The Gregorian calendar, also called the Western calendar and the Christian calendar, is internationally the most widely used civil calendar. It is named for Pope Gregory XIII, who introduced it in 1582.
The calendar was a refinement in 1582 to the Julian calendar amounting to a 0.002% correction in the length of the year. The motivation for the reform was to bring the date for the celebration of Easter to the time of the year in which the First Council of Nicaea had agreed upon in 325. Because the celebration of Easter was tied to the spring equinox, the Roman Catholic Church considered this steady drift in the date of Easter undesirable. The reform was adopted initially by the Catholic countries of Europe. Protestants and Eastern Orthodox countries continued to use the traditional Julian calendar and adopted the Gregorian reform after a time, for the sake of convenience in international trade. The last European country to adopt the reform was Greece, in 1923.
The Gregorian reform contained two parts: a reform of the Julian calendar as used prior to Pope Gregory XIII's time and a reform of the lunar cycle used by the Church, with the Julian calendar, to calculate the date of Easter. The reform was a modification of a proposal made by Aloysius Lilius. His proposal included reducing the number of leap years in four centuries from 100 to 97, by making 3 out of 4 centurial years common instead of leap years. Lilius 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.
The Gregorian reform modified the Julian calendar's scheme of leap years as follows:
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.
In addition to the change in the mean length of the calendar year from 365.25 days (365 days 6 hours) to 365.2425 days (365 days 5 hours 49 minutes 12 seconds), a reduction of 10 minutes 48 seconds per year, the Gregorian calendar reform also dealt with the accumulated difference between these lengths. Between AD 325 (when the First Council of Nicaea was held, and the vernal equinox occurred approximately 21 March), and the time of Pope Gregory's bull in 1582, the vernal equinox had moved backward in the calendar, so that in 1582 it occurred about 11 March, 10 days earlier than 21 March. The Gregorian calendar therefore began by skipping 10 calendar days, to restore 21 March as the date of the vernal equinox.
To unambiguously specify the date, dual dating or Old Style (O.S.) and New Style (N.S.) are sometimes used with dates. Dual dating uses two consecutive years because of differences in the starting date of the year, or includes both the Julian and Gregorian dates. Old Style and New Style (N.S.) indicate either whether the start of the Julian year has been adjusted to start on 1 January (N.S.) even though documents written at the time use a different start of year (O.S.), or whether a date conforms to the Julian calendar (O.S.) rather than the Gregorian (N.S.).
The Gregorian calendar continued to use the previous calendar era (year-numbering system), which counts years from the traditional date of the nativity (Anno Domini), originally calculated in the 6th century by Dionysius Exiguus. This year-numbering system, also known as Dionysian era or Common Era, is the predominant international standard today.
The Gregorian calendar is a solar calendar. A regular Gregorian year consists of 365 days and in a leap year, an intercalary or leap day is added to February making the year 366 days. Using the Roman notation, the leap day is a.d. bis VI Kal. Mart. (24 February). From the sixteenth century it has become customary to number the days from the beginning of the month. The leap day is regarded as the 29th, this being the day which does not occur in three years out of four. Normally a leap year occurs every 4 years, but the Gregorian calendar omits 3 leap days every 400 years, unlike the Julian calendar, which retains those leap days.
A Gregorian year is divided into twelve months, as follows:
|No.||Name||Length in days|
|2||February||28 or 29|
Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A calendar mean year is 365+97/400 days = 365.2425 days = 365 days, 5 hours, 49 minutes and 12 seconds. 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
For patterns within the calendar consider Zeller's Congruence.
A calendar date is fully specified by the year (numbered by some scheme beyond the scope of the calendar itself), the month (identified by name or number), and the day of the month (numbered sequentially starting at 1).
Although the calendar year 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.)
The calendar was a reform in 1582 to the Julian calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by papal bull Inter gravissimas dated 24 February 1582. The motivation for the adjustment was to bring the date for the celebration of Easter to the time of year in which the First Council of Nicaea had agreed upon in 325.
Although a canon of the council 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).
Because the spring equinox was tied to the date of Easter, the 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 as the equinox (until 342) and used a different cycle to compute the day of the moon. 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.
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.
The Council of Trent approved a plan in 1563 for correcting the calendrical errors, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of Easter. 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 3 out of 4 centurial years common instead of leap years: this part of the proposal had been suggested before by, among others, Pietro Pitati. Lilius 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.
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, while the mean vernal equinox year is 365.2424 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 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 40 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.
Gregory dropped 10 days to bring the calendar back into synchronisation with the seasons. Accordingly, when the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of ten days. The 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).
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, 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.
Philip II of Spain decreed the change from the Julian to the Gregorian calendar, which 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.
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):
|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
A more extensive list is available at Conversion between Julian and Gregorian calendars.
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.
where is the secular difference; is the hundreds digits of the year using astronomical year numbering, that is, use (year BC) − 1 for BC years; and is integer division of H by 4. This truncates (removes) any decimal fraction (remainder) of the division, for both positive and negative numbers. Thus during the 1900s, 19/4 = 4, while during the −500s, −5/4 = −1.
The calculated difference increases by one in a centurial year (a year ending in '00) at either 29 February Julian or 1 March Gregorian, whichever is later. For positive differences, 29 February Julian is later, whereas for negative differences, 1 March Gregorian is later.
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. 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), 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 modern 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) though in England the start of the tax year remained at 25 March (O.S.), 5 April (N.S.) till 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.
In some countries, an official decree or law specified that the start of the year should be 1 January. For such countries we can identify a specific year when a 1 January-year became the norm. 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.
|Country||Start numbered year
on 1 January
|Denmark||Gradual change from
13th to 16th centuries
|Holy Roman Empire (Catholic states)||1544||1583|
|Holy Roman Empire (Protestant states)||1559||1700|
|Great Britain and the British Empire
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.
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" (OS) and "New Style" (NS) are sometimes added to dates to identify which system is used in the British Empire and other countries that did not immediately change. Because the Calendar Act of 1750 altered the start of the year, 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).
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. The Battle of Agincourt is universally known 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 arrived at Brixham in England on 5 November 1688 (Julian calendar), after setting sail from the Netherlands on 11 November 1688 (Gregorian 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.
English speakers sometimes remember the number of days in each month by memorising a traditional mnemonic verse:
Thirty days hath September,
April, June, and November.
All the rest have thirty-one,
Excepting February alone,
Which hath but twenty-eight days clear,
And twenty-nine in each leap year.
For variations and alternate endings, see Thirty days hath September.
A language-independent alternative used in many countries is to hold up one's two fists with the index knuckle of the left hand against the index knuckle of the right hand. Then, starting with January from the little knuckle of the left hand, count knuckle, space, knuckle, space through the months. A knuckle represents a month of 31 days, and a space represents a short month (a 28- or 29-day February or any 30-day month). The junction between the hands is not counted, so the two index knuckles represent July and August.
This method also works by starting the sequence on the right hand's little knuckle, then continuing towards the left. It can also be done using just one hand: after counting the fourth knuckle as July, start again counting the first knuckle as August. A similar mnemonic can be found on a piano keyboard: starting on the key F for January, moving up the keyboard in semitones, the black notes give the short months, the white notes the long ones.
Numerical methods were described in the Journal of the Department of Mathematics, Open University, in 1997 and 1998.
The following algorithm gives the number of days (d) in month m of year y. The value of m is given on the right of the month in the following list:
January 11 February 12 March 1 April 2 May 3 June 4 July 5 August 6 September 7 October 8 November 9 December 10.
The algorithm utilises the integral or floor function: thus is that part of the number x which lies to the left of the decimal point. It is only necessary to work through the complete function when calculating the length of February in a year which is divisible by 100 without remainder. When calculating the length of February in any other year it is only necessary to evaluate the terms to the left of the fifth + sign. When calculating the length of any other month it is only necessary to evaluate the terms to the left of the third - sign.
To find the length of, for example, February 2000 the calculation is
The origins of English naming used by the Gregorian calendar:
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 list Mondays in the first (left) column of dates and Sundays in the last. Software often starts with Sunday=0, which places Sundays in the left column of a monthly calendar page.
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 3,300 years with respect to the mean tropical year. However, because of the precession of the equinoxes, the error with respect to the vernal equinox (which occurs, on average, 365.24237 days apart near 2000) is 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 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. Borkowski reviewed mathematical models in the literature, and found that the results generally fall between a model by McCarthy and Babcock, and another by Stephenson and Morrison. If so, in the year 4000, the calendar will fall behind by at least 0.8 but less than 1.1 days. In the year 12,000 the calendar would fall behind by at least 8 but less than 12 days.
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—2.25 days of variation compared with the seasonal event.
The following are proposed reforms of the Gregorian calendar: