by Thursday, September 14, 1752 to account for February 29, 1700 (Julian). After 1753, the British tax year in Britain continued to operate on the Julian calendar and began on 5 April, which was the "old style" new tax year of 25 March. A 12th skipped Julian leap day in 1800 changed its start to 6 April. It was not changed when a 13th Julian leap day was skipped in 1900, so the tax year in the United Kingdom still begins on 6 April.

In Alaska, the change took place when Friday, October 6, 1867 was followed again by Friday, October 18 after the US purchase of Alaska from Russia, which was still on the Julian calendar. Instead of 12 days, only 11 were skipped, and the day of the week was repeated on successive days, because the International Date Line was shifted from Alaska's eastern to western boundary along with the change to the Gregorian calendar.

In Russia the Gregorian calendar was accepted after the October Revolution (so named because it took place in October 1917 in the Julian calendar). On 24 January 1918 the Council of People's Commissars issued a Decree that Wednesday, 31 January 1918 was to be followed by Thursday, 14 February 1918. The last country of Eastern Orthodox Europe to adopt the Gregorian calendar was Greece on Thursday, 1 March 1923, following Wednesday, 15 February 1923. However, these were all civil adoptions - none of the national churches accepted it. Instead, a Revised Julian calendar was proposed in May 1923 which dropped 13 days in 1923 and adopted a different leap year rule that resulted in no difference between the two calendars until 2800.

The Orthodox churches of Constantinople, Alexandria, Antioch, Greece, Cyprus, Romania, Poland, and Bulgaria adopted the Revised Julian calendar, so these New calendarists would celebrate the Nativity along with the Western churches on 25 December in the Gregorian calendar until 2800. The Orthodox churches of Jerusalem, Russia, Serbia, Georgia and the Greek Old Calendarists did not accept the Revised Julian calendar.

These Old Calendarists continue to celebrate the Nativity on 25 December in the Julian calendar, which is 7 January in the Gregorian calendar until 2100. All of the other Eastern churches, the Oriental Orthodox churches (Coptic, Ethiopian, Eritrean, Syrian, Armenian) and the Assyrian Church, continue to use their own calendars, which usually result in fixed dates being celebrated in accordance with the Julian calendar. All Eastern churches continue to use the Julian Easter with the sole exception of the Finnish Orthodox Church, which has adopted the Gregorian Easter.

The Republic of China (ROC) formally adopted the Gregorian calendar at its founding on 1 January 1912, but China soon descended into a period of warlordism with different warlords using different calendars. With the unification of China under the Kuomintang in October 1928, the Nationalist Government decreed that effective 1 January 1929 the Gregorian calendar would be used thenceforth. However, China retained the Chinese traditions of numbering the months and a modified Era System, backdating the first year of the ROC to 1912; this system is still in use in Taiwan where this ROC government retains control. Upon its foundation in 1949, the People's Republic of China continued to use the Gregorian calendar with numbered months, but abolished the ROC Era System and adopted the Western fashion of naming years.

Japan replaced the traditional lunisolar calendar with the Gregorian calendar on 1 January 1873, but, like China, continued to number the months, and used reign names instead of the Common Era: Meiji 1=1868, Taisho 1=1912, Showa 1=1926, Heisei 1=1989, and so on. The "Western calendar" using western year numbers, is also widely accepted by civilians and to a lesser extent by government agencies.

Korea started using the Gregorian calendar on 1 January 1896 due to Japanese influence. The lunisolar Korean calendar used immediately before that day was based on the lunisolar Chinese calendar.

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long, which has an error of about one day per 3300 years with respect to the mean tropical year of 365.24219 days but less than half this error with respect to the vernal equinox year of 365.24237 days.

Both are substantially more accurate than the one day in 128 years error of the Julian calendar (average year 365.25 days).

On timescales of thousands of years, the Gregorian calendar falls behind the seasons drastically because the slowing down of the Earth's rotation makes each day slightly longer over time (see tidal acceleration and leap second) while the year maintains a more uniform duration. The equinox will occur earlier than now by a number of days approximately equal to [years into future/5000]. This is a problem that the Gregorian calendar shares with any rule-based calendar. Gregorian Calendar