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Encyclopedia: Gregorian calendar, Talk:Gregorian Calendar, Proleptic Gregorian calendar, Talk:Proleptic Gregorian Calendar, Wikipedia:Featured article candidates/Gregorian calendar, august 29, Image:Gregorian calendar - Chart of national adoption dates - after Wikipedia (vertically ordered & compressed).png

Gregorian calendar is the most widely used calendar 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 based on the traditional birth year of Jesus, which is labeled the "anno Domini" (AD) eraThis era was created in the 6th century by Roman monk Dionysius Exiguus and sometimes "common era" (CE).

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.
thumb|300px|right|Tomb of Pope Gregory XIII in St. Peter's Basilica.

The Gregorian calendar system dealt with these problems by dropping a certain number of days to bring the calendar back into synchronization with the seasons, and then slightly shortening the average number of days in a calendar year, by omitting three Julian leap-days every 400 years.

Description

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 solar calendar repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20871 seven-day weeks. Of these 400 years, 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 - or 365 days, 5 hours, 49 minutes and 12 seconds.

A Gregorian year is divided into twelve months of irregular length (but note that there is a period of 153 days divided over 5 months in an alternating pattern from March to July that repeats from August to December):

{| align="right" width="300"
|| thumb|300px|right|Detail of the tomb of Pope Gregory XIII celebrating the introduction of the Gregorian Calendar.
|-
||
|}
{| class="wikitable"
! No. || Name || Days
|-
| 1 || January || 31
|-
| 2 || February || 28 or 29
|-
| 3 || March || 31
|-
| 4 || April || 30
|-
| 5 || May || 31
|-
| 6 || June || 30
|-
| 7 || July || 31
|-
| 8 || August || 31
|-
| 9 || September || 30
|-
| 10 || October || 31
|-
| 11 || November || 30
|-
| 12 || December || 31
|}

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).

Leap years are all years divisible by 4, with the exception of those divisible by 100, but not by 400. These 366-day years add a 29th day to February, which normally has 28 days. Thus, the essential ongoing differential feature of the Gregorian calendar, as opposed to the Julian calendar, is that the Gregorian omits 3 leap days every 400 years. This difference would have been more noticeable in modern memory, were it not for the fact that the year 2000 was a leap year in both the Julian and Gregorian calendar systems.

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 were 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. See the section below for more discussion of this issue.

History

Invention

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 approximation 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). See Accuracy.

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. 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).

Beginning of the year

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). The following list is partially based on http://www.genfair.com/dates.htm Old Style and New Style Dates and http://homepages.tesco.net/~jk.calisto/calisto/calendars/change_dates_ny.htm The Change of New Year's Day.

{| class="wikitable"
|+Adoption of January 1 as beginning of numbered year
versus Gregorian Calendar adoption year
! Country || 1 January New Year || Greg Cal
|-
| Venice || 1522 || 1582
|-
| Germany || 1544 || from 1583
|-
| Spain, Portugal, and Southern Netherlands || 1556 || 1582
|-
| Prussia || 1559 || 1700
|-
| Denmark || 1559 || 1700
|-
| Sweden || 1559 || 1753
|-
| France || 1564 || 1582
|-
| Lorraine || 1579 || 1682
|-
| Dutch Republic || 1583 || from 1582
|-
| Scotland || 1600 || 1752
|-
| Russia || 1700 || 1918
|-
| Tuscany || 1721 || 1750
|-
| England || 1752 || 1752
|}

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.Benjamin Woolley, The Queen's Conjurer: The science and magic of Dr. John Dee, adviser to Queen Elizabeth I (New York: Henry Holt, 2001) p.173

Adoption of the Gregorian calendar

thumb|right|1755) painting which is the main source for "Give us our Eleven Days"">[William Hogarth (c. 1755) painting which is the main source for "Give us our Eleven Days"]

