Gregorian Calendar

The Gregorian calendar is the only civil calendar that is internationally accepted worldwide. It was first proposed by the Calabrian doctor Aloysius Lilius and put into decree by Pope Gregory XIII on 24 February 1582 through the papal bull Inter gravissimas. The calendar was derived from the name of the Pope.

The Gregorian Calendar is a rectify version of the Julian calendar. It does not follow any particular year numbering system or ordering system instead it uses the Anno Domini system that counts years from the traditional Incarnation of Jesus. This calendar had spread throughout Europe during the middle ages. In the same year of 1582, the same year numbering system that is the de facto is being used in the international standard today.

The Gregorian calendar had customized the regular four-year cycle of leap years of Julian calendar. And it is as follows:

Each year that is exactly divisible by four is a leap year, except for the years that are exactly divisible by 100. However, the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year, but the year 2000 is a leap year.

Description of the Gregorian Calendar

The Gregorian solar calendar is an arithmetical calendar since it counts days as the basic unit of time. It is grouped into years of 365 or 366 days and repeats completely every 146,097 days that will fill the 400 years that also happens to be 20,871 seven-day weeks. Of these 400 years, the 303 common years have 365 days, and 97 leap years have 366 days. This gives an average year length of exactly 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.

A Gregorian year is divided into twelve months with irregular length whereas the months do not have a regular relationship among their lengths:

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

A calendar date is fully specified by the year and numbered by some scheme beyond the scope of the calendar itself. The month is identified by name or number, and the day of the month is numbered sequentially starting from 1.

The leap years are added to the 29th day of February, which normally has 28 days. With this, the essential and unique feature of the Gregorian calendar, as opposed to the Julian calendar, is that the Gregorian omits 3 leap days for every 400 years. This feature would have been more noticeable in the modern memory. Apparently, the year 2000 was a leap year in both the Julian and Gregorian calendar systems.

The intercalary day in a leap year is also known as the leap day. Since the Roman times, the date of February 24 or bissextile was counted as the leap day. But now in most countries, the February 29 is regarded as the leap day.

Though the calendar year runs from January 1 to December 31, there are times that the year numbers were based on a different starting point within the calendar. Obviously, the term Anno Domini is not specific at this point instead it actually refers to a family of year numbering systems with various starting points for the years.

Lunar Calendar

Throughout the centuries, the Catholic Church had maintained a tabular lunar calendar, which was primarily to calculate the date of Easter as well as the lunar calendar required reform. A constant lunar calendar was created with 30 different arrangements wherein lines in the expanded table of epacts for lunar months were created. One of the 30 arrangements applies to a century. In this case, the century begins with a year divisible by 100. When the arrangement to be used for a given century is communicated, anyone who has the tables can be able to find the age of the moon on any date, and calculate the date of Easter as well.

History

Gregorian Reform

The motivation of the Catholic Church in adjusting the calendar was to celebrate Easter at the time according to the old beliefs when the First Council of Nicaea had agreed upon in 325. Though the order of the council implies that all churches must use the same Easter, the Catholic Church did not follow. 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 had placed on March 21. And this is computed using the Metonic cycle. However, the Church of Rome still regarded March 25 as the equinox, and they used a different cycle to compute the day of the moon.

In the Alexandrian system, the first day could fall not earlier than March 8 but not later than April 5. It is because the 14th day of the Easter moon could fall as early as March 21. With this, the Easter can vary between March 22 and April 25. In Rome, Easter was not allowed to fall later April 21 since it is the same day of the Parilia or the birthday of Rome and the pagan festival. The first day of the Easter moon could fall not earlier than March 5 but not later than April 2. Easter was the Sunday after the 15th day of this moon wherein the 14th day was allowed to anticipate the equinox.

Since the two systems had produced different dates, there was generally a compromise for both churches to celebrate on the same day. By the tenth century, all churches except some of those on the eastern border of the Byzantine Empire had adopted the Alexandrian Easter. The Alexandrian still placed the vernal equinox on March 21, although Bede had already noted its drift in 725. Eventually, it had drifted even further by the sixteenth century.

Even worse, the approximately Moon that was used to compute the Easter had become fixed to the Julian year by a 19-year cycle. However, this approximation had built up an error of one day for every 310 years therefore by the sixteenth century the lunar calendar had become out of phase against the real Moon by four days.

