The Gregorian calendar is the calendar used in most of the world. It was introduced in October 1582 by Pope Gregory XIII as a minor modification of the Julian calendar, reducing the average year from 365.25 days to 365.2425 days, and adjusting for the drift in the 'tropical' or 'solar' year that the inaccuracy had caused during the intervening centuries.
The calendar spaces leap years to make its 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 years 1600 and 2000 are.
There were two reasons to establish the Gregorian calendar. First, the Julian calendar assumed incorrectly that the average solar year is exactly 365.25 days long, an overestimate of a little under one day per century. The Gregorian reform shortened the average (calendar) year by 0.0075 days to stop the drift of the calendar with respect to the equinoxes. Second, in the years since the First Council of Nicaea in AD 325,[Note 1] the excess leap days introduced by the Julian algorithm had caused the calendar to drift such that the (Northern) spring equinox was occurring well before its nominal 21 March date. This date was important to the Christian churches because it is fundamental to the calculation of the date of Easter. To reinstate the association, the reform advanced the date by 10 days: Thursday 4 October 1582 was followed by Friday 15 October 1582. In addition, the reform also altered the lunar cycle used by the Church to calculate the date for Easter, because astronomical new moons were occurring four days before the calculated dates.
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 (for civil use only) in 1923. To unambiguously specify a date during the transition period (in contemporary documents or in history texts), both notations were given, tagged as 'Old Style' or 'New Style' as appropriate. During the 20th century, most non-Western countries also adopted the calendar, at least for civil purposes.
The Gregorian calendar, like the Julian calendar, is a solar calendar with 12 months of 28–31 days each. The year in both calendars consists of 365 days, with a leap day being added to February in the leap years. The months and length of months in the Gregorian calendar are the same as for the Julian calendar. The only difference is that the Gregorian reform omitted a leap day in three centurial years every 400 years and left the leap day unchanged.
A leap year normally occurred every 4 years, and the leap day was historically inserted by doubling 24 February. However, it is now customary to number the days of February sequentially with no gaps, and 29 February is typically considered the leap day. Before the 1969 revision of its General Roman Calendar, the 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.
|No.||Name||Length in days|
|2||February||28 (29 in leap years)|
Gregorian years are identified by consecutive year numbers. 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).
Calendar cycles repeat completely every 400 years, which equals 146,097 days.[Note 2][Note 3] 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 4]
Christopher Clavius (1538–1612), one of the main authors of the reform
Pope Gregory XIII, portrait by Lavinia Fontana, 16C.
First page of the papal bull Inter gravissimas
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 by papal bull Inter gravissimas dated 24 February 1582 by Pope Gregory XIII, after whom the calendar is named. 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 5]
Because the date of Easter is a function – the computus – of the date of the (northern hemisphere) spring equinox, the Catholic Church considered unacceptable the increasing divergence between the canonical date of the equinox and observed reality. Easter is celebrated on the Sunday after the ecclesiastical full moon on or after 21 March, which was adopted as an approximation to the March equinox. 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 time 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 for calendar reform. An 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. 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, but the project was not taken up again until the 1540s, and implemented only under Pope Gregory XIII (r. 1572–1585).
In 1545, the Council of Trent authorised 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 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. The reform adopted was a modification of a proposal made by the Calabrian doctor Aloysius Lilius (or Lilio).
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. 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. 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 0;14,33,9,57 (Alfonsine), 0;14,33,11,12 (Copernicus) and 0;14,33,9,24 (Reinhold). In decimal notation, these are equal to 0.24254606, 0.24255185, and 0.24254352, respectively. All values are the same to two sexagesimal places (0;14,33, equal to decimal 0.2425) and this is also the mean length of the Gregorian year. Thus Pitatus' solution would have commended itself to the astronomers.
Lilius's proposals had two components. First, he proposed a correction to the length of the year. The mean tropical year is 365.24219 days long. A commonly used value in Lilius's time, from the Alfonsine tables, is 365.2425463 days. 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 have drifted 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 that prevailed with Gregory.
The second component consisted of an approximation that 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 required revision because the astronomical new moon was, at the time of the reform, four days before the calculated new moon. It was 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. The method proposed by Lilius was revised somewhat in the final reform.
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).
First printed Gregorian calendar
A month after having decreed the reform, the pope (with a brief of 3 April 1582) granted to one Antoni Lilio the exclusive right to publish the calendar for a period of ten years. The Lunario Novo secondo la nuova riforma[a] was 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 revoked on 20 September 1582, because Antonio Lilio proved unable to keep up with the demand for copies.