Only Spain and her territories, Portugal, the Polish-Lithuanian Commonwealth, and most of Italy implemented the new calendar on Friday, 15 October 1582, following Julian Thursday, 4 October 1582. France adopted the new calendar on Monday, 20 December 1582, following Sunday, 9 December 1582.http://www.norbyhus.dk/calendar.html#France Toke Nørby. The Perpetual Calendar: What about France? 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. England, Scotland and thereby the rest of the British Empire (including the eastern part of what is now the United States) did not adopt the Gregorian calendar until 1752; by which time it was necessary to correct by eleven days (Wednesday, 2 September 1752 being followed by Thursday, 14 September 1752) to account for 29 February 1700 (Julian). A few years later, when the son of the Earl of Macclesfield (who had been influential in passing the calendar law) ran for a seat in Parliament in Oxfordshire as a Whig in 1754, dissatisfaction with the calendar reforms was one of a number of issues raised by his Tory opponents. In 1755, William Hogarth made a painting (and an engraved print from the painting) loosely based on these elections, in which the campaign slogan "Give us our Eleven Days" appears (on floor at lower right); this was later misunderstood, giving rise to apocryphal stories of widespread riots at the change-over.

Great Britain legislated special provisions to make sure that monthly or yearly payments would not become due until the dates that they originally would have in the Julian calendar. From 1753 until 1799, the tax year in Great Britain began on 5 April, which was the "old style" new 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 is still 6 April.

"Old Style" (OS) and "New Style" (NS) are sometimes added to dates to identify which system is used in the British Empire and other countries that did not immediately change. In Britain it is usual to map most dates from the Julian year onto the Gregorian year without converting the day and month. But because the start of the year did not change until the same year that the Gregorian calendar was introduced, OS/NS is particularly relevant for dates which fall between 1 January and 25 March. For example the execution of King Charles I is usually recorded as having taken place on 30 January 1649 (NS), but in contemporary documents it is recorded as having taken place on 30 January 1648.http://www.british-history.ac.uk/report.asp?compid=26211#s5 House of Commons Journal Volume 8, 9 June, 1660 Regicides.

Denmark, Norway and the Protestant states of Germany adopted the solar portion of the new calendar on Monday, 1 March 1700,http://www.norbyhus.dk/calendar.html Toke Nørby. The Perpetual Calendar, following Sunday, 18 February 1700, due to the influence of Ole Rømer, 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 recognised 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.Mike Spathaky http://www.genfair.com/dates.htm Old Style and New Style Dates and the change to the Gregorian Calendar: A summary for genealogists

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 east of to west of Alaska 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 decreed that Wednesday, 31 January 1918 was to be followed by Thursday, 14 February 1918.

The last country of Eastern 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 Greek Orthodox church and the churches of Bulgaria, Romania, Poland adopted the Revised Julian calendar, so these New calendarists will celebrate the Nativity along with the Western churches on 25 December in the Gregorian calendar until 2800. The Orthodox churches of Russia, Serbia, Jerusalem, and a few bishops in Greece 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 that are not Orthodox churches, like the Coptic, Ethiopic, Nestorian, Jacobite, and Armenian, 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.

Adoption in East Asia

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 henceforth. 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" (西暦, seireki) 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.http://times.hankooki.com/lpage/opinion/200502/kt2005020616470454130.htm The Korea Times : [The Dawn of Modern Korea (266) Lunar Calendar]

Timeline

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from:1582 till:1582 text:"1582~France, Netherlands, Savoy, Luxembourg"
from:1583 till:1583 text:"1583~Austria; Catholic Switzerland and Germany"
from:1587 till:1587 text:"1587~Hungary"
from:1605 till:1710 text:"1605-1710~Nova Scotia" color:bleuclair anchor:from
from:1610 till:1610 text:"1610~Prussia"
from:1582 till:1735 text:"1582-1735~Duchy of Lorraine" color:bleuclair anchor:from
from:1648 till:1648 text:"1648~Alsace"
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from:1700 till:1700 text:"1700~Protestant Germany, Switzerland;~Denmark & Norway (and Iceland)" shift:(2,5)
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from:1896 till:1896 text:"1896~Korea"
from:1912 till:1912 text:"1912~Albania"
from:1915 till:1915 text:"1915~Latvia, Lithuania"
from:1916 till:1916 text:"1916~Bulgaria"
from:1918 till:1918 text:"1918~Russia, Estonia"
from:1919 till:1919 text:"1919~Romania, Yugoslavia
from:1922 till:1922 text:"1922~USSR"
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Proleptic Gregorian calendar

