Gregorian calendar

The Gregorian calendar is the most widely used civil calendar in the world.[1][Note 1] It is named after Pope Gregory XIII, who introduced it in October 1582. The calendar spaces leap years to make the average year 365.2425 days long, approximating the 365.2422-day tropical year that is determined by the Earth's revolution around the Sun. The rule for leap years is:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is.[2]

The calendar was developed as a correction to the Julian calendar,[3] shortening the average year by 0.0075 days to stop the drift of the calendar with respect to the equinoxes. To deal with the 10 days' difference (between calendar and reality) that this drift had already reached, the date was advanced so that 4 October 1582 was followed by 15 October 1582. There was no discontinuity in the cycle of weekdays or of the Anno Domini calendar era.[Note 2] The reform also altered the lunar cycle used by the Church to calculate the date for Easter (computus), restoring it to the time of the year as originally celebrated by the early Church.

The reform was adopted initially by the Catholic countries of Europe and their overseas possessions. Over the next three centuries, the Protestant and Eastern Orthodox countries also moved to what they called the Improved calendar, with Greece being the last European country to adopt the calendar in 1923.[5] To unambiguously specify a date during the transition period, dual dating is sometimes used to specify both Old Style and New Style dates. Due to globalization in the 20th century, the calendar has also been adopted by most non-Western countries for civil purposes. The calendar era carries the alternative secular name of "Common Era".

2019 in various calendars
Gregorian calendar2019
MMXIX
Ab urbe condita2772
Armenian calendar1468
ԹՎ ՌՆԿԸ
Assyrian calendar6769
Bahá'í calendar175–176
Balinese saka calendar1940–1941
Bengali calendar1426
Berber calendar2969
British Regnal year67 Eliz. 2 – 68 Eliz. 2
Buddhist calendar2563
Burmese calendar1381
Byzantine calendar7527–7528
Chinese calendar戊戌(Earth Dog)
4715 or 4655
    — to —
己亥年 (Earth Pig)
4716 or 4656
Coptic calendar1735–1736
Discordian calendar3185
Ethiopian calendar2011–2012
Hebrew calendar5779–5780
Hindu calendars
 - Vikram Samvat2075–2076
 - Shaka Samvat1940–1941
 - Kali Yuga5119–5120
Holocene calendar12019
Igbo calendar1019–1020
Iranian calendar1397–1398
Islamic calendar1440–1441
Japanese calendarHeisei 31
(平成31年)
Javanese calendar1952–1953
Juche calendar108
Julian calendarGregorian minus 13 days
Korean calendar4352
Minguo calendarROC 108
民國108年
Nanakshahi calendar551
Thai solar calendar2562
Tibetan calendar阳土狗年
(male Earth-Dog)
2145 or 1764 or 992
    — to —
阴土猪年
(female Earth-Pig)
2146 or 1765 or 993
Unix time1546300800 – 1577836799

Description

A year is divided into twelve months
No. Name Length in days
1 January 31
2 February 28 (29 in leap years)
3 March 31
4 April 30
5 May 31
6 June 30
7 July 31
8 August 31
9 September 30
10 October 31
11 November 30
12 December 31

The Gregorian calendar is a solar calendar with 12 months of 28–31 days each. A regular Gregorian year consists of 365 days, but in certain years known as leap years, a leap day is added to February. Gregorian years are identified by consecutive year numbers.[6] A calendar date is fully specified by the year (numbered according to a calendar era, in this case Anno Domini or Common Era), the month (identified by name or number), and the day of the month (numbered sequentially starting from 1). Although the calendar year currently runs from 1 January to 31 December, at previous times year numbers were based on a different starting point within the calendar (see the "beginning of the year" section below).

In the Julian calendar, a leap year occurred every 4 years, and the leap day was inserted by doubling 24 February. The Gregorian reform omitted a leap day in three of every 400 years and left the leap day unchanged. However, it has become customary in the modern period to number the days sequentially with no gaps, and 29 February is typically considered as the leap day. Before the 1969 revision of the Roman Calendar, the Roman Catholic Church delayed February feasts after the 23rd by one day in leap years; Masses celebrated according to the previous calendar still reflect this delay.[7]

Calendar cycles repeat completely every 400 years, which equals 146,097 days.[Note 3][Note 4] Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A mean calendar year is 365 97/400 days = 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.[Note 5]

Gregorian reform

Christopher Clavius

Christopher Clavius (1538–1612), one of the main authors of the reform

Pope Gregory XIII

Pope Gregory XIII in an early 17th-century engraving

Inter-grav

First page of the papal bull Inter gravissimas

Gregorianscher Kalender Petersdom

Detail of the pope's tomb by Camillo Rusconi (completed 1723); Antonio Lilio is genuflecting before the pope, presenting his printed calendar.

The Gregorian calendar was a reform of the Julian calendar. It was instituted in 1582 by Pope Gregory XIII, after whom the calendar was named, by papal bull Inter gravissimas dated 24 February 1582.[3] The motivation for the adjustment was to bring the date for the celebration of Easter to the time of year in which it was celebrated when it was introduced by the early Church. The error in the Julian calendar (its assumption that there are exactly 365.25 days in a year) had led to the date of the equinox according to the calendar drifting from the observed reality, and thus an error had been introduced into the calculation of the date of Easter. Although a recommendation of the First Council of Nicaea in 325 specified that all Christians should celebrate Easter on the same day, it took almost five centuries before virtually all Christians achieved that objective by adopting the rules of the Church of Alexandria (see Easter for the issues which arose).[Note 6]

Background

Because the date of Easter was tied to the Spring Equinox, the Roman Catholic Church considered the seasonal drift in the date of Easter undesirable. The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the moon (computed using the Metonic cycle) that falls on or after the vernal equinox, which they placed on 21 March. However, the Church of Rome still regarded 25 March (Lady Day) as the equinox (until 342), and used a different cycle to compute the day of the moon.[9] In the Alexandrian system, since the 14th day of the Easter moon could fall at earliest on 21 March its first day could fall no earlier than 8 March and no later than 5 April. This meant that Easter varied between 22 March and 25 April. In Rome, Easter was not allowed to fall later than 21 April, that being the day of the Parilia or birthday of Rome and a pagan festival. The first day of the Easter moon could fall no earlier than 5 March and no later than 2 April.

Easter was the Sunday after the 15th day of this moon, whose 14th day was allowed to precede the equinox. Where the two systems produced different dates there was generally a compromise so that both churches were able to celebrate on the same day. By the 10th century all churches (except 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 16th century.[10]

Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by a 19-year cycle. That approximation built up an error of one day every 310 years, so by the 16th century the lunar calendar was out of phase with the real Moon by four days.

European scholars had been well aware of the calendar drift since the early medieval period. Bede, writing in the 8th century, showed that the accumulated error in his day was more than three days. Roger Bacon in c. 1200 estimated the error at seven or eight days. Dante, writing c. 1300, was aware of the need of a calendar reform. The first attempt to go forward with such a reform was undertaken by Pope Sixtus IV, who in 1475 invited Regiomontanus to the Vatican for this purpose. However, the project was interrupted by the death of Regiomontanus shortly after his arrival in Rome.[11] The increase of astronomical knowledge and the precision of observations towards the end of the 15th century made the question more pressing. Numerous publications over the following decades called for a calendar reform, among them two papers sent to the Vatican by the University of Salamanca in 1515 and 1578,[12] but the project was not taken up again until the 1540s, and implemented only under Pope Gregory XIII (r. 1572–1585).

Preparation

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

In 1577, a Compendium was sent to expert mathematicians outside the reform commission for comments. Some of these experts, including Giambattista Benedetti and Giuseppe Moleto, believed Easter should be computed from the true motions of the sun and moon, rather than using a tabular method, but these recommendations were not adopted.[13] The reform adopted was a modification of a proposal made by the Calabrian doctor Aloysius Lilius (or Lilio).[14]

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

Ancient tables provided the sun's mean longitude.[15] The German mathematician Christopher Clavius, the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the sun passed through the vernal equinox nor on the length of the mean tropical year. Tycho Brahe also noticed discrepancies.[16] The Gregorian leap year rule (97 leap years in 400 years) was put forward by Petrus Pitatus of Verona in 1560. He noted that it is consistent with the tropical year of the Alfonsine tables and with the mean tropical year of Copernicus (De revolutionibus) and Erasmus Reinhold (Prutenic tables). The three mean tropical years in Babylonian sexagesimals as the excess over 365 days (the way they would have been extracted from the tables of mean longitude) were 14,33,9,57 (Alfonsine), 14,33,11,12 (Copernicus) and 14,33,9,24 (Reinhold). All values are the same to two places (14:33) and this is also the mean length of the Gregorian year. Thus Pitatus' solution would have commended itself to the astronomers.[17]

Lilius's proposals had two components. Firstly, he proposed a correction to the length of the year. The mean tropical year is 365.24219 days long.[18] A commonly used value in Lilius's time, from the Alfonsine tables, is 365.2425463 days.[19] As the average length of a Julian year is 365.25 days, the Julian year is almost 11 minutes longer than the mean tropical year. The discrepancy results in a drift of about three days every 400 years. Lilius's proposal resulted in an average year of 365.2425 days (see Accuracy). At the time of Gregory's reform there had already been a drift of 10 days since the Council of Nicaea, resulting in the vernal equinox falling on 10 or 11 March instead of the ecclesiastically fixed date of 21 March, and if unreformed it would drift further. Lilius proposed that the 10-day drift should be corrected by deleting the Julian leap day on each of its ten occurrences over a period of forty years, thereby providing for a gradual return of the equinox to 21 March.

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

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

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

When the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of 10 days. The Julian calendar day Thursday, 4 October 1582 was followed by the first day of the Gregorian calendar, Friday, 15 October 1582 (the cycle of weekdays was not affected).

Adoption

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

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

A month after having decreed the reform, the pope with a brief of 3 April 1582 granted to Antonio Lilio, the brother of Luigi Lilio, the exclusive right to publish the calendar for a period of ten years. The Lunario Novo secondo la nuova riforma printed by Vincenzo Accolti, one of the first calendars printed in Rome after the reform, notes at the bottom that it was signed with papal authorization and by Lilio (Con licentia delli Superiori... et permissu Ant(onii) Lilij). The papal brief was later revoked, on 20 September 1582, because Antonio Lilio proved unable to keep up with the demand for copies.[20]

On 29 September 1582, Philip II of Spain decreed the change from the Julian to the Gregorian calendar.[21] This affected much of Roman Catholic Europe, as Philip was at the time ruler over Spain and Portugal as well as much of Italy. In these territories, as well as in the Polish–Lithuanian Commonwealth (ruled by Anna Jagiellon) and in the Papal States, the new calendar was implemented on the date specified by the bull, with Julian Thursday, 4 October 1582, being followed by Gregorian Friday, 15 October 1582. The Spanish and Portuguese colonies followed somewhat later de facto because of delay in communication.[22]

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

Britain and the British Empire (including the eastern part of what is now the United States) adopted the Gregorian calendar in 1752. Sweden followed in 1753.

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

Adoption of the Gregorian Calendar
1500 1600 1700 1800 1900

1582: Spain, Portugal, France, Poland, Italy, Catholic Low Countries, Luxemburg, and colonies
1584: Kingdom of Bohemia

1610: Prussia
1648: Alsace
1682: Strasbourg

1700: 'Germany',[Note 7] Swiss Cantons, Protestant Low Countries, Norway, Denmark
1752: Great Britain and colonies
1753: Sweden and Finland

1873: Japan
1875: Egypt
1896: Korea

1912: China, Albania
1915: Latvia, Lithuania
1916: Bulgaria
1918: Russia, Estonia
1919: Romania, Yugoslavia[Note 8]
1923: Greece
1926: Turkey

Difference between Gregorian and Julian calendar dates

Conversion from Julian to Gregorian dates.[24]
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
From 1 March 2100
to 28 February 2200
From 16 February 2100
to 14 February 2200
14 days

Since the introduction of the Gregorian calendar, the difference between Gregorian and Julian calendar dates has increased by three days every four centuries (all date ranges are inclusive):

This section always places the intercalary day on 29 February even though it was always obtained by doubling 24 February (the bissextum (twice sixth) or bissextile day) until the late Middle Ages. The Gregorian calendar is proleptic before 1582 (assumed to exist before 1582).

The following equation gives the number of days (actually, dates) that the Gregorian calendar is ahead of the Julian calendar, called the secular difference between the two calendars. A negative difference means the Julian calendar is ahead of the Gregorian calendar.[25]

where is the secular difference and is the year using astronomical year numbering, that is, use (year BC) − 1 for BC years. means that if the result of the division is not an integer it is rounded down to the nearest integer. Thus during the 1900s, 1900/400 = 4, while during the −500s, −500/400 = −2.

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

Up to 28 February in the calendar being converted from, add one day less or subtract one day more than the calculated value. Give February the appropriate number of days for the calendar being converted into. When subtracting days to calculate the Gregorian equivalent of 29 February (Julian), 29 February is discounted. Thus if the calculated value is −4 the Gregorian equivalent of this date is 24 February.[26]

Beginning of the year

Country Start numbered year
on 1 January
Adoption of
Gregorian calendar
Denmark Gradual change from
13th to 16th centuries[27]
1700
Holy Roman Empire (Catholic states) 1544 1583
Spain, Poland, Portugal 1556 1582
Holy Roman Empire (Protestant states) 1559 1700[Note 7]
Sweden 1559 1753
France 1564[29] 1582[n 1]
Southern Netherlands 1576[30] 1582
Lorraine 1579 1582[Note 9]
Dutch Republic 1583 1582
Scotland 1600[31][32] 1752
Russia 1700[33] 1918
Tuscany 1750[34] 1582[35]
Great Britain and the British Empire
except Scotland
1752[31] 1752
Venice 1797[36] 1582

The year used in dates during the Roman Republic and the Roman Empire was the consular year, which began on the day when consuls first entered office—probably 1 May before 222 BC, 15 March from 222 BC and 1 January from 153 BC.[37] The Julian calendar, which began in 45 BC, continued to use 1 January as the first day of the new year. Even though the year used for dates changed, the civil year always displayed its months in the order January to December from the Roman Republican period until the present.

During the Middle Ages, under the influence of the Catholic Church, many Western European countries moved the start of the year to one of several important Christian festivals—25 December (supposed Nativity of Jesus), 25 March (Annunciation), or Easter (France),[38] while the Byzantine Empire began its year on 1 September and Russia did so on 1 March until 1492 when the new year was moved to 1 September.[39]

In common usage, 1 January was regarded as New Year's Day and celebrated as such,[40] but from the 12th century until 1751 the legal year in England began on 25 March (Lady Day).[41] So, for example, the Parliamentary record lists the execution of Charles I on 30 January as occurring in 1648 (as the year did not end until 24 March),[42] although later histories adjust the start of the year to 1 January and record the execution as occurring in 1649.[43]

Most Western European countries changed the start of the year to 1 January before they adopted the Gregorian calendar. For example, Scotland changed the start of the Scottish New Year to 1 January in 1600 (this means that 1599 was a short year). England, Ireland and the British colonies changed the start of the year to 1 January in 1752 (so 1751 was a short year with only 282 days) though in England the start of the tax year remained at 25 March (O.S.), 5 April (N.S.) until 1800, when it moved to 6 April. Later in 1752 in September the Gregorian calendar was introduced throughout Britain and the British colonies (see the section Adoption). These two reforms were implemented by the Calendar (New Style) Act 1750.[44]

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

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

  1. ^ In 1793 France abandoned the Gregorian calendar in favour of the French Republican Calendar. This change was reverted in 1805.

Dual dating

During the period between 1582, when the first countries adopted the Gregorian calendar, and 1923, when the last European country adopted it, it was often necessary to indicate the date of some event in both the Julian calendar and in the Gregorian calendar, for example, "10/21 February 1750/51", where the dual year accounts for some countries already beginning their numbered year on 1 January while others were still using some other date. Even before 1582, the year sometimes had to be double dated because of the different beginnings of the year in various countries. Woolley, writing in his biography of John Dee (1527–1608/9), notes that immediately after 1582 English letter writers "customarily" used "two dates" on their letters, one OS and one NS.[45]

Old Style and New Style dates

"Old Style" (OS) and "New Style" (NS) are sometimes added to dates to identify which calendar reference system is used for the date given. In Britain and its Colonies, where the Calendar Act of 1750 altered the start of the year,[Note 10] and also aligned the British calendar with the Gregorian calendar, there is some confusion as to what these terms mean. They can indicate that the start of the Julian year has been adjusted to start on 1 January (NS) even though contemporary documents use a different start of year (OS); or to indicate that a date conforms to the Julian calendar (OS), formerly in use in many countries, rather than the Gregorian calendar (NS).[43][46]

Proleptic Gregorian calendar

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

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

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

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

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

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

Months

The Gregorian calendar continued to employ the Julian months, which have Latinate names and irregular numbers of days:

Europeans sometimes attempt to remember the number of days in each month by memorizing some form of the traditional verse "Thirty Days Hath September". It appears in Latin,[64] Italian,[65] and French,[66] and belongs to a broad oral tradition but the earliest currently attested form of the poem is the English marginalia inserted into a calendar of saints c. 1425:[67][68]

Thirti dayes hath novembir
April june and Septembir.
Of xxviij is but oon
And alle the remenaunt xxx and j[67]

  

Thirty days have November,
April, June, and September.
Of 28 is but one
And all the remnant 30 and 1.

Month - Knuckles (en)
The knuckle mnemonic for the days of the months of the year

Variations appeared in Mother Goose and continue to be taught at schools. The unhelpfulness of such involved mnemonics has been parodied as "Thirty days hath September / But all the rest I can't remember"[69] but it has also been called "probably the only sixteenth-century poem most ordinary citizens know by heart".[70] A common nonverbal alternative is the knuckle mnemonic, considering the knuckles of one's hands as months with 31 days and the lower spaces between them as the months with fewer days. Using two hands, one may start from either pinkie knuckle as January and count across, omitting the space between the index knuckles (July and August). The same procedure can be done using the knuckles of a single hand, returning from the last (July) to the first (August) and continuing through. A similar mnemonic is to move up a piano keyboard in semitones from an F key, taking the white keys as the longer months and the black keys as the shorter ones.

Weeks

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. When the Gregorian calendar was adopted by each country, the weekly cycle continued uninterrupted. For example, in the case of the few countries that adopted the reformed calendar on the date proposed by Gregory XIII for the calendar's adoption, Friday, 15 October 1582, the preceding date was Thursday, 4 October 1582 (Julian calendar).

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

Accuracy

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long.[71] This approximation has an error of about one day per 3,030 years[72] with respect to the current value of the mean tropical year. However, because of the precession of the equinoxes, which is not constant, and the movement of the perihelion (which affects the Earth's orbital speed) the error with respect to the astronomical vernal equinox is variable; using the average interval between vernal equinoxes near 2000 of 365.24237 days[73] implies an error closer to 1 day every 7,700 years. By any criterion, the Gregorian calendar is substantially more accurate than the 1 day in 128 years error of the Julian calendar (average year 365.25 days).

In the 19th century, Sir John Herschel proposed a modification to the Gregorian calendar with 969 leap days every 4000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period.[74] This would reduce the average year to 365.24225 days. Herschel's proposal would make the year 4000, and multiples thereof, common instead of leap. While this modification has often been proposed since, it has never been officially adopted.[75]

On time scales of thousands of years, the Gregorian calendar falls behind the astronomical seasons 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.

Calendar seasonal error

Gregorian calendar seasons difference

Gregorian calendar seasons difference

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

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

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

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

Proposed reforms

The following are proposed reforms of the Gregorian calendar:

See also

Precursors of the Gregorian reform

Notes

  1. ^ The international standard for the representation of dates and times, ISO 8601, uses the Gregorian calendar. Section 3.2.1.
  2. ^ Two era names occur within the bull Inter gravissimas itself, anno Incarnationis dominicæ ("in the year of the Incarnation of the Lord") for the year it was signed, and anno à Nativitate Domini nostri Jesu Christi ("in the year from the Nativity of our Lord Jesus Christ") for the year it was printed.[4]
  3. ^ The cycle described applies to the solar, or civil, calendar. If one also considers the ecclesiastical lunar rules, the lunisolar Easter computus cycle repeats only after 5,700,000 years of 2,081,882,250 days in 70,499,183 lunar months, based on an assumed mean lunar month of 29 days 12 hours 44 minutes 2 49928114/70499183 seconds. (Seidelmann (1992), p. 582) [To properly function as an Easter computus, this lunisolar cycle must have the same mean year as the Gregorian solar cycle, and indeed that is exactly the case.]
  4. ^ The extreme length of the Gregorian Easter computus is due to its being the product of the 19-year Metonic cycle, the thirty different possible values of the epact, and the least common multiple (10,000) of the 400-year and 2,500-year solar and lunar correction cycles.[8]
  5. ^ The same result is obtained by summing the fractional parts implied by the rule: 365 + 1/41/100 + 1/400 = 365 + 0.25 − 0.01 + 0.0025 = 365.2425
  6. ^ The last major Christian region to accept the Alexandrian rules was the Carolingian Empire (most of Western Europe) during 780–800. The last monastery in England to accept the Alexandrian rules did so in 931, and a few churches in southwest Asia beyond the eastern border of the Byzantine Empire continued to use rules that differed slightly, causing four dates for Easter to differ every 532 years.
  7. ^ a b Protestant states in Germany used an astronomical Easter from 1700 to 1774, based on Tycho Brahe's tables, differing from the Gregorian Easter twice, one week early in 1724 and 1744.[28]
  8. ^ 1919 in the regions comprising the former Kingdoms of Serbia and Montenegro (present-day Kosovo, Montenegro, Serbia and Macedonia). The western and northern regions of what became Yugoslavia were already using the Gregorian calendar. For example, most of Slovenia adopted the Gregorian calendar at the same time as Austria in 1583. Coastal Croatia, which was at the time ruled by Venice, adopted the Gregorian calendar in 1582. Inland Croatia, ruled by the Habsburgs, adopted it in 1587 along with Hungary. The Gregorian calendar was used in Bosnia and Herzegovina since the 16th century by the Catholic population and was formally adopted for government use in 1878 following occupation by Austria-Hungary.
  9. ^ Lorraine reverted to Julian in 1735 and adopted Gregorian again in 1760
  10. ^ In Scotland the legal start of year had been moved to 1 January in 1600 (Mike Spathaky. Old Style New Style dates and the change to the Gregorian calendar).

