Gregorian calendar

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The Gregorian calendar is the calendar that is used nearly everywhere in the world. A modification of the Julian calendar, it was first proposed by the Neapolitan doctor Aloysius Lilius, and was decreed by Pope Gregory XIII, for whom it was named, on 24 February 1582 (Note: The papal bull Inter gravissimas was signed in the year 1581 for unknown reasons, but printed on 1 March in 1582. Although 1581 is often attributed to the use of years beginning on 25 March by the papacy, other contemporaneous papal bulls have years that do not agree with March years, let alone years since a pope was named or other types of years.)

The Gregorian calendar was devised because the mean year in the Julian Calendar was a little too long, causing the vernal equinox to slowly drift backwards in the calendar year.

The dates in this article may be in either the Julian or Gregorian calendars — Julian for dates before the calendar change and Gregorian for dates after it. They are indiscriminately mixed with dates from the other calendar in the linked "Month day" article.




The motivation of the Catholic Church in adjusting the calendar was to have Easter celebrated at the time that they thought had been agreed to at the First Council of Nicaea in 325. Although a canon of the council implies that all churches used the same Easter, they did not. The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the Moon that falls on or after the vernal equinox, which they placed on 21 March. However, the Church of Rome still regarded 25 March as the equinox and used a different day of the moon. By the tenth century all churches (except for some on the eastern border of the Byzantine Empire) had adopted the Alexandrian Easter, which still placed the vernal equinox on 21 March, although Bede had already noted its drift in 725 — it had drifted even further by the sixteenth century.

Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by a 19-year cycle. However, that is an approximation that built up an error of 1 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 calendrial errors, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of Easter.

The fix was to come in two stages. First, it was necessary to approximate the correct length of a solar year. The value chosen was 365.2425 days in decimal notation. This is 365;14,33 days in sexagesimal notation - the length of the tropical year, rounded to two sexagesimal positions; this was the value used in the major astronomical tables of the day. Although close to the mean tropical year of 365.2422 days, it is even closer to the vernal equinox year of 365.2424 days; this fact made the choice of approximation particularly appropriate as the purpose of creating the calendar was to ensure that the vernal equinox would be near a specific date (March 21). See Accuracy.

The second stage was to devise a model based on the approximation which would provide an accurate yet simple, rule-based calendar. The formula designed by Aloysius Lilius was ultimately successful. It proposed a ten-day correction to revert the drift since Nicaea and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. To implement the model, it was provided that years divisible by 100 would be leap years only if they were divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300 and 2500 will not be leap years, but 2400 will be. This theory was expanded upon by Christopher Clavius in a closely argued, 800-page volume. He would later defend his and Lilius's work against detractors.

The 19-year cycle used for the lunar calendar was also to be corrected by 1 day every 300 or 400 years (8 times in 2500 years) along with corrections for the years (1700, 1800, 1900, 2100 etc.) that are no longer leap years. In fact, a new method for computing the date of Easter was introduced.

Lilius originally proposed that the ten-day correction should be implemented by deleting the Julian leap day on each of its ten occurrences during a period of 40 years, thereby providing for a gradual return of the equinox to 21 March. However, Clavius's opinion was that the correction should take place in one move and it was this advice which prevailed with Gregory. Accordingly, when the new calendar was put in use, the error accumulated in the thirteen centuries since the Council of Nicaea was corrected by a deletion of ten days. The last day of the Julian calendar was 4 October 1582 and this was followed by the first day of the Gregorian calendar 15 October 1582. Nevertheless, the dates "5 October 1582" to "14 October 1582" (inclusive) are still valid in virtually all countries because even most Roman Catholic countries did not adopt the new calendar on the date specified by the bull, but months or even years later (the last in 1587).

Beginning of the year

During the Middle Ages 1 January was given the name New Year's Day (or an equivalent name) in all Western European countries (those dominated by the Roman Catholic Church), even while most of those countries began their numbered year on 25 December (the Nativity of Jesus), then 25 March (the Incarnation of Jesus), and even Easter, as in France. This name was the result of always displaying the months of the medieval calendar from January to December (in twelve columns containing 28 to 31 days each), just like the Romans did. Furthermore, all Western European countries (except for a few Italian states) shifted the first day of their numbered year to 1 January while they were still using the Julian calendar, before they adopted the Gregorian calendar, many during the sixteenth century. Eastern European countries (under the control of the Orthodox Church) began their numbered year on 1 September (since about 988). The following list is from Old Style and New Style Dates.

Adoption of January 1 as beginning of numbered year and Gregorian Calendar adoption year
Country 1 Jan NY Greg Cal
Venice 1522 1582
Germany 1544 from 1583
Spain, Portugal, and Roman Catholic Netherlands 1556 from 1582
Prussia, Denmark, and Sweden 1559  ?
France 1564 1582
Lorraine 1579 1682
Protestant Netherlands 1583 from 1700
Scotland 1600 1752
Russia 1700 (not 1725) from 1918
Tuscany 1721  ?
England 1752 1752

Neither the papal bull nor its attached canons explicitly state that the year of the Gregorian calendar is to begin on 1 January, contrary to popular opinion. However, it does imply such a year by including two tables of saint's days, one labeled 1582 which ends on 31 December, and another for any full year that begins on 1 January. It also specifies its epact relative to 1 January, in contrast with the Julian calendar, which specified it relative to 22 March. These would have been the inevitable result of the above shift in the beginning of the Julian year.