The Gregorian calendar can, for certain purposes, be extended backwards to dates preceding its official introduction, producing the proleptic Gregorian calendar. However, this proleptic calendar should be used with great caution.

For ordinary purposes, the dates of events occurring prior to 15 October 1582 are generally shown as they appeared in the Julian calendar, and not converted into their Gregorian equivalents.

However, events occurring in countries where the Gregorian calendar was introduced later than 4 October 1582 are a little more contentious. For example, in Great Britain and its overseas possessions (then including the American colonies), the new calendar was not introduced until 14 September 1752. How, then, would people date events occurring in Britain and her possessions in the 170 years between 1582 and 1752? The answer depends very much on the context, but writers who want to avoid confusion make it absolutely clear which calendar is being used. People have avoided changing historical records in Britain deriving from this period; however, it is often highly desirable to translate particular Old Style dates into their New Style equivalents, such as where the context includes reference to other countries that had already converted to New Style before Britain did. Astronomers avoid this ambiguity by the use of the Julian day number.

If comparisons of dates are done using different calendars, we can encounter logical absurdities such as William and Mary of Orange seeming to arrive in London to accept the English crown, a week or so before they left the Netherlands; and Shakespeare and Cervantes apparently dying on exactly the same date (23 April 1616), when in fact Cervantes predeceased Shakespeare by 10 days in real time. This coincidence however has allowed UNESCO to make 23 April the World Book and Copyright Day.

For dates before the year 1, unlike the proleptic Gregorian calendar used in the international standard ISO 8601, the traditional proleptic Gregorian calendar (like the Julian calendar) does not have a year 0 and instead uses the ordinal numbers 1, 2, … both for years AD and BC and for CE and BCE. Thus the traditional timeline is 2 BC, 1 BC, AD 1, and AD 2. ISO 8601 uses astronomical year numbering which includes a year 0 and negative numbers before it. Thus the ISO 8601 timeline is -0001, 0000, 0001, and 0002.

Confusion with British versus American usage

Dates of events in Britain prior to 1752 are usually now shown in their original Old Style form, whereas dates of events in (then British) America prior to 1752 are usually now shown in the New Style form.

* For example, Shakespeare died on 23 April (OS), and it is rare to see this converted to 3 May (NS). But while George Washington was born on 11 February (OS), his birthday is now celebrated on 22 February (NS). (He changed its celebration date himself, as a twenty-one-year-old surveyor.)

However, neither of these practices is universal in either country, so it is sometimes very unclear which calendar is being used, and this can lead to false assumptions, which can lead to dates being inaccurately converted from one calendar to the other. Since the resurgence of interest in the history of the calendar, more information about the real dates (according to various calendars) of events has been forthcoming and many previous errors have been corrected. While these changes are welcome, there is still much scope for confusion; therefore, noting the calendar being used in transitional periods would help the reader understand the dates involved.

Difference between Gregorian and Julian calendar dates

Since the introduction of the Gregorian calendar, the difference between faster Gregorian (New Style) and slower Julian (Old Style) calendar dates has increased as follows:

{| class="wikitable"
! Gregorian range || Julian range || Difference
|-
|From 15 October 1582
to 28 February 1700
|From 5 October 1582
to 18 February 1700
|10 days
|-
|From 1 March 1700
to 28 February 1800
|From 19 February 1700
to 17 February 1800
|11 days
|-
|From 1 March 1800
to 28 February 1900
|From 18 February 1800
to 16 February 1900
|12 days
|-
|From 1 March 1900
to 28 February 2100
|From 17 February 1900
to 15 February 2100
|13 days
|}

The difference grows by 3 days in every four centuries.

