Gregorian calendar

gigatos | May 28, 2022


The Gregorian calendar is the calendar used today in the Western World and has become more prevalent worldwide. It is a variant of the Julian calendar, which had been in use since the 1st century BC, proposed by the Neapolitan physician Aloysius Lilius and adopted by Pope Gregory XIII, from whom it takes its name, on 24 February 1582: The papal bull (decree) Inter gravissimas was signed in 1581 for unknown reasons, but was printed on March 1, 1582). However, other papal decrees of the time contain years that do not correspond to March years, other papal years, or other types of years. It was invented because, according to Julian, the vernal equinox was shifted by one day every 128 years, an undesirable event. Thus, it was replaced by the Gregorian, according to which the vernal equinox shifts just one day every 3,300 years, and the change in the average length of the calendar year went from Julian”s 365.25 days (365 days and 6 hours) to 365.2425 days (365 days 5 hours 49 minutes 12 seconds), a reduction of 10 minutes and 48 seconds per year. Most Catholic countries adopted the calendar in the 16th, 17th and 18th centuries, while among non-Catholic countries Greece was the last European country to adopt the new calendar in 1923.


The Catholic Church”s motive in changing the calendar was to celebrate Easter at the time they believed had been agreed upon at the First Ecumenical Council of Nicea in 325 A.D. Although a canon of the Council implies that all churches used the same date for Easter, this was not the case. For example, the Church of Alexandria celebrated Easter on the Sunday after the 14th day of the moon fell on or after the vernal equinox, which they placed on March 21. However, the Church of Rome still placed the equinox on March 25 and used a different lunar 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 Venerable Bede (monk, 672 – 735 AD) had already observed its movement in 725 AD – and it had moved even further by the 16th century (having moved one day every 128 years).

Even worse, the phases of the Moon used to calculate Easter in the Julian calendar were fixed, resulting in the loss of one day every 310 years. Thus in the 16th century, the phases of the lunar calendar were off by four days from the actual phases.

The correction for the vernal equinox was as follows: Years divided by 100 would only be correct if they were also divided by 400. Therefore, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900, for example, were not. In the current millennium, 2100, 2200 and 2300 will not be leap years, while 2400 will be.

When the new calendar was implemented, in order to correct the error that had already been built into the measurement of time over the thirteen centuries since the First Ecumenical Council of Nicea (which established the Julian calendar), it was deemed appropriate to omit ten days from the solar calendar. The last day of the Julian calendar was October 4, 1582, and the next day, and the first day of the Gregorian calendar, was October 15, 1582. However, the dates from October 5 to 14, 1582 still exist in almost all countries, as even most Catholic countries did not adopt the new calendar on the exact day established by Bula, but months or even years later (the last country in 1587). The first day of the new year had already been fixed in all Western countries on 1 January in the fifteenth and sixteenth centuries, including countries that became Protestant at that time, such as Germany, Sweden and England. However, although in England 1 January was called the “first day of the year”, the year changed on 25 March, Lady Day, until 1752 (Scotland adopted 1 January as the day of the year change on 1 January 1600, still using the Julian calendar).

Consequently, we often find double dates due to confusion of calendars and the change of the first day of the year. This confusion predates the Gregorian calendar, since the state and the church used different dating systems.

The 19-year cycle used in the lunar calendar was also corrected, by one day every 300 or 400 years, (8 times in 2,500 years), along with corrections for years that are not leap years (because they are divided by a hundred and not by four hundred). A new way of calculating Passover was even established.

Denmark-Norway and the Protestant parts of Germany adopted the sun part of the new calendar in 1700, due to the influence of Ole Remer, but did not adopt the lunar part. Instead, they decided to calculate Easter Day astronomically, using the vernal equinox and full moon according to Kepler”s Rudolphian Tables (1672). They eventually adopted the lunar part of the Gregorian calendar in 1776.

Sweden”s relationship with the Gregorian calendar had a difficult beginning. Sweden began to switch from its old calendar in 1700, but it was decided to shift the 11 days gradually, subtracting the extra days from the leap years between 1700 and 1740. In the meantime, the Swedish calendar would be out of sync with both the Gregorian and Julian calendars for 40 years, and also the difference would not be fixed but would change every 4 years. It is obvious that this system was conducive to confusion as to the date of events that occurred in Sweden during this period. As if that were not enough, the system was mismanaged, resulting in the extra days of 1704 and 1708 being counted as normal. So while after 1708 Sweden should have been 8 days behind the countries that had adopted the Gregorian calendar, it was behind by 10 days. King Charles IV then realised that the gradual change was not working properly and decided to abandon it. However, instead of moving the country forward 10 days to coincide with the Gregorian calendar, he decided to bring the country back to the Julian calendar. This was accomplished by counting the unique date of February 30 in the year 1712. Sweden finally adopted the Gregorian calendar in 1753, when the 17th of February was followed by the 1st of March.

The Eastern Orthodox Church for centuries did not accept to use the Gregorian calendar for fear that it would become a cause of misleading the flock, i.e. the faithful. When in 1582 Pope Gregory III invited by letter the Patriarch Jeremiah II of Trano to introduce it into the Orthodox Church, the Patriarch did not accept it after a synodal decision, considering it to be an attempt at conversion. The development of civilization, however, imposed new needs and the matter began to be approached from a different angle. In 1895, Ecumenical Patriarch Anthimos VII expressed the wish that there should be a single calendar for all Christian peoples. And Joachim III sent an encyclical in 1902 to all the Orthodox Churches to study the question of the calendar and asked for their opinions. The Church of Greece replied that it did not in principle reject the prospect of changing the calendar. A study committee was even set up, which decided in 1919 that: “the change, not being contrary to doctrinal and canonical reasons, could be made after consultation of all the autocephalous Churches, especially the Ecumenical Patriarchate”. Waiting for such a consultation to take place, the Church of Greece continued to use the old Julian calendar, but agreed that the State should introduce the Gregorian calendar for political use only. By royal decree, the Gregorian calendar was introduced in Greece on February 16, 1923, which was set as March 1, 1923. But a few days later it was considered improper on March 25 to separate the celebration of the Annunciation from the celebration of the National Revolt. It then became clear that the coexistence of two calendars would cause problems. In order to break the deadlock, the Church of Greece decided to use the Gregorian calendar for religious festivals with the exception of Easter (Revised Julian calendar). The Ecumenical Patriarchate consented to the change in a telegram from Patriarch Gregory VII on 23 February 1924, which stated: “By synodal decision, it has been definitively approved to adjust the calendar and the civil calendar as of March 10 next”. Thus on March 10, 1924, the Revised Julian calendar was introduced in Greece for ecclesiastical use and this day was counted as March 23.

Russia did not accept the new calendar until 1918, when January 31 was followed by February 14. Consequently, the anniversary of the October Revolution now falls in November.

The Revised Julian calendar was proposed in May 1923 which omitted 13 days in 1923 and used a different rule for leap years which has the same practical effect as the Gregorian up to the year 2800. The Orthodox churches of Greece, Bulgaria, Romania, Albania, Albania, Poland and a few more in the Eastern Mediterranean (Constantinople, Alexandria, Antioch and Cyprus) have adopted the Revised Julian, and thus these New Calendarists will celebrate the Nativity with the Western churches on December 25 up to the year 2800.

The Orthodox churches of Russia, Serbia, Jerusalem and some bishops who broke away from the Church of Greece did not accept the Revised Julian calendar. These Old Calendarists will celebrate the Nativity on December 25 on the Julian calendar, i.e. January 7 of the Gregorian calendar until 2100. All other Eastern churches that are not Orthodox, such as Coptic, Ethiopian, Nestorian, Jacobite and Armenian, continue to use their own calendars, usually celebrating on fixed dates according to the Julian calendar. All Eastern churches continue to use the Julian Easter with the only exceptions being the Orthodox Church of Finland and the Orthodox Church of Estonia, which have adopted the Gregorian Easter.

The Republic of China officially adopted the Gregorian calendar at its founding on 1 January 1912, but China soon entered an era of conflict between local governors with various warring parties using different calendars. With the unification of China under Kuomitang in October 1928, the government of the Republic of China decided by decree that from 1 January 1929 the Gregorian calendar would be used. However, the Republic of China kept the Chinese traditions of numbering the months and a modified Historical Period System, retroactively adopting 1912 as the first year of the Republic of China. This system is still in use in Taiwan where the government of the Republic of China remains. Upon its founding in 1949, the People”s Republic of China continued to use the Gregorian calendar with numbered months, but numbered its years in the Western way.

Japan replaced its traditional calendar with the Gregorian calendar on January 1, 1873, but, like China, it continued to number the months, and used (and still uses) dynasty names to separate periods instead of the Common Era system: Meiji 1=1867, Taisho 1=1912, Showa 1=1926, Heisei 1=1989, and so on. The “Western calendar” (西暦, seireki) is, however, widely accepted by citizens and somewhat less so by government agencies.

The values of the difference in days are also given by the equation:

where D{displaystyle D} is the difference; H{displaystyle H} is the hundredth of years using astronomical year counting, i.e. (and ⌊H4⌋{displaystyle lfloor { frac {H}{4}} floor } is the function by which it truncates the decimal digits of positive numbers (example ⌊4, 75⌋ = 4) and by the same logic, in negative numbers it truncates the digits, but results in the most negative of the neighboring integers (⌊-1,25⌋ = -2).

The calculated difference is increased by one in each year of a new century (year ending in “00”) on either February 29 of the Julian or March 1 of the Gregorian calendar, whichever comes last. For positive differences, 29 February Julian follows, and for positive differences, 1 March Gregorian follows.

The Gregorian calendar may, for certain reasons, extend backwards to dates before its establishment, producing the Superstitious Gregorian calendar. However, this should be used with great caution.

Under normal circumstances, the dates of events before 15 October 1582 should be given according to the Julian calendar, and not converted to their Gregorian counterpart.

However, events that occurred in countries where the Gregorian calendar was established after 4 October 1582 present difficulties. For example, in Great Britain and its American colonies, the new calendar was not established until 14 September 1752. How should we therefore number the dates of events that occurred in Britain between these two dates? The answer depends on where we need the date, but in each case the author should make clear which calendar he or she is using. It would be absurd to change all the historical dates of Britain at that time, yet it is often desirable to convert old dates to their new equivalent when countries that used different calendars at the same time are mentioned together.

If date comparisons are made using different calendars, absurd results are obtained, for example: William and Mary of Orange seem to arrive in London to receive the English crown about a week before they leave Holland. Shakespeare and Cervantes appear to have died on the same date, when in fact Cervantes died ten days earlier.

For dates before year 1, we should bear in mind that, unlike the currently prevailing international standard, ISO 8601 superstitious Gregorian calendar, the traditional superstitious Gregorian calendar (like the Julian calendar) does not have a year 0 and instead uses the numbers 1, 2 and so on for both the years before Christ and the years after. Therefore, under this traditional system, after the year 1 BC, the year 1 AD follows, while under ISO 8601, the year 0 follows.

The year in the Gregorian calendar is divided into 12 months:

An easy mnemonic rule used in Greece for the number of days in each month is the following: place your hands closed in fists next to each other and starting from the joint of the little finger, count the joints and the gaps between the fingers, corresponding each month with a joint or a gap. Those months that correspond to a joint have 31 days, while the rest have 30 (except of course February, which has 28 days, or 29 in leap years). We note that the only two consecutive months with 31 days, July and August, correspond to the last joint of the first hand and the first joint of the second hand, so the rule proves to be correct in this case as well.

The Gregorian calendar improves on the Julian calendar”s approach to the length of the year by omitting 3 extra days in corresponding leap years over the course of 400 years (those divided by 100 rather than 400). Thus, the average year lasts 365.2425 average solar days, causing an error of about one day every 3,300 years, compared to the average tropical year of 365.2422… days, but less than half the error compared to the vernal equinox year, which is 365.2424 days. In any case it is 29 times better than the Julian, which was off by one day every 128 years (average year 365.25 days).

At the millennial level, the Gregorian calendar is falling behind quite rapidly, because the slowing of the Earth”s rotation lengthens the length of the average day (see extra second), while the year maintains a more constant duration. The equinox will occur earlier than now in a given year in the future, roughly at a time interval of (ϵthan5000)2{{displaystyle}{left({{frac {{{{acute {{epsilon }}}{tau}{eta}{alpha}{pi}{{acute {{o}}}{tau}{{acute {{omega }}{rho}{alpha }{5000}}{right}}^{2}} days. This is a problem that the Gregorian calendar shares with any rule-based calendar. However, we would say that a calendar based on the motions of the heavenly bodies would be practically unfeasible.

Suppose we have a given year. Each dot represents a fixed date of the year on the x-axis. Each year we have a shift of about a quarter of a day (about 6 hours, which is the error in the Gregorian calendar”s calculation of the year – see leap year). Every four years the shift is corrected and the calendar goes back one day.

But the error is not exactly 6 hours, with the result that every year there is a small remainder beyond the 6 hours, which slowly shifts the calendar in the opposite direction. To correct this error as well, the years that are multiples of 100 but not four hundred are not leap years. The exception for years divided by 400 is made precisely because again the calculation is not completely accurate and so on.

Consequently, the days corresponding to specific phases of the Earth”s motion such as the vernal equinox and the winter solstice do not correspond exactly to these phases, but differ by a multiple of 1

For example, 23 December 1903 was the latest winter solstice, 2.25 days after the solar event, while 20 December 2096 will be the earliest.

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

A normal 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 contain an extra second)

The 400-year cycle of the Gregorian calendar has 146,097 days which is exactly 20,871 weeks. So, for example, the days of the week of the year 1603 were exactly the same as those of 2003. This also results in more months starting on Sunday (Friday 13 is also shown there).

A shorter cycle is every 28 years (1,461 weeks), as long as there is no leap year in between (i.e. a year divided by 400).The days of the week can also be repeated every 6, 11, 12, 28 or 40 years. The period of 6 or 11 years occurs with common years while the period of 28 or 40 years occurs with leap years. A 12-year period can occur with both types of years, provided that a leap year is intervened by a leap year.

The Doomsday algorithm is a method by which we determine which of the 14 forms of the calendar produced by using the Gregorian calendar is valid for a given year after its implementation. It is based on the last day of February, often called Doomsday.


  1. Γρηγοριανό ημερολόγιο
  2. Gregorian calendar
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