Citations

  1. ^
  2. ^ Introduction to Calendars. (15 May 2013). United States Naval Observatory.
  3. ^ a b See Wikisource English translation of the (Latin) 1582 papal bull Inter gravissimas.
  4. ^ Les canons of Les textes fondateurs du calendrier grégorien (in Latin) (in French)
  5. ^ Blegen n.d.
  6. ^ Clause 3.2.1 ISO 8601
  7. ^ Richards, p. 101
  8. ^ Walker (1945), p.218.
  9. ^ Pedersen (1983), pp. 42–43.
  10. ^ For example, in the Julian calendar, at Rome in 1550, the March equinox occurred at 11 Mar 6:51 AM local mean time. "Seasons calculator", Time and Date AS, 2014.
  11. ^ Ari Ben-Menahem, Historical Encyclopedia of Natural and Mathematical Sciences vol. 1 (2009), p. 863.
  12. ^ Carabias Torres, 2012, p. 241
  13. ^ Ziggelaar (1983), pp. 211, 214.
  14. ^ Moyer 1983.
  15. ^
    • See, for example,Tabule illustrissimi principis regis alfonsii, Prague 1401 −4 (Latin). A full set of Alphonsine Tables (including tables for mean motions, conjunctions of sun and moon, equation of time, spherical astronomy, longitudes and latitudes of cities, star tables, eclipse tables).
    • For an example of the information provided see Jacques Cassini, Tables astronomiques du soleil, de la lune, des planetes, des etoiles fixes, et des satellites de Jupiter et de Saturne, Paris 1740, available at [1] (go forward ten pages to Table III on p. 10).
  16. ^
    • Dreyer, J L E (2014). Tycho Brahe. Cambridge. p. 52. ISBN 978-1-108-06871-0. He remarks that both the Alphonsine and the Prutenic Tables are several hours wrong with regard to the time of the equinoxes and solstices.
    • North, J (1989). The Universal frame: historical essays in astronomy, natural philosophy and scientific method. London. p. 29. ISBN 978-0-907628-95-8. He noted on one occasion that the Alphonsine tables differed from the Prutenic by nineteen hours as to the time of the vernal equinox of 1588.
  17. ^ Swerdlow (1986).
  18. ^ Meeus and Savoie (1992).
  19. ^ Moyer (1983). p.
  20. ^ Mezzi, E., and Vizza, F., Luigi Lilio Medico Astronomo e Matematico di Cirò, Laruffa Editore, Reggio Calabria, 2010, p. 14; p. 52, citing as primary references: Biblioteca Nazionale Centrale die Firenze, Magl. 5.10.5/a, ASV A.A., Arm. I‑XVII, 5506, f. 362r.
  21. ^ Kamen, Henry (1998). Philip of Spain. Yale University Press. p. 248. ISBN 978-0300078008.
  22. ^ "Pragmatica" on the Ten Days of the Year World Digital Library, the first known South American imprint, produced in 1584 by Antonio Ricardo, of a four-page edict issued by King Philip II of Spain in 1582, decreeing the change from the Julian to the Gregorian calendar.
  23. ^ 24 Geo. II Ch. 23, § 3.
  24. ^ A more extensive list is available at Conversion between Julian and Gregorian calendars
  25. ^ Blackburn & Holford-Strevens (1999), p. 788.
  26. ^
    • James Evans, The history and practice of ancient astronomy (Oxford: Oxford University Press, 1998) 169. ISBN 0-19-509539-1.
    • Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac (London: Her Majesty's Stationery Office, 1961) 417.
  27. ^ Herluf Nielsen: Kronologi (2nd ed., Dansk Historisk Fællesforening, Copenhagen 1967), pp. 48–50.
  28. ^ Lamont, Roscoe (1920), "The reform of the Julian calendar", Popular Astronomy, 28: 18–32
  29. ^ Le calendrier grégorien en France (in French)
  30. ^ Per decree of 16 June 1575. Hermann Grotefend, "Osteranfang" (Easter beginning), Zeitrechnung de Deutschen Mittelalters und der Neuzeit (Chronology of the German Middle Ages and modern times) (1891–1898)
  31. ^ a b Blackburn & Holford-Strevens (1999), p. 784.
  32. ^ John James Bond, Handy-book of rules and tables for verifying dates with the Christian era Scottish decree on pp. xvii–xviii.
  33. ^ Roscoe Lamont, The reform of the Julian calendar, Popular Astronomy 28 (1920) 18–32. Decree of Peter the Great is on pp. 23–24.
  34. ^
  35. ^ Lorenzo Cattini, Legislazione toscana raccolta e illustrata, vol. 10, p. 208.
  36. ^ Fora Febraro.
  37. ^ "Roman Dates: Eponymous Years". Tyndalehouse.com. Retrieved 14 September 2010.
  38. ^ Mike Spathaky Old Style and New Style Dates and the change to the Gregorian Calendar: A summary for genealogists
  39. ^ S. I. Seleschnikow: Wieviel Monde hat ein Jahr? (Aulis-Verlag, Leipzig/Jena/Berlin 1981, p. 149), which is a German translation of С. И. Селешников: История календаря и хронология (Издательство "Наука", Moscow 1977). The relevant chapter is available online here: История календаря в России и в СССР (Calendar history in Russia and the USSR). Anno Mundi 7000 lasted from 1 March 1492 to 31 August 1492. (in Russian)
  40. ^ Tuesday 31 December 1661, The Diary of Samuel Pepys "I sat down to end my journell for this year, ..."
  41. ^ Nørby, Toke. The Perpetual Calendar: What about England Version 29 February 2000
  42. ^ "House of Commons Journal Volume 8, 9 June 1660 (Regicides)". British History Online. Retrieved 18 March 2007.
  43. ^ a b Death warrant of Charles I web page of the UK National Archives. A demonstration of New Style meaning Julian calendar with a start of year adjustment.
  44. ^ Nørby, Toke. The Perpetual Calendar
  45. ^ 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
  46. ^
    • Spathaky, Mike Old Style New Style dates and the change to the Gregorian calendar. "increasingly parish registers, in addition to a new year heading after 24th March showing, for example '1733', had another heading at the end of the following December indicating '1733/4'. This showed where the New Style 1734 started even though the Old Style 1733 continued until 24th March. ... We as historians have no excuse for creating ambiguity and must keep to the notation described above in one of its forms. It is no good writing simply 20th January 1745, for a reader is left wondering whether we have used the Old or the New Style reckoning. The date should either be written 20th January 1745 OS (if indeed it was Old Style) or as 20th January 1745/6. The hyphen (1745-6) is best avoided as it can be interpreted as indicating a period of time."
    • The October (November) Revolution Britannica encyclopaedia, A demonstration of New Style meaning the Gregorian calendar.
    • Stockton, J.R. Date Miscellany I: The Old and New Styles "The terms 'Old Style' and 'New Style' are now commonly used for both the 'Start of Year' and 'Leap Year' [(Gregorian calendar)] changes (England & Wales: both in 1752; Scotland: 1600, 1752). I believe that, properly and historically, the 'Styles' really refer only to the 'Start of Year' change (from March 25th to January 1st); and that the 'Leap Year' change should be described as the change from Julian to Gregorian."
  47. ^ "January, n.", Oxford English Dictionary, Oxford: Oxford University Press.
  48. ^ a b c "February, n.", Oxford English Dictionary.
  49. ^ a b c d e f g Liberman, Anatoly (7 March 2007), "On a Self-Congratulatory Note", Oxford Etymologist Archives, Oxford: Oxford University Press.
  50. ^ "March, n.", Oxford English Dictionary.
  51. ^ "April, n.", Oxford English Dictionary.
  52. ^ It's not unusual for month names to be based on natural descriptions but this etymology is sometimes doubted since no other Roman months have such names.[49]
  53. ^ Plutarch, Life of Numa, Ch. xix.
  54. ^
    • Scullard, Festivals and Ceremonies of the Roman Republic, p. 96.
    • Forsythe, Time in Roman Religion, p. 10.
  55. ^ This derivation was apparently a popular one in ancient Rome, given by Plutarch[53] but rejected by Varro and Cincius.[54]
  56. ^ a b "May, n.", Oxford English Dictionary.
  57. ^ "June, n.", Oxford English Dictionary.
  58. ^ "July, n.", Oxford English Dictionary.
  59. ^ "August, n.", Oxford English Dictionary.
  60. ^ a b c d "September, n.", Oxford English Dictionary.
  61. ^ "October, n.", Oxford English Dictionary.
  62. ^ "November, n.", Oxford English Dictionary.
  63. ^ "December, n.", Oxford English Dictionary.
  64. ^
  65. ^ Onofri, Francesca Romana; et al. (2012), Italian for Dummies, Berlitz, pp. 101–2, ISBN 9781118258767.
  66. ^ Bond, Otto Ferdinand; et al. (1918), Military Manual of Elementary French, Austin: E.L. Steck, p. 11.
  67. ^ a b Bryan, Roger (30 October 2011), "The Oldest Rhyme in the Book", The Times, London: Times Newspapers.
  68. ^
  69. ^ The Cincinnati Enquirer, Cincinnati, 20 September 1924, p. 6.
  70. ^ Holland, Norman N. (1992), The Critical I, New York: Columbia University Press, p. 64–5, ISBN 9780231076517.
  71. ^ Seidelmann (1992), pp. 580–581.
  72. ^ Using value from Richards (2013, p. 587) for tropical year in mean solar days, the calculation is 1/(365.2425-365.24217)
  73. ^ Meeus and Savoie (1992), p. 42
  74. ^ John Herschel, Outlines of Astronomy, 1849, p. 629.
  75. ^ Steel, Duncan (2000). Marking Time: The Epic Quest to Invent the Perfect Calendar. John Wiley & Sons. p. 185. ISBN 978-0-471-29827-4.