On average, 48,700 Gregorian years and 48,699 Julian years each equal 17,787,309.75 days. Any 194,800 consecutive Gregorian years and any consecutive 194,796 Julian years each have exactly 71,149,239 days. Approximately every 487 centuries, there is a period during which the difference between the calendars is approximately an integral number of years and the day of the year can be the same on both calendars. Every fourth one of these is a period that occurs exactly every 71,149,239 days (194,800 Gregorian years or 194,796 Julian years) and lasts 36,524 days (100 years on Gregorian calendar, and 99 years, 365 days on the Julian calendar), during which the difference between the calendars is an integral multiple of 1,461 days (four years) and the month and day of the month (but not the year) are the same on both calendars for the entire period. The remainder are periods of several centuries each, during which the day of the year coincides for approximately 25–75% of the months in each century.

Months of the year

English speakers sometimes remember the number of days in each month by the use of the traditional mnemonic verse:http://www.leapzine.com/30Days.htm The Month Poem

:Thirty days hath September,

:April, June, and November.

:All the rest have thirty-one,

:excepting February alone,

:which hath twenty-eight.

:Leap year cometh one year in four,

:in which February hath one day more.

(The hath in the first line of the poem is also given as has or have.)

Alternate endings include:

:excepting February alone,

:which has twenty-eight days or,

:in a leap year, adds one more.

:which has but twenty-eight, in fine,

:till leap year gives it twenty-nine.

:which has eight and a score,

:until leap year gives it one day more.

:which hath twenty-eight days clear,

:and twenty-nine in each leap year.

:in each leap we assign,

:February twenty-nine.

:When short February's done,

:all the rest have thirty-one.

:(except February,)

:February alone don't hold the line,

:for three years it has twenty-eight,

:and the fourth year twenty-nine.

:but February, it is done

:at twenty-eight, but add one more

:whenever the year divides by four.

A language-independent alternative used in many countries is to hold up your two fists with the index knuckle of your left hand against the index knuckle of your right hand. Then, starting with January from the little knuckle of your left hand, count knuckle, space, knuckle, space through the months. A knuckle represents a month of 31 days, and a space represents a short month (a 28- or 29-day February or any 30-day month). The junction between the hands is not counted, so the two index knuckles represent July and August. (The knuckle method also works by starting the sequence on the right hand's index knuckle, and continue afterwards to the left hand's index knuckle.) You can also use just one hand; after counting the fourth knuckle as July, start again counting the first knuckle as August.

The Origins of English naming used by the Gregorian calendar:
* January: Janus (Roman god of gates, doorways, beginnings and endings)
* February: februarius (mensis) (Latin for "month of purification (rituals)", of unknown origin, said to be Sabine word, last month of ancient pre-450 BC Roman calendar)
* March: Mars (Roman god of war)
* April: (mensis) Aprilis (Latin for "month of Venus", second month of ancient Roman calendar)
* May: Maia Maiestas (Roman goddess)
* June: Juno (Roman goddess, wife of Jupiter)
* July: Julius Caesar (Roman dictator)
* August: Augustus (first Roman emperor)
* September: septem (Latin for seven, the seventh month in the calendar of Romulus)
* October: octo (Latin for eight, the eighth month in the calendar of Romulus)
* November: novem (Latin for nine, the ninth month in the calendar of Romulus)
* December: decem (Latin for ten, the tenth month in the calendar of Romulus)

Accuracy

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 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/5000². This is a problem that the Gregorian calendar shares with any fixed rule-based calendar.

Calendar seasonal error

nome|640px|Gregorian calendar seasons difference

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

The y-axis is "days error" and the x-axis is Gregorian calendar years.

Each point represents a single date on a given year. The error shifts by about a quarter of a day per year. Years that are multiples of 100 but not 400 are not leap years. This causes a correction on years 1700, 1800, 1900, 2100, 2200, and 2300.