In 1563, the Council of Trent had approved a plan in correcting the calendrical errors. This plan requires the date of the vernal equinox to be restored wherein it is held at the time of the First Council of Nicaea in 325. In addition, an alteration to the calendar was designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the Easter Festival.

The fix came in two stages. The first stage is that it would be necessary to estimate the correct length of the solar year. The value chosen was 365.2425 days in decimal notation. Although close to the mean tropical year of 365.24219 days, it is even closer to the vernal equinox year of 365.2424 days. This fact made the choice of estimation that is particularly appropriate for the purpose of creating the calendar. It had also ensured that the vernal equinox would be near a specific date of March 21.

The second stage was to arrange a model that is based on the estimation that would provide an accurate but simple and rule-based calendar. The formula in this estimation was designed by Aloysius Lilius and ultimately become successful. A 10-day correction to revert the drift was proposed since Nicaea and the imposition of a leap day is only 97 years in 400 years instead of 1 year in 4.

In able to implement the model, it was given that the years divisible by 100 would be leap years only if they were divisible by 400 as well. Therefore, in the last millennium, 1600 and 2000 were leap years, but years 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 by Christopher Clavius in a closely argued 800-page volume. Against any detractors, he would later defend his and Lilius’s work.

The 19-year cycle used for the lunar calendar was also to be corrected by one day in every 300 or 400 years, which is 8 times in 2500 years, along with other corrections for the years 1700, 1800, 1900, 2100 and more that are no longer leap years. As a matter of fact, there was a new method introduced for computing the date of Easter.

In 1577, a Compendium was sent to professional mathematicians for comments outside of the reform commission. Some of these professionals, including Giambattista Benedetti and Giuseppe Moleto, believed that Easter should be computed from the true motions of the sun and moon and not by using a tabular method. However, these recommendations were not adopted.

Gregory dropped 10 days to bring the calendar back into its original synchronization with the seasons. Lilius originally proposed that the 10-day correction should be implemented by deleting the Julian calendar’s leap day on each of its ten occurrences during a period of 40 years. Therefore, it will provide a gradual return of the equinox to March 21.

However, the opinion of Clavius was that the correction should take place in one move and this advice prevailed with Gregory. Accordingly, when the new calendar was put in use, the error accumulated in the 13th centuries because the Council of Nicaea was corrected by a deletion of ten days. The last day of the Julian calendar was Thursday, October 4, 1582, and this was followed by the first day of the Gregorian calendar, which is Friday, October 15, 1582. Since then, the cycle of weekdays was not affected.

Adoption of the Gregorian Calendar

Although the reformation of Gregorian Calendar was executed in the most deliberated forms available to the Church, still the bull had no authority beyond the Catholic Church as well as the Papal States. The changes which he was proposing were changes to the civil calendar in which he had no authority. The changes will require adoption from the civil authorities in every country before they legally take effect.

The Nicene Council of 325 had sought to arrange the rules wherein all Christians would celebrate Easter Festival on the same day. As a matter of fact, it took a very long time before the Christians had achieved that objective. However, the bull Inter gravissimas had become the law of the Catholic Church. But, the law was not recognized either by the Protestant Churches or the Orthodox Churches as well as other churches. Appropriately, the days wherein the Easter Festival and related holidays were celebrated by different Christian Churches had brought up conflicts again.

Adoption in Europe

There were only four Catholic countries that had adopted the new calendar based on the date specified by the bull. Meanwhile, other Catholic countries had experienced some delays prior to the adoption of the reformed calendar. For non-Catholic countries, since the calendar is not being subject to the decrees of the Pope, they initially rejected or simply ignored the reform altogether, but eventually, they have adopted it. Hence, from the dates of October 5, 1582, until October 14, 1582, these are all valid dates in many countries.

The countries of Spain, Portugal, the Polish-Lithuanian Commonwealth, and the whole of Italy implemented the new calendar on October 15, 1582; it was Friday then following the Julian calendar on October 4, 1582, which was Thursday. The Spanish and Portuguese colonies adopted the calendar later due to the delays of communication.

The country of France had adopted the new calendar on December 10, 1582, which was Monday following December 9, 1582, which was Sunday. The Dutch provinces of Brabant, Zeeland, and the Staten-Generaal had also adopted the new calendar on December 25 of the same year. These provinces formed the Southern Netherlands, which is the modern Belgium on January 1, 1583. Meanwhile, the province of Holland also followed suit on January 12, 1583.

