Gregorian calendar

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 there is one day less in the leap month (February) every four hundred years. 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.[5]

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).

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.
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  First page of the papal bull Inter gravissimas
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  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,[3] 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]

First printed Gregorian calendar

Lunario Novo, Secondo la Nuova Riforma della Correttione del l'Anno Riformato da N.S. Gregorio XIII, printed in Rome by Vincenzo Accolti in 1582, one of the first printed editions of the new 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[lower-alpha 1] 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.[18]

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.[23]

${\displaystyle D=\left\lfloor {Y/100}\right\rfloor -\left\lfloor {Y/400}\right\rfloor -2}$

where ${\displaystyle D}$ is the secular difference and ${\displaystyle Y}$ is the year using astronomical year numbering, that is, use (year BC) − 1 for BC years. ${\displaystyle \left\lfloor {x}\right\rfloor }$ 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.[24]

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).[34] 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),[35] 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.[36]

In common usage, 1 January was regarded as New Year's Day and celebrated as such,[37] but from the 12th century until 1751 the legal year in England began on 25 March (Lady Day).[38] 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),[39] although later histories adjust the start of the year to 1 January and record the execution as occurring in 1649.[40]

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.[41]

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.

Memorial plaque to John Etty in All Saints' Church, North Street, York, recording his date of death as 28 January 170+8/9

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.[42]

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.

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

• January (31 days), from Latin mēnsis Iānuārius, "Month of Janus",[44] 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,[45][46] cognate with fever,[45] the Etruscan death god Februus ("Purifier"), and the Proto-Indo-European word for sulfur[45]
• March (31 days), from Latin mēnsis Mārtius, "Month of Mars",[47] the Roman war god[46]
• April (30 days), from Latin mēnsis Aprīlis, of uncertain meaning[48] but usually derived from some form of the verb aperire ("to open")[49] or the name of the goddess Aphrodite[46][52]
• May (31 days), from Latin mēnsis Māius, "Month of Maia",[53] a Roman vegetation goddess[46] whose name is cognate with Latin magnus ("great")[53] and English major
• June (30 days), from Latin mēnsis Iūnius, "Month of Juno",[54] the Roman goddess of marriage, childbirth, and rule[46]
• July (31 days), from Latin mēnsis Iūlius, "Month of Julius Caesar", the month of Caesar's birth, instituted in 44 BC[55] as part of his calendrical reforms[46]
• 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[56]
• September (30 days), from Latin mēnsis september, "seventh month", of the ten-month Roman year of Romulus c. 750 BC[57]
• October (31 days), from Latin mēnsis octōber, "eighth month", of the ten-month Roman year of Romulus c. 750 BC[58]
• November (30 days), from Latin mēnsis november, "ninth month", of the ten-month Roman year of Romulus c. 750 BC[59]
• December (31 days), from Latin mēnsis december, "tenth month", of the ten-month Roman year of Romulus c. 750 BC[60]

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,[61] Italian,[62] and French,[63] 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:[64][65]

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"[66] but it has also been called "probably the only sixteenth-century poem most ordinary citizens know by heart".[67] 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.[68] This approximation has an error of about one day per 3,030 years[69] 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[70] 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.[71] 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.[72]

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.

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
  • Pax Calendar
  • Symmetry454
  • Hanke–Henry Permanent Calendar

• 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
  • Greek 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

• 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