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Gregorian calendar

The Gregorian calendar is the calendar currently used in the Western 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 February 24, 1582 (Note: The papal bull Inter gravissimas was signed in the year 1581 for unknown reasons, but printed on 1 March in 1582. But other contemporaneous papal bulls have years that do not agree with March years, let alone papal years 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 earlier in the calendar year.




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 fix for the equinox was to define that years divisible by 100 will be leap years only if they are 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.

When the new calendar was put in use, to correct the error already accumulated in the thirteen centuries since the Council of Nicaea, a deletion of ten days was made in the solar calendar. The last day of the Julian calendar was October 4, 1582 and this was followed by the first day of the Gregorian calendar October 15, 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). New Year's Day had already been standardized by all Western European countries on 1 January during the late fifteenth and early sixteenth centuries, including all countries that became Protestant during that period such as Germany, Sweden, and England. However, even though England called 1 January New Year's Day, it changed the number of its year on Lady Day, 25 March, and continued to do so until 1752 (Scotland adopted 1 January for its numbered year on 1 January, 1600, while countinuing to use the Julian calendar).

It is also sometimes necessary to indicate that the year itself had two different designations because of the change to the beginning of the year, for example, "February 10/February 21, 1751/1752". This confusion pre-dated the change to the calendar because the Church and the State had always used different systems for different purposes.

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.

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 (September 2 1752 being followed by September 14 1752). 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. "Old Style" and "New Style" are sometimes added to dates to identify which system is used in the British Empire and other countries that did not immediately change.

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 on what dates events in Sweden actually occurred in this period. To make matters worse, the system was poorly administered and the leap days that should have been excluded from 1704 and 1708 were still for some reason included. 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 February 30 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 February 17 was followed by March 1.

In Russia the Gregorian calendar was accepted after the October Revolution by a decree of the Council of People's Commissars 1918 January 24, according to it January 31 1918 was followed by February 14 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 January 1, 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 January 1, 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.

Japan replaced the traditional lunisolar calendar with the Gregorian calendar January 1 1873, but, like China, continued to number the months, and used reign names instead of the Common Era: Meiji 1=1867, 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.

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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 should be 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, should we 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 in all cases the writer should make it absolutely clear which calendar is being used. It would be absurd to go back and change all 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.

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, when in fact Cervantes predeceased Shakespeare by 10 days in real time.

For dates before the year 1, one should also bear in mind that, unlike the now often preferred, international standard ISO 8601 modern proleptic Gregorian calendar, the traditional proleptic Gregorian calendar (like the Julian calendar) does not have a year 0 and instead uses the counting numbers 1, 2, … for both years AD and BC. 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.

  • For example, Shakespeare died on 23 April (OS), and it is rare to see this converted to 3 May (NS). But while George Washington was born on 11 February (OS), his birthday is now celebrated on 22 February (NS).

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 of events has been forthcoming and many previous errors have been corrected. While these changes are welcome, there is still much scope for confusion.

It is therefore incumbent upon those who refer to dates in transitional periods to make it clear which calendar is being used; and if the writer does not know, he or she should say so.

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


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 December 23, 1903 to be the latest December solstice, and December 20, 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.

See also

External links

Last updated: 08-07-2005 22:24:57
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