References

External links

1876

1876 (MDCCCLXXVI)

was a leap year starting on Saturday of the Gregorian calendar and a leap year starting on Thursday of the Julian calendar, the 1876th year of the Common Era (CE) and Anno Domini (AD) designations, the 876th year of the 2nd millennium, the 76th year of the 19th century, and the 7th year of the 1870s decade. As of the start of 1876, the Gregorian calendar was

12 days ahead of the Julian calendar, which remained in localized use until 1923.

2020

2020 (MMXX)

will be a leap year starting on Wednesday of the Gregorian calendar, the 2020th year of the Common Era (CE) and Anno Domini (AD) designations, the 20th year of the 3rd millennium, the 20th year of the 21st century, and the 1st year of the 2020s decade.

2044

2044 (MMXLIV)

will be a leap year starting on Friday of the Gregorian calendar, the 2044th year of the Common Era (CE) and Anno Domini (AD) designations, the 44th year of the 3rd millennium, the 44th year of the 21st century, and the 5th year of the 2040s decade.

Adoption of the Gregorian calendar

The adoption of the Gregorian Calendar was an event in the modern history of most nations and societies, marking a change from their traditional (or old style) dating system to the modern (or new style) dating system that is widely used around the world today. Some countries adopted the new calendar from 1582, some did not do so before the early twentieth century, and others did so at various dates between; however a number continue to use a different civil calendar. For many the new style calendar is only used for civil purposes and the old style calendar remains used in religious contexts. Today, the Gregorian calendar is the world's most widely used civil calendar. During – and for some time after – the change between systems, it has been common to use the terms Old Style and New Style when giving dates, to indicate which calendar was used to reckon them.

The Gregorian calendar was decreed in 1582 by the papal bull Inter gravissimas by Pope Gregory XIII, to correct a divergence in the canonical date of the [northern] spring equinox from observed reality (due to an error in the Julian system) that affected the calculation of the date of Easter. Although Gregory's reform was enacted in the most solemn of forms available to the Church, the bull had no authority beyond the Catholic Church and the Papal States. The changes he was proposing were changes to the civil calendar, over which he had no formal authority. They required adoption by the civil authorities in each country to have legal effect.

The bull became the canon law of the Catholic Church in 1582, but it was not recognised by Protestant churches, Eastern Orthodox Churches, and a few others. Consequently, the days on which Easter and related holidays were celebrated by different Christian churches again diverged.

August 29

August 29 is the 241st day of the year (242nd in leap years) in the Gregorian calendar. There are 124 days remaining until the end of the year.

Common year starting on Friday

A common year starting on Friday is any non-leap year (i.e. a year with 365 days) that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2010 and the next one will be 2021 in the Gregorian calendar, or, likewise, 2011 and 2022 in the obsolete Julian calendar. The century year, 2100, will also be a common year starting on Friday in the Gregorian calendar. See below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.

Common year starting on Monday

A common year starting on Monday is any non-leap year (i.e., a year with 365 days) that begins on Monday, 1 January, and ends on Monday, 31 December. Its dominical letter hence is G. The most recent year of such kind was 2018 and the next one will be 2029 in the Gregorian calendar, or likewise, 2013 and 2019 (the current year) in the obsolete Julian calendar. The century year, 1900, was also a common year starting on Monday in the Gregorian calendar. See below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year of this type contains two Friday the 13ths in April and July. Leap years starting on Sunday share this characteristic, but also have another in January.

Common year starting on Saturday

A common year starting on Saturday is any non-leap year (i.e. a year with 365 days) that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2011 and the next one will be 2022 in the Gregorian calendar or, likewise, 2017 and 2023 in the obsolete Julian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in May. Leap years starting on Friday share this characteristic.

Common year starting on Sunday

A common year starting on Sunday is any non-leap year (i.e. a year with 365 days) that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2017 and the next one will be 2023 in the Gregorian calendar, or, likewise, 2018 and 2029 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in January and October.

Common year starting on Thursday

A common year starting on Thursday is any non-leap year (i.e. a year with 365 days) that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar or, likewise, 2010 and 2021 in the obsolete Julian calendar, see below for more. This common year contains the most Friday the 13ths; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic.

From February until March in this type of year is also the shortest period (one month) that occurs within a Friday the 13th.

Common year starting on Wednesday

A common year starting on Wednesday is any non-leap year (i.e. a year with 365 days) that begins on Wednesday, 1 January, and ends on Wednesday, 31 December. Its dominical letter hence is E. The most recent year of such kind was 2014, and the next one will be 2025 in the in the Gregorian calendar or, likewise, 2009, 2015, and 2026 in the obsolete Julian calendar. The century year, 1800, was also a common year starting on Wednesday in the Gregorian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in June. Leap years starting on Tuesday share this characteristic.

February 29

February 29, also known as leap day or leap year day, is a date added to most years that are divisible by 4, such as 2016, 2020, and 2024. A leap day is added in various solar calendars (calendars based on the Earth's revolution around the Sun), including the Gregorian calendar standard in most of the world. Lunisolar calendars (whose months are based on the phases of the Moon) instead add a leap or intercalary month.In the Gregorian calendar, years that are divisible by 100, but not by 400, do not contain a leap day. Thus, 1700, 1800, and 1900 did not contain a leap day; neither will 2100, 2200, and 2300. Conversely, 1600 and 2000 did and 2400 will. Years containing a leap day are called leap years. Years not containing a leap day are called common years. February 29 is the 60th day of the Gregorian calendar, in such a year, with 306 days remaining until the end of the year. In the Chinese calendar, this day will only occur in years of the monkey, dragon, and rat.

A leap day is observed because the Earth's period of orbital revolution around the Sun takes approximately 6 hours longer than 365 whole days. A leap day compensates for this lag, realigning the calendar with the Earth's position in the Solar System; otherwise, seasons would occur later than intended in the calendar year. The Julian calendar used in Christendom until the 16th century added a leap day every four years; but this rule adds too many days (roughly 3 every 400 years), making the equinoxes and solstices shift gradually to earlier dates. By the 16th century the vernal equinox had drifted to March 11, and the Gregorian calendar was introduced both to shift it back by omitting several days, and to reduce the number of leap years via the "century rule" to keep the equinoxes more or less fixed and the date of Easter consistently close to the vernal equinox.

Julian day

Julian day is the continuous count of days since the beginning of the Julian Period and is used primarily by astronomers, and in software for easily calculating elapsed days between two events (e.g. food production date and sell by date).

The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Universal time, with Julian day number 0 assigned to the day starting at noon on Monday, January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar), a date at which three multi-year cycles started (which are: Indiction, Solar, and Lunar cycles) and which preceded any dates in recorded history. For example, the Julian day number for the day starting at 12:00 UT on January 1, 2000, was 2 451 545.The Julian date (JD) of any instant is the Julian day number plus the fraction of a day since the preceding noon in Universal Time. Julian dates are expressed as a Julian day number with a decimal fraction added. For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2 456 293.520 833.The Julian Period is a chronological interval of 7980 years; year 1 of the Julian Period was 4713 BC. It has been used by historians since its introduction in 1583 to convert between different calendars. The Julian calendar year 2019 is year 6732 of the current Julian Period. The next Julian Period begins in the year AD 3268.

Leap year

A leap year (also known as an intercalary year or bissextile year) is a calendar year containing one additional day (or, in the case of lunisolar calendars, a month) added to keep the calendar year synchronized with the astronomical or seasonal year. Because seasons and astronomical events do not repeat in a whole number of days, calendars that have the same number of days in each year drift over time with respect to the event that the year is supposed to track. By inserting (also called intercalating) an additional day or month into the year, the drift can be corrected. A year that is not a leap year is called a common year.

For example, in the Gregorian calendar, each leap year has 366 days instead of 365, by extending February to 29 days rather than the common 28. These extra days occur in years which are multiples of four (with the exception of centennial years not divisible by 400). Similarly, in the lunisolar Hebrew calendar, Adar Aleph, a 13th lunar month, is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Bahá'í Calendar, a leap day is added when needed to ensure that the following year begins on the vernal equinox.

The name "leap year" probably comes from the fact that while a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, the day of the week in the 12 months following the leap day (from March 1 through February 28 of the following year) will advance two days due to the extra day (thus "leaping over" one of the days in the week). For example, Christmas Day (December 25) fell on a Sunday in 2016, Monday in 2017, and Tuesday in 2018, then will fall on Wednesday in 2019 but then "leaps" over Thursday to fall on a Friday in 2020.

The length of a day is also occasionally changed by the insertion of leap seconds into Coordinated Universal Time (UTC), owing to the variability of Earth's rotational period. Unlike leap days, leap seconds are not introduced on a regular schedule, since the variability in the length of the day is not entirely predictable.

List of calendars

This is a list of calendars. Included are historical calendars as well as proposed ones. Historical calendars are often grouped into larger categories by cultural sphere or historical period; thus O'Neil (1976) distinguishes the groupings Egyptian calendars (Ancient Egypt), Babylonian calendars (Ancient Mesopotamia), Indian calendars (Hindu and Buddhist traditions of the Indian subcontinent), Chinese calendars and Mesoamerican calendars.

These are not specific calendars but series of historical calendars undergoing reforms or regional diversification.

In Classical Antiquity, the Hellenic calendars inspired the Roman calendar, including the solar Julian calendar introduced in 45 BC. Many modern calendar proposals, including the Gregorian calendar itself, are in turn modifications of the Julian calendar.

Lunar calendar

A lunar calendar is a calendar based upon the monthly cycles of the Moon's phases (synodic months), in contrast to solar calendars, whose annual cycles are based only directly upon the solar year. The most commonly used calendar, the Gregorian calendar, is a solar calendar system that originally evolved out of a lunar calendar system. A purely lunar calendar is also distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation. The details of when months begin varies from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.

Since each lunation is approximately ​29 1⁄2 days (29 days, 12 hours, 44 minutes, 3 seconds, or 29.530588 days), it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of twelve such lunations, a lunar year, is only 354 days, 8 hours, 48 minutes, 34 seconds (354.367056 days), purely lunar calendars lose around 11 days per year relative to the Gregorian calendar. In purely lunar calendars like the Islamic calendar, the lack of intercalation causes the lunar months to cycle through all the seasons of the Gregorian year over the course of a 33 lunar-year cycle.

Although the Gregorian calendar is in common and legal use in most countries, traditional lunar and lunisolar calendars continue to be used throughout the Old World to determine religious festivals and national holidays. Examples of such holidays include Ramadan (Islamic calendar); Easter; the Chinese, Japanese, Korean, Vietnamese, and Mongolian New Year (Chinese, Japanese, Korean, Vietnamese, and Mongolian calendars); the Nepali New Year (Nepali calendar); the Mid-Autumn Festival and Chuseok (Chinese and Korean calendars); Loi Krathong (Thai calendar); Sunuwar calendar; Vesak/Buddha's Birthday (Buddhist calendar); Diwali (Hindu calendars); and Rosh Hashanah (Hebrew calendar).

Minguo calendar

The Republic of China Calendar (traditional Chinese: 民國紀年(中華民國曆); simplified Chinese: 民国纪年(中华民国历); pinyin: Mínguó Jìyuán; Wade–Giles: Min2-kuo2 Chi4-yüan2; literally: 'Republic[an] year numbering system (Republic of China calendar)') is the official calendar of the Republic of China. It is used to number the years for official purposes only in the Taiwan area after 1949. It was used in the Chinese mainland from 1912 until the establishment of the People's Republic of China in 1949.

Following the Chinese imperial tradition of using the sovereign's era name and year of reign, official ROC documents use the Republic (traditional Chinese: 民國; simplified Chinese: 民国; pinyin: Minguo; literally: 'Civilian Nation/ Republic') system of numbering years in which the first year was 1912, the year of the establishment of the Republic of China. Months and days are numbered according to the Gregorian calendar.

Old Style and New Style dates

Old Style (O.S.) and New Style (N.S.) are terms sometimes used with dates to indicate that the calendar convention used at the time described is different from that in use at the time the document was being written. There were two calendar changes in Great Britain and its colonies, which may sometimes complicate matters: the first was to change the start of the year from Lady Day (25 March) to 1 January; the second was to discard the Julian calendar in favour of the Gregorian calendar. Closely related is the custom of dual dating, where writers gave two consecutive years to reflect differences in the starting date of the year, or to include both the Julian and Gregorian dates.

Beginning in 1582, the Gregorian calendar replaced the Julian in Roman Catholic countries. This change was implemented subsequently in Protestant and Orthodox countries, usually at much later dates. In England and Wales, Ireland, and the British colonies, the change to the start of the year and the changeover from the Julian calendar occurred in 1752 under the Calendar (New Style) Act 1750. In Scotland, the legal start of the year had already been moved to 1 January (in 1600), but Scotland otherwise continued to use the Julian calendar until 1752. Thus "New Style" can either refer to the start of year adjustment, or to the adoption of the Gregorian calendar.

In Russia, new style dates came into use in early 1918. Other countries in Eastern Orthodoxy adopted new style dating for their civil calendars but most continue to use the Julian calendar for religious use. In English-language histories of other countries (especially Russia), the Anglophone OS/NS convention is often used to identify which calendar is being used when giving a date.

Proleptic Gregorian calendar

The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582. In countries that adopted the Gregorian calendar later, dates occurring in the interim (between 1582 and the local adoption) are sometimes "Gregorianized" as well. For example, George Washington was born on February 11, 1731 (Old Style), as Great Britain and its possessions were using the Julian calendar with English years starting on March 25 until September 1752. After the switch, that day became February 22, 1732, which is the date commonly given as Washington's birthday.

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