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.
On 29 September 1582, Philip II of Spain decreed the change from the Julian to the Gregorian calendar. 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.
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.
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 by country
|1582||Spain, Portugal, France, Poland, Italy, Catholic Low Countries, Luxemburg, and colonies|
|1584||Kingdom of Bohemia, some catholic Swiss cantons[Note 6]|
|1700||'Germany',[Note 7] Protestant Low Countries, Norway, Denmark, some protestant Swiss cantons[Note 6]|
|1752||Great Britain, Ireland, and colonies|
|1753||Sweden and Finland|
|1919||Romania, Yugoslavia[Note 8]|
|1926||Turkey (common era years; Gregorian dates in use since 1917 Ottoman adoption)|
Difference between Gregorian and Julian calendar dates
|Gregorian range||Julian range||Difference|
|From 15 October 1582
to 28 February 1700
|From 5 October 1582
to 18 February 1700
|From 1 March 1700
to 28 February 1800
|From 19 February 1700
to 17 February 1800
|From 1 March 1800
to 28 February 1900
|From 18 February 1800
to 16 February 1900
|From 1 March 1900
to 28 February 2100
|From 17 February 1900
to 15 February 2100
|From 1 March 2100
to 28 February 2200
|From 16 February 2100
to 14 February 2200
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 (calculated backwards on the same basis, for years before 1582), and the difference between Gregorian and Julian calendar dates increases by three days every four centuries (all date ranges are inclusive).
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.
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.
Beginning of the year
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|Country||Start numbered year
on 1 January
|Roman Empire||153 BC|
|Denmark||Gradual change from
13th to 16th centuries
|Holy Roman Empire (Catholic states)||1544||1583|
|Spain, Poland, Portugal||1556||1582|
|Holy Roman Empire (Protestant states)||1559||1700[Note 7]|
|Great Britain and the British Empire
|Republic of Venice||1522||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 AUC 532 (222 BC), 15 March from AUC 532 (222 BC) and 1 January from AUC 601 (153 BC). The Julian calendar, which began in AUC 709 (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), 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.
In common usage, 1 January was regarded as New Year's Day and celebrated as such, but from the 12th century until 1751 the legal year in England began on 25 March (Lady Day). 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), although later histories adjust the start of the year to 1 January and record the execution as occurring in 1649.
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). 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.
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.
- In 1793 France abandoned the Gregorian calendar in favour of the French Republican Calendar. This change was reverted in 1805.
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.
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).
Proleptic Gregorian calendar
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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.
- January (31 days), from Latin mēnsis Iānuārius, "Month of Janus", the Roman god of gates, doorways, beginnings and endings
- February (28 days in common and 29 in leap years), from Latin mēnsis Februārius, "Month of the Februa", the Roman festival of purgation and purification, cognate with fever, the Etruscan death god Februus ("Purifier"), and the Proto-Indo-European word for sulfur
- March (31 days), from Latin mēnsis Mārtius, "Month of Mars", the Roman war god
- April (30 days), from Latin mēnsis Aprīlis, of uncertain meaning but usually derived from some form of the verb aperire ("to open") or the name of the goddess Aphrodite
- May (31 days), from Latin mēnsis Māius, "Month of Maia", a Roman vegetation goddess whose name is cognate with Latin magnus ("great") and English major
- June (30 days), from Latin mēnsis Iūnius, "Month of Juno", the Roman goddess of marriage, childbirth, and rule
- July (31 days), from Latin mēnsis Iūlius, "Month of Julius Caesar", the month of Caesar's birth, instituted in 44 BC as part of his calendrical reforms
- August (31 days), from Latin mēnsis Augustus, "Month of Augustus", instituted by Augustus in 8 BC in agreement with July and from the occurrence during the month of several important events during his rise to power
- September (30 days), from Latin mēnsis september, "seventh month", of the ten-month Roman year of Romulus c. 750 BC
- October (31 days), from Latin mēnsis octōber, "eighth month", of the ten-month Roman year of Romulus c. 750 BC
- November (30 days), from Latin mēnsis november, "ninth month", of the ten-month Roman year of Romulus c. 750 BC
- December (31 days), from Latin mēnsis december, "tenth month", of the ten-month Roman year of Romulus c. 750 BC
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, Italian, and French, 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:
Thirti dayes hath novembir
Thirty days have November,
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" but it has also been called "probably the only sixteenth-century poem most ordinary citizens know by heart". 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.
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.
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. This approximation has an error of about one day per 3,030 years 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 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. 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.