For instance, these corrections cause 23 December 1903 to be the latest December solstice, and 20 December 2096 to be the earliest solstice—2.25 days of variation compared with the seasonal event.

Numerical facts

When leap years and common years are taken into account, there are a total of 14 possible Gregorian calendars.

When different dates of Easter are also taken into account, there are a total of 70 possible Gregorian calendars.

An average year is 365.2425 days = 52.1775 weeks = 8,765.82 hours = 525,949.2 minutes = 31,556,952 seconds. All these numbers are exact, apart from leap seconds.

A common year is 365 days = 8,760 hours = 525,600 minutes = 31,536,000 seconds.

A leap year is 366 days = 8,784 hours = 527,040 minutes = 31,622,400 seconds.

Since 1971, some years may also contain one or more leap seconds, to account for cumulative irregularities in the Earth's rotation. So far, these have always been positive and have occurred on average once every 18 months.

The day of the year is somewhat inconvenient to compute, not in the least because of the leap day somewhere in the middle; but the calendar has this repeating pattern for the months March through July and August through December: 31, 30, 31, 30, 31 days, totalling 153 days. In fact, any 5 consecutive months not containing February, count 153 days. 153 happens to be the 17th triangular number, and the sum of the first 5 factorials (among other numerical trivia).

See also common year starting on Sunday and dominical letter.

The 400-year cycle of the Gregorian calendar has 146,097 days and hence exactly 20,871 weeks. So, for example, the days of the week in Gregorian 1603 were exactly the same as for 2003. This also causes more months to begin on a Sunday (and hence have Friday 13) than any other day of the week (see below for a more detailed explanation of how this happens). 688 out of every 4800 months (or 172/1200) begin on a Sunday, while only 684 out of every 4800 months (171/1200) begin on each of Saturday and Monday, the least common cases.

A smaller cycle is 28 years (1,461 weeks), provided that there is no dropped leap year in between. Days of the week in years may also repeat after 6, 11, 12, 28 or 40 years. Intervals of 6 and 11 are only possible with common years, while intervals of 28 and 40 are only possible with leap years. An interval of 12 years only occurs with common years when there is a dropped leap year in between.

The Doomsday algorithm is a method by which you can discern which of the 14 calendar variations should be used in any given year (after the Gregorian reformation). It is based on the last day in February, referred to as the Doomsday.

The Gregorian serial date, also called Rata Die, is the number of days from January 1, 1 A.D. (counting that day as day 1). For , , the serial date is Gregorian serial . It is 678576 more than the Modified Julian date, and 1721425 less than the Julian date round .

Week

In conjunction with the system of months there is a system of weeks. A physical or electronic calendar provides conversion from a given date to the weekday, and shows multiple dates for a given weekday and month. Calculating the day of the week is not very simple, because of the irregularities in the Gregorian system.

The ISO week date connects Gregorian years and weeks, defining a leap week calendar with so-called "ISO years" deviating at the beginning and end up to 3 days from Gregorian years, and with week numbers by year.

Origins of English naming used by the Gregorian Calendar:

* Monday - moon day (celestial)
* Tuesday - Tyr's day (Old Norse god)
* Wednesday - Woden's day (Old English god)
* Thursday - Thor's day (Old Norse god)
* Friday - Frigg's day (Old Norse goddess) (Friday is often erroneously associated with Freyja)
* Saturday - Saturn's day (Roman god)
* Sunday - sun day (celestial)

Distribution of dates by day of the week

Because there are 97 leap years in every 400 years in the Gregorian Calendar, there are on average for each starting weekday in each cycle. This already shows that the frequency is not the same for each weekday, which is due to the effects of the "common" centennial years (1700, 1800, 1900, 2100, 2200 etc.).

The absence of an extra day in such years causes the following leap year (1704, 1804, 1904, 2104 etc.) to start on the same day of the week as the leap year twelve years before (1692, 1792, 1892, 2092 etc.). Similarly, the leap year eight years after a "common" centennial year (1708, 1808, 1908, 2108 etc.) starts on the same day of the week as the leap year immediately prior to the "common" centennial year (1696, 1796, 1896, 2096 etc.). Thus, those days of the week on which such leap years begin gain an extra year or two in each cycle. In each cycle there are:

* 13 leap years starting on Monday
* 14 leap years starting on Tuesday
* 14 leap years starting on Wednesday
* 13 leap years starting on Thursday
* 15 leap years starting on Friday
* 13 leap years starting on Saturday
* 15 leap years starting on Sunday

Note that as a cycle, this pattern is symmetric with respect to the low Saturday value.

A leap year starting on Sunday means the next year does not start on Monday, so more leap years starting on Sunday means less years starting on Monday, etc. Thus the pattern of number of years starting on each day is inverted and shifted by one weekday: 56, 58, 57, 57, 58, 56, 58 (symmetric with respect to the high Sunday value).

The number of common years starting on each day is found by subtraction: 43, 44, 43, 44, 43, 43, 43.

The frequency of a particular date being on a particular weekday can easily be derived from the above (for dates in March and later, relate them to the next New Year).

See also the cycle of Doomsdays.

Days of the week

January 1 of any year whose number is a multiple of 400 is a Saturday. From this you can work out the day of the week of any date.

See also:
*Days of the week
*Calculating the day of the week

Trivia

The Roman calendar was modified by Julius Caesar when he occupied the office of Pontifex Maximus and the Julian calendar was subsequently modified by Gregory XIII, who, as pope, also held the title Pontifex Maximus.

Non-leap years always begin and end on the same day of the week. For example, 2003 began on a Wednesday and ended on a Wednesday. Leap years end on the next day of the week from which they begin. For example, 2004 began on a Thursday and ended on a Friday.

Not counting leap years, any calendar date will move to the next day of the week the following year. For example, if your birthday fell on a Tuesday in 2002, it fell on a Wednesday in 2003. Leap years make things a little more complicated. 2004 was a leap year, so calendar days of March 1 or later in the year, moved two days of the week from 2003. However, calendar days occurring before March 1 do not make the extra day of the week jump until the year following a leap year. So, if your birthday is June 15, then it must have fallen on a Sunday in 2003 and a Tuesday in 2004. If, however, your birthday is February 15, then it must have fallen on a Saturday in 2003, a Sunday in 2004 and a Tuesday in 2005.

In any year (even a leap year), July always begins on the same day of the week that April does. Therefore, the only difference between a July calendar page and an April calendar page in the same year is the extra day July has. The same relationship exists between September and December as well as between March and November. Add an extra day to the September page and you've got December. Take a day away from the March page and you've got November. In non-leap years only, there are additional matches: October duplicates January, and March and November duplicate February in their first 28 days. In leap years only, there is a different set of additional matches: July is a duplicate of January while February is duplicated in the first 29 days of August.

Saint Teresa of Ávila died on the night from 4 October to 15 October 1582, that is, exactly when Spain and the Catholic world switched to the Gregorian calendar.

References

*http://articles.adsabs.harvard.edu//full/book/grc../1983//0000001,001.html Gregorian reform of the calendar: Proceedings of the Vatican conference to commemorate its 400th anniversary, 1582-1992, ed. G. V. Coyne, M. A. Hoskin, and O. Pedersen (Vatican City: Pontifical Academy of Sciences, Specolo Vaticano, 1983).
*The Oxford Companion to the Year. Bonnie Blackburn & Leofranc Holford-Strevens. Oxford University Press 1999. ISBN 0-19-214231-3. Pages 98-99.
*http://www.davidewingduncan.net/books.htm#calendar Calendar: Humanity's Epic Struggle To Determine A True And Accurate Year, http://www.davidewingduncan.net David Ewing Duncan, Harper Perennial, 1999, ISBN 0-380-79324-5.
*http://www.etymonline.com/ Online Etymology Dictionary retrieved August 23, 2006