During the period between 1582, when the first countries adopted the Gregorian calendar, and 1923, when the last European country adopted it, it was often necessary to indicate the date of some event in both the Julian calendar and in the Gregorian calendar, for example, "10/21 February 1751/52", where the dual year accounts for some countries already beginning their numbered year on 1 January while others were still using some other date. Even before 1582, the year sometimes had to be double dated because of the different beginnings of the year in various countries.

Adoption outside of Roman Catholic nations

Very few countries implemented the new calendar on 15 October 1582 — only Italy, Poland, Spain and Portugal. Non-Catholic countries objected to adopting a Catholic invention. England, Scotland and thereby the rest of the British Empire (including part of what is now the United States) did not adopt it until 1752, by which time it was necessary to correct by eleven days (2 September 1752 being followed by 14 September 1752) to account for 29 February 1700 (Julian). Britain legislated special provisions to make sure that monthly or yearly payments would not become due until the dates that they originally would have in the Julian calendar, and to this day the tax year in the United Kingdom start on April 6 which is the "old style" new year of 25 March. "Old Style" (OS) and "New Style" (NS) are sometimes added to dates to identify which system is used in the British Empire and other countries that did not immediately change.

In Alaska, the change took place when Friday 6 October 1867 was followed again by Friday 18 October after the US purchase of Alaska from Russia, who was still on the Julian calendar. The day of the week was repeated on successive days because the International Date Line was shifted from east of to west of Alaska along with the change to the Gregorian calendar.

Denmark-Norway and the Protestant parts of Germany adopted the solar portion of the new calendar in 1700, due to the influence of Ole Rømer, but did not adopt the lunar portion. Instead, they decided to calculate the date of Easter astronomically using the instant of the vernal equinox and the full moon according to Kepler's Rudolphine Tables of 1627. They finally adopted the lunar portion of the Gregorian calendar in 1776.

Sweden's relationship with the Gregorian Calendar had a difficult birth. Sweden started to make the change from the OS calendar and towards the NS calendar in 1700, but it was decided to make the (now 11-day) adjustment gradually, by excluding the leap days (29 February) from each of 11 successive leap years, 1700 to 1740. In the meantime, not only would the Swedish calendar be out of step with both the Julian calendar and the Gregorian calendar for 40 years, but also the difference would not be static but would change every 4 years. This strange system clearly had great potential for endless confusion when working out the dates of Swedish events in this 40-year period. To make matters worse, the system was poorly administered and the leap days that should have been excluded from 1704 and 1708 were not excluded. The Swedish calendar should by now have been 8 days behind the Gregorian, but it was still in fact 10 days behind. King Charles XII wisely recognised that the gradual change to the new system was not working and he abandoned it. However, rather than now proceeding directly to the Gregorian calendar (as in hindsight seems to have been the sensible and obvious thing to do), it was decided to revert to the Julian calendar. This was achieved by introducing the unique date 30 February in the year 1712, adjusting the discrepancy in the calendars from 10 back to 11 days. Sweden finally adopted the Gregorian calendar in 1753, when 17 February was followed by 1 March.

In Russia the Gregorian calendar was accepted after the October Revolution (so named because it took place in October 1917 in the Julian calendar). On 24 January 1918 the Council of People's Commissars decreed that 31 January 1918 was to be followed by 14 February 1918.

The last country of Eastern Europe to adopt the Gregorian calendar was Greece in 1923. However, these were all civil adoptions — none of the national churches accepted it. Instead, a Revised Julian calendar was proposed in May 1923 which dropped 13 days in 1923 and adopted a different leap year rule that resulted in no difference between the two calendars until 2800. The Orthodox churches of Greece, Bulgaria, Romania, Poland, and a few others around the Eastern Mediterranean (Constantinople, Alexandria, Antioch, and Cyprus) adopted the Revised Julian calendar, so these New calendarists will celebrate the Nativity along with the Western churches on 25 December in the Gregorian calendar until 2800. The Orthodox churches of Russia, Serbia, Jerusalem, and a few bishops in Greece did not accept the Revised Julian calendar. These Old Calendarists will continue to celebrate the Nativity on 25 December in the Julian calendar, which is 7 January in the Gregorian calendar until 2100. All of the other Eastern churches that are not Orthodox churches, like the Coptic, Ethiopic, Nestorian, Jacobite, and Armenian, continue to use their own calendars, which usually result in fixed dates being celebrated in accordance with the Julian calendar. All Eastern churches continue to use the Julian Easter with the sole exception of the Finnish Orthodox Church, which has adopted the Gregorian Easter.