On time scales of thousands of years, the Gregorian calendar falls behind the astronomical seasons. This is because the Earth's speed of rotation is gradually slowing down, which makes each day slightly longer over time (see tidal acceleration and leap second) while the year maintains a more uniform duration.
Calendar seasonal error
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.
The following are proposed reforms of the Gregorian calendar:
- Holocene calendar
- International Fixed Calendar (also called the International Perpetual calendar)
- World Calendar
- World Season Calendar
- Leap week calendars
- Calendar (New Style) Act 1750
- Calendar reform
- Conversion between Julian and Gregorian calendars
- Doomsday rule
- French revolutionary calendar
- Hebrew calendar
- Dionysius Exiguus
- Inter gravissimas in English – Wikisource
- Julian day
- History of calendars
- ISO 8601, an international standard for the representation of dates and times, which uses the Gregorian calendar (see Section 3.2.1).
- List of adoption dates of the Gregorian calendar per country
- List of calendars
- Old Calendarists
- Revised Julian calendar (Milanković) – used in Eastern Orthodoxy
Precursors of the Gregorian reform
- Johannes de Sacrobosco, De Anni Ratione ("On reckoning the years"), c. 1235
- Roger Bacon, Opus Majus ("Greater Work"), c. 1267
- "New Almanac according to the new reform".
- rather than AUC 709 (45 BC) when the Roman Empire adopted the Julian calendar.
- 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.]
- 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.
- The same result is obtained by summing the fractional parts implied by the rule: 365 + 1/4 − 1/100 + 1/400 = 365 + 0.25 − 0.01 + 0.0025 = 365.2425
- 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.
- In the Old Swiss Confederacy, Helvetic Republic or in Switzerland adoptions were made between 1584 and 1811. Some catholic cantons switched in 1584, some protestant in 1700/1701. For a complete list see List of adoption dates of the Gregorian calendar per country.
- Protestant states in Germany used an astronomical Easter from 1700 to 1774, based on Kepler's Rudolphine Tables, differing from the Gregorian Easter twice, one week early in 1724 and 1744.
- 1919 in the regions comprising the former Kingdoms of Serbia and Montenegro (present-day Kosovo, Montenegro, Serbia and North 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.
- Lorraine reverted to Julian in 1735 and adopted Gregorian again in 1760
- In Scotland the legal start of year had been moved to 1 January in 1600.
- Dershowitz & Reingold (2008), p. 45. "The calendar in use today in most of the world is the Gregorian or new-style calendar designed by a commission assembled by Pope Gregory XIII in the sixteenth century.".
- "Introduction to Calendars". United States Naval Observatory. 15 May 2013.
- See Wikisource English translation of the (Latin) 1582 papal bull Inter gravissimas.
- Blegen (n.d.). sfnp error: no target: CITEREFBlegenn.d. (help)
- Richards (1998), p. 101.
- Clause 3.2.1 ISO 8601
- Walker (1945), p. 218.
- Richards (2013), p. 599.
- Ben-Menahem, Ari (2009). Historical Encyclopedia of Natural and Mathematical Sciences. 1. p. 863. ISBN 9783540688310.
- Carabias Torres (2012), p. 241.
- Ziggelaar (1983), pp. 211, 214.
- Moyer (1983).
- See, for example, Tabule illustrissimi principis regis alfonsii (Prague 1401−4). 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 planètes, des étoiles fixes, et des satellites de Jupiter et de Saturne (Paris 1740), available at  (go forward ten pages to Table III on p. 10).
- 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.
- Dreyer, J L E (2014). Tycho Brahe. Cambridge. p. 52. ISBN 978-1-108-06871-0.
- Swerdlow (1986).
- Meeus & Savoie (1992). sfnp error: no target: CITEREFMeeusSavoie1992 (help)
- Ziggelaar (1983), p. 220.
- Mezzi, E.; Vizza, F. (2010). Luigi Lilio Medico Astronomo e Matematico di Cirò. Reggio Calabria: Laruffa Editore. pp. 14, 52. citing as primary references: Biblioteca Nazionale Centrale die Firenze, Magl. 5.10.5/a, ASV A.A., Arm. I‑XVIII, 5506, f. 362r.
- Kamen, Henry (1998). Philip of Spain. Yale University Press. p. 248. ISBN 978-0300078008.
- ""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.
- "Calendar (New Style) Act 1750, Section 3". Parliament of Great Britain – via National Archives.
- A more extensive list is available at Conversion between Julian and Gregorian calendars
- Blackburn & Holford-Strevens (1999), p. 788.
- Herluf Nielsen: Kronologi (2nd ed., Dansk Historisk Fællesforening, Copenhagen 1967), pp. 48–50.
- Lamont, Roscoe (1920), "The reform of the Julian calendar", Popular Astronomy, 28: 18–32, Bibcode:1920PA.....28...18L
- "Calendrier grégorien en France". www.henk-reints.nl.
- 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)
- Blackburn & Holford-Strevens (1999), p. 784.
- John James Bond, Handy-book of rules and tables for verifying dates with the Christian era Scottish decree on pp. xvii–xviii.
- Roscoe Lamont, The reform of the Julian calendar, Popular Astronomy 28 (1920) 18–32. Decree of Peter the Great is on pp. 23–24.
- Lorenzo Cattini, Legislazione toscana raccolta e illustrata, vol. 10, p. 208.
- "Roman Dates: Eponymous Years". Tyndalehouse.com. Retrieved 14 September 2010.
- Spathaky, Mike. "Old Style and New Style Dates and the change to the Gregorian Calendar: A summary for genealogists".
- 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)
- Tuesday 31 December 1661, The Diary of Samuel Pepys "I sat down to end my journell for this year, ..."
- Nørby, Toke. The Perpetual Calendar: What about England Version 29 February 2000
- "House of Commons Journal Volume 8, 9 June 1660 (Regicides)". British History Online. Retrieved 18 March 2007.
- 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.
- Nørby, Toke. The Perpetual Calendar
- Woolley, Benjamin (2001). The Queen's Conjurer: The science and magic of Dr. John Dee, adviser to Queen Elizabeth I. New York: Henry Holt. p. 173.
- 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."
- "January, n.", Oxford English Dictionary, Oxford: Oxford University Press.
- "February, n.", Oxford English Dictionary.
- Liberman, Anatoly (7 March 2007), "On a Self-Congratulatory Note", Oxford Etymologist Archives, Oxford: Oxford University Press.
- "March, n.", Oxford English Dictionary.
- "April, n.", Oxford English Dictionary.
- 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.
- Plutarch, Life of Numa, Ch. xix.
- Scullard, Festivals and Ceremonies of the Roman Republic, p. 96.
- Forsythe, Time in Roman Religion, p. 10.
- This derivation was apparently a popular one in ancient Rome, given by Plutarch but rejected by Varro and Cincius.[where?]
- "May, n.", Oxford English Dictionary.
- "June, n.", Oxford English Dictionary.
- "July, n.", Oxford English Dictionary.
- "August, n.", Oxford English Dictionary.
- "September, n.", Oxford English Dictionary.
- "October, n.", Oxford English Dictionary.
- "November, n.", Oxford English Dictionary.
- "December, n.", Oxford English Dictionary.
- Onofri, Francesca Romana; et al. (2012), Italian for Dummies, Berlitz, pp. 101–2, ISBN 9781118258767.
- Bond, Otto Ferdinand; et al. (1918), Military Manual of Elementary French, Austin: E.L. Steck, p. 11.
- Bryan, Roger (30 October 2011), "The Oldest Rhyme in the Book", The Times, London: Times Newspapers.
- Misstear, Rachael (16 January 2012), "Welsh Author Digs Deep to Find Medieval Origins of Thirty Days Hath Verse", Wales Online, Media Wales, archived from the original on 6 February 2012.
- "Memorable Mnemonics", Today, London: BBC Radio 4, 30 November 2011.
- The Cincinnati Enquirer, Cincinnati, 20 September 1924, p. 6.
- Holland, Norman N. (1992), The Critical I, New York: Columbia University Press, p. 64–5, ISBN 9780231076517.
- Seidelmann (1992), pp. 580–581.
- Using value from Richards (2013, p. 587) for tropical year in mean solar days, the calculation is 1/(365.2425-365.24217)
- Meeus & Savoie (1992), p. 42. sfnp error: no target: CITEREFMeeusSavoie1992 (help)
- Herschel, John (1849). Outlines of Astronomy. p. 629.
- Steel, Duncan (2000). Marking Time: The Epic Quest to Invent the Perfect Calendar. John Wiley & Sons. p. 185. ISBN 978-0-471-29827-4.
- Barsoum, Ignatius A. (2003). The Scattered Pearls. Piscataway: Georgias Press.
- Blackburn, Bonnie; Holford-Strevens, Leofranc (1999). The Oxford Companion to the Year. Oxford University Press. ISBN 9780192142313..
- Blackburn, Bonnie; Holford-Strevens, Leofranc (2003). The Oxford Companion to the Year: An exploration of calendar customs and time-reckoning (corrected reprinting of 1999 ed.). Oxford University Press. ISBN 9780192142313.
- Blegen, Carl W. (25 December 2013) [n.d.]. Vogeikoff-Brogan, Natalia (ed.). "An Odd Christmas". From the Archivist's Notebook. Retrieved 1 April 2018.
- Borkowski, K. M. (1991). "The tropical calendar and solar year". Journal of the Royal Astronomical Society of Canada. 85 (3): 21–130. Bibcode:1991JRASC..85..121B.
- Carabias Torres, A. M (2012). Salamanca y la medida del tiempo (in Spanish). Salamanca: Ediciones Universidad de Salamanca.
- Coyne, G. V.; Hoskin, M. A.; Pedersen, O., eds. (1983). Gregorian Reform of the Calendar. Vatican Conference to Commemorate its 400th Anniversary, 1582–1982. Vatican City: Pontifical Academy of Sciences, Vatican Observatory (Pontificia Academia Scientarum, Specola Vaticana).
- Dershowitz, D.; Reingold, E. M (2008). Calendrical Calculations (3rd ed.). Cambridge: Cambridge University Press.
- Duncan, D. E (1999). Calendar: Humanity's Epic Struggle To Determine A True And Accurate Year. HarperCollins. ISBN 9780380793242.
- Gregory XIII (1582). Inter Gravissimas [Amongst the most serious tasks of our pastoral office]. Translated by Wikisource.
- Meeus, J.; Savoie, D. (1992). "The history of the tropical year". Journal of the British Astronomical Association. 102 (1): 40–42. Bibcode:1992JBAA..102...40M.
- Morrison, L. V.; Stephenson, F. R. (2004). "Historical values of the Earth's clock error ΔT and the calculation of eclipses". Journal for the History of Astronomy. 35, part 3 (120): 327–336. Bibcode:2004JHA....35..327M. doi:10.1177/002182860403500305. S2CID 119021116.
- Moyer, Gordon (May 1982). "The Gregorian Calendar". Scientific American. Vol. 246 no. 5. pp. 144–152.
- Moyer, Gordon (1983). Coyne, G. V.; Hoskin, M. A.; Pedersen, O. (eds.). Aloisius Lilius and the Compendium Novae Rationis Restituendi Kalendarium. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican City: Pontifical Academy of Sciences, Specolo Vaticano. pp. 171–188.
- Pattie, T.S. (1976). "An unexpected effect of the change in calendar in 1752" (PDF). British Library Journal.
- Pedersen, O (1983). Coyne, G. V.; Hoskin, M. A.; Pedersen, O. (eds.). The Ecclesiastical Calendar and the Life of the Church. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican City: Pontifical Academy of Sciences, Specolo Vaticano. pp. 17–74.
- Richards, E. G. (1998). Mapping Time: The Calendar and its History. Oxford University Press.
- Richards, E. G. (2013). "Calendars". In Urban, S. E.; Seidelmann, P. K. (eds.). Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley CA: University Science Books. pp. 585–624. ISBN 978-1-891389-85-6.
- Seidelmann, P. K., ed. (1992). Explanatory Supplement to the Astronomical Almanac (2nd ed.). Sausalito, CA: University Science Books.
- Swerdlow, N. M. (1986). "The Length of the Year in the Original Proposal for the Gregorian Calendar". Journal for the History of Astronomy. 17 (49): 109–118. Bibcode:1986JHA....17..109S. doi:10.1177/002182868601700204. S2CID 118491152.
- Walker, G. W. (June 1945). "Easter Intervals". Popular Astronomy. Vol. 53 no. 6. pp. 162–178, 218–232. Bibcode:1945PA.....53..218W.
- Ziggelaar, A. (1983). Coyne, G. V.; Hoskin, M. A.; Pedersen, O. (eds.). The Papal Bull of 1582 Promulgating a Reform of the Calendar. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican City: Pontifical Academy of Sciences, Specolo Vaticano. pp. 201–239.
- Inter gravissimas in English – Wikisource
- Gregorian calendar on In Our Time at the BBC
- Calendar Converter
- Inter Gravissimas (Latin and French plus English)
- History of Gregorian Calendar
- The Perpetual Calendar Gregorian Calendar adoption dates for many countries.
- World records for mentally calculating the day of the week in the Gregorian Calendar
- The Calendar FAQ – Frequently Asked Questions about Calendars
- Today's date (Gregorian) in over 800 more-or-less obscure foreign languages