Most of the non-Catholic countries have initially rejected in adopting the Catholic invention. This is despite the efforts of the Counter-Reformation wherein the Gregory was the leading proponent. Some Protestants feared that the new calendar was a part of the plot for them to return to the Catholic fold. In the Czech lands, Protestants had resisted the use of the calendar imposed by the Habsburg Monarchy. In some parts of Ireland, the Catholic rebels in the Nine Years War kept the new Easter in disregard of the English-loyal authorities until their defeat. Eventually, Catholics who practiced in secret had petitioned the Propaganda Fide for management from observing the new calendar since it signals their disloyalty.

The country of Denmark, which then included Norway and other Protestant states of Germany had adopted the solar portion of the new calendar on March 1, 1700, which was Monday following on February 18, 1700, which was Sunday on the Julian calendar. However, due to the influence of Ole Romer, they but did not adopt the lunar portion. Instead, they decided to calculate the date of Easter Feast astronomically with the use of instant vernal equinox and the full moon according to Kepler’s Rudolphine Tables of 1627. Finally, in 1776, they adopted the lunar portion of the Gregorian calendar. The remaining provinces of the Dutch Republic had also adopted the Gregorian calendar in July 1700 by Gelderland, December 1700 by Utrecht and Overijssel, and January 1701 by Friesland and Groningen.

The relationship of Sweden with the Gregorian Calendar had been a difficult one since Sweden started to make the changes from the Julian calendar towards the Gregorian calendar in 1700. However, the country had decided to make the adjustments gradually by excluding the leap days from each of the 11 successive leap years, from 1700 to 1740.
Meanwhile, the Swedish calendar would be out of step with both the Julian calendar and the Gregorian calendar for 40 years. In addition, the difference would not be constant but would rather change for every 4 years. Apparently, this strange system had great potential for endless confusion in working out the dates of the Swedish events in a 40-year period. To make things worse, the system was poorly administered since the leap days that should have been excluded from 1704 to 1708 were not excluded. According to the transition plan, the Swedish calendar should have been 8 days late from the Gregorian calendar, but the truth is that its still 10 days behind. King Charles XII was able to recognize that the gradual adjustments with the new system were not working. Because of this, he had abandoned it.

Apparently, instead of proceeding directly to the Gregorian calendar, Sweden had decided to revert to the traditional Julian calendar. The reversal was achieved through the introduction of the unique date February 30 in the year 1712 whereas adjustments were made on the discrepancies in the calendars from 10 days back to 11 days. On February 17, 1753, Sweden had finally adopted the Gregorian calendar that was Wednesday then. It was followed by Thursday, March 1 of the Julian calendar. Since Finland was under the Swedish rule at that time, the country did the same.

In 1752, the country of Britain, as well as the British Empire including the eastern part of what is now the United States, had adopted the Gregorian calendar. It is the same time when it was necessary to correct the calendar by 11 days. The date of adoption was September 2, 1752, which was Wednesday and was followed by Thursday, September 14, 1752, of the Julian calendar. It takes to account for February 29, 1700.

There were claims that protesters had demanded for their eleven days to be given. The protest had emerged from the misinterpretation of a painting done by William Hogarth. After 1753, the British tax year in Britain continued to operate using the Julian calendar. The operation began on April 5 of the same year whereas the traditional new tax year of March 25 was applied. The 12th leap day had skipped the leap day in Julian calendar in 1800. Because of this, it had changed its start to April 6. However, it did not change when the 13th Julian leap day was skipped in 1900, therefore, the tax year in the United Kingdom still begins on April 6.

In Alaska, the changes took place when the date of Friday, October 6, 1867, was followed again by the date of Friday, October 18, 1867. This is after the United States had purchased Alaska from Russia. The October 18 falls under the Julian calendar. Instead of 12 days, there were only 11 that had skipped whereas the day of the week was repeated on successive days. One reason for this is because the International Date Line was shifted from Alaska’s eastern to western boundary along with the changes to the Gregorian calendar.

In Russia, the Gregorian calendar was accepted after the October Revolution. The revolution was named this way because it took place in October 1917 of the Julian calendar. On January 24, 1918, the Council of Peoples Commissars had issued a Decree that the date of Wednesday, January 31, 1918, should be followed by Thursday, February 14, 1918.

The last country in Eastern Orthodox Europe that was last to adopt the Gregorian calendar was Greece. It was on the date of Thursday, March 1, 1923, following the date of Wednesday, February 15, 1923, in Julian calendar.

Adoption in Eastern Asia

Japan was the first country in Asia that had adopted the western calendar. The country had replaced its traditional lunisolar calendar with the Gregorian calendar on January 1, 1873. As the country adopted the Gregorian calendar, it started to change its traditional month names into numbered months. However, it still continued to use Gengo, reign names instead of the Common Era or Anno Domini system. The names are labeled as Meiji 1=1868, Taisho 1=1912, Showa 1=1926, Heisei 1=1989, and so on. Eventually, the Gregorian calendar with the use of western year numbers had been widely accepted by the citizens except for the government agencies that had only used the calendar to a lesser extent.

Next after Japan, the Republic of China had formally adopted the Gregorian calendar on January 1, 1912, however, the country had soon descended into a period of warlordism whereas the different warlords had used different calendars during their reigns. When China was unified under the Kuomintang in October 1928, the Nationalist Government had effectively decreed the use of Gregorian calendar on January 1, 1929.

Apparently, China had retained the Chinese traditions of numbering the months and a customized Era System, which backdates the first year of the Republic of China to 1912. This system is still being used in Taiwan where Chinese government retains control. Since its foundation in 1949, China continued to use the Gregorian calendar with numbered months after abolishing the traditional and customized Era System. Through the Gregorian calendar, China had adopted the Western style of numbered years.

Because of Japanese influence, Korea started using the Gregorian calendar on January 1, 1896. The lunisolar calendar that Korea used before adopting the Gregorian calendar was based on the lunisolar Chinese calendar.

Adoption by Orthodox Churches

Despite all the civil adoptions, none of the national Orthodox Churches have recognized the Gregorian calendar merely because of church or religious purposes. Instead, a reformed Julian calendar was proposed in May 1923, which dropped 13 days in 1923 and adopted a more different leap year rule. No differences were made between the two calendars until 2800. The Orthodox churches of Constantinople, Alexandria, Antioch, Greece, Cyprus, Romania, and Bulgaria, adopted the reformed Julian calendar. Therefore until 2800, the reformed calendar would celebrate Christmas on December 25 in the Gregorian calendar, which is the same day as the Western churches.
The Orthodox churches of Jerusalem, Russia, Serbia, the Republic of Macedonia, Georgia, Poland and the Greek Old Calendarists did not accept the reformed Julian calendar. Instead, they continued to celebrate Christmas on December 25 of the Julian calendar, which is January 7 in the Gregorian calendar until 2100. The refusal to accept the Gregorian reforms also had an impact on the date of Easter Feast. The reason for this is because the date of Easter is identified with reference to March 21 as the functional equinox. This continues to apply in the Julian calendar, even though the civil calendar in the native countries now use the Gregorian calendar.

All of the other Eastern churches, the Oriental Orthodox churches including Coptic, Ethiopian, Eritrean, Syrian, Armenian, and the Assyrian Church have continued to use their own calendars that usually result in fixed dates being celebrated in accordance with the Julian calendar.

All Eastern churches continued to use the Julian Easter with the sole exception of the Finnish Orthodox Church, which has adopted the Gregorian Easter instead.

Beginning of the Year>

The ancient Roman calendar had started its year on March 1. The year being used in dates during the Roman Republic and the Roman Empire was the consular year that began on the day when consuls first entered office. It was probably May 1 before 222 BC, March 15 from 222 BC and January 1 from 153 BC. In 45 BC, Julius Caesar had introduced the Julian calendar, wherein he continued to use January 1 as the first day of the New Year. Even though the year used for dates had changed, the civil year had always displayed its months in the order January through December and from the Roman Republican period until the present.

During the Middle Ages, under the influence of the Christian Church, most of the Western European countries had moved the start of the year to one on various important Christian festivals like December 25 as the Nativity of Jesus, March 25 as the Annunciation or Easter in France. Meanwhile, the Byzantine Empire had begun its year on September 1 and Russia did so on March 1. This continued until 1492 before the year was moved to September 1.

In common terms, January 1 was regarded and celebrated as the New Year. However, from the 12th century until 1751 the legal year in England had begun on March 25, which is the Lady Day. Therefore, for example, the Parliamentary record shows the execution of Charles 1 occurring in 1648 since the year did not end until 24 March although modern histories adjusted the beginning of the year to January 1 and recorded the execution as occurring in 1649.
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Most of the Western European countries have changed the beginning of the year to January 1 prior adopting the Gregorian calendar. For example, Scotland changed the start of the Scottish New Year to January 1 in 1600, which means that 1599 was a short year. Meanwhile, England, Ireland and other British colonies changed the start of the year to January 1 in 1752 therefore 1751 was also a short year with only 282 days. Later that year in September, the Gregorian calendar was introduced throughout Britain as well as in British colonies. These two reforms were implemented by the Calendar (New Style) Act of 1750.

In some countries, an official decree or law had specified that the start of the year should be January 1. In these countries, we can identify a specific year when the date of 1 January-year had become the norm. However, in some countries, the customs may vary whereas the start of the year was moved back and forth like fashion because of influence from other countries as well as other dictated several customs.

Neither the papal bull nor its attached canons had definitely fixed such a date, though it is implied by two tables of Saints days, one labeled 1582 which ends on December 31, and another for any full year that begins on January 1. 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.

Dual Dating

Between the period of 1582 and 1923, it was often necessary to indicate the date of some event in both the Julian calendar and in the Gregorian calendar as well. During this period, the first countries had also adopted the Gregorian calendar. Even before 1582, the year sometimes had to be double dated because of the different beginnings of the year in various countries. Woolley as he wrote in his biography of John Dee (1527-1608/9), notes that immediately after 1582 the English letter writers customarily used two dates on their letters, which are one OS and one NS.

Old Style and New Style Dates

The Old Style (OS) and New Style (NS) dates are sometimes added to dates to identify which system is used in the British Empire and other countries that did not immediately change or adopt the Gregorian Calendar. Since the Calendar Act of 1750 had altered the start of the year and also aligned the British calendar with the Gregorian calendar, there had been some confusions as to what these terms mean. They can indicate that the start of the Julian year had been adjusted to January 1 (NS) even though there are modern documents that use a different start of the year (OS). It also indicates that a date conforms to the Julian calendar (OS), rather than the Gregorian calendar (NS)

Use of dates from historical documents

There was a great deal of confusion when the calendar changed, and the confusion continues until today. In some cases, historians did not differentiate between the years. This is to force some researchers to guess between two years when interpreting the historical information.

In translating dates from the historical documents to the current documents, dates that have been incorrectly double-dated by historians, both years should be entered into present-day documents until a copy of the original primary source verifies in which year was written in the official record. Errors have often been perpetuated from the early 19th century, which may still exist today. In addition, the standard practice is to enter the earlier year first, and then followed by the later year.

Proleptic Gregorian Calendar

For certain purposes, the Gregorian calendar can be extended backward to dates preceding its official introduction. This will result into a proleptic Gregorian calendar that should be used with great caution.

For ordinary purposes, the dates of events that have occurred before October 15, 1582, are generally shown as they appeared in the Julian calendar whereas the year begins with January 1 without any conversion to their Gregorian equivalents. The Battle of Agincourt is universally known to have occurred on October 25, 1415, which is the Saint Crispins 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. However, for the period between the first introduction of the Gregorian calendar on October 15, 1582, and its introduction in Britain on September 14, 1752, there can be considerable confusion between the events in the continental western Europe and in British colonies in English language histories. Events in continental western Europe are usually reported in English language histories as occurred under the Gregorian calendar. For example, the Battle of Blenheim had occurred on August 13, 1704. The confusion would usually occur when an event affects both. For example, William III of England had arrived at Brixham in England onNovember 5 from the Julian calendar after setting sail from the Netherlands on November 11 from the Gregorian calendar.

Apparently, Shakespeare and Cervantes have died on exactly the same date, which is April 23, 1616, where in fact Cervantes predeceased Shakespeare by ten days in real time. It is because Spain used had the Gregorian calendar in dating these events whereas Britain had used the Julian calendar. This coincidence had allowed UNESCO to make April 23 as the World Book and Copyright Day.

Astronomers avoid this uncertainty by using the Julian day number instead. For dates before the year 1, unlike the proleptic Gregorian calendar used in the international standard ISO 8601, the traditional proleptic Gregorian calendar does not have a year 0 and uses the ordinal numbers 1, 2, 3 and so on for both years of AD and BC instead. Thus, the traditional timeline had resulted to 2 BC, 1 BC, AD 1, and AD 2. ISO 8601 uses the astronomical year numbering that includes a year 0 and negative numbers prior it. Thus, the ISO 8601 timeline is -0001, 0000, 0001, and 0002.

Months of the Gregorian Year

English speakers sometimes remember