The Republic of China formally adopted the Gregorian calendar at its founding on 1 January 1912, but China soon descended into a period of warlordism with different warlords using different calendars. With the unification of China under the Kuomintang in October 1928, the ROC government decreed that effective 1 January 1929 the Gregorian calendar would be used henceforth. However, the ROC retained the Chinese traditions of numbering the months and a modified Era System, backdating the first year of the ROC to 1912; this system is still in use in Taiwan where this ROC government remains. Upon its foundation in 1949, the People's Republic of China continued to use the Gregorian calendar with numbered months, but numbered its years in the Western fashion and abolished the ROC Era System.

Japan replaced the traditional lunisolar calendar with the Gregorian calendar on 1 January 1873, but, like China, continued to number the months, and used reign names instead of the Common Era: Meiji 1=1868, Taisho 1=1912, Showa 1=1926, Heisei 1=1989, and so on. The "western calendar" (西暦, seireki) is nonetheless widely accepted by civilians and to a less extent by government agencies.


Proleptic Gregorian calendar

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

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

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

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

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 counting numbers 1, 2, … both for years AD and BC and for CE and BCE. Thus the traditional timeline is 2 BC, 1 BC, AD 1, and AD 2. ISO 8601 uses astronomical year numbering which includes a year 0 and negative numbers before it. Thus the ISO 8601 timeline is -0001, 0000, 0001, and 0002.

Confusion with British vs. American usage

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

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

Difference between Gregorian and Julian calendar dates

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

Gregorian range Julian range Difference
From 15 October 1582
to 28 February 1700
From 5 October 1582
to 18 February 1700
10 days
From 1 March 1700
to 28 February 1800
From 19 February 1700
to 17 February 1800
11 days
From 1 March 1800
to 28 February 1900
From 18 February 1800
to 16 February 1900
12 days
From 1 March 1900
to 28 February 2100
From 17 February 1900
to 15 February 2100
13 days

Months of the year

The Gregorian calendar's year is divided into 12 months:

No. Name Days
1 January 31
2 February 28 or 29
3 March 31
4 April 30
5 May 31
6 June 30
7 July 31
8 August 31
9 September 30
10 October 31
11 November 30
12 December 31

English speakers sometimes remember the number of days in each month by the use of the traditional mnemonic verse: Thirty days hath September / April, June and November / All the rest have thirty-one / Excepting February alone / Which has but twenty-eight, in fine / Till leap year gives it twenty-nine. Alternate endings are: Which has eight and a score / Until leap year gives it one day more, or Which hath twenty-eight days clear / And twenty-nine in each leap year.

A language-independent alternative is to hold up your two fists with the index knuckle of your left hand against the index knuckle of your right hand. Then, starting with January from the little knuckle of your left hand, count knuckle, space, knuckle, space through the months. A knuckle represents a month of 31 days, and a space represents a short month.


The Gregorian calendar improves the approximation made by the Julian calendar by skipping 3 Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long, which has an error of about 1 day per 3300 years with respect to the mean tropical year of 365.2422 days but less than half this error with respect to the vernal equinox year of 365.2424 days. Both are substantially more accurate than the 1 day in 128 years error of the Julian calendar (average year 365.25 days).

On timescales of thousands of years, the Gregorian calendar falls behind the seasons drastically because the slowing down of the Earth's rotation makes each day slightly longer over time (see tidal acceleration and leap second) while the year maintains a more uniform duration. The equinox will occur earlier than now by a number of days approximately equal to [years into future/5000]2. This is a problem that the Gregorian calendar shares with any rule-based calendar.

Calendar seasonal error

Gregorian calendar seasons difference

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

The Y axis is "days error" and the X axis is Gregorian calendar years.

Each point represents a single date on a given year. The error shifts by about 1/4 day per year. Years that are multiples of 100 but not 400 are NOT leap years. This causes a correction on years 1700, 1800, 1900, 2100, 2200, and 2300.

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

Numerical facts

When leap years, common years and different dates of Easter are taken into account, there are a total of 70 possible Gregorian calendars.

An average year is 365.2425 days = 52.1775 weeks = 8,765.82 hours = 525,949.2 minutes = 31,556,952 seconds.

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

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

(Some years may also contain a leap second.)

See also common year starting on Sunday and dominical letter.

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

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

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

Number of leap years starting on a given day of the week

Because there are 97 leap years in every 400 in the Gregorian Calendar, there should, in each "cycle", be either 13 or 14 leap years starting on each day of the week. However, the effects of the "common" centennial years (1700, 1800, 1900, 2100, 2200 etc.) cause major alterations.

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

Days of the week

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


  • Gregorian reform of the calendar: Proceedings of the Vatican conference to commemorate its 400th anniversary, 1582-1992, ed. G. V. Coyne, M. A. Hoskin, and O. Pedersen (Vatican City: Pontifical Academy of Sciences, Specolo Vaticano, 1983).

See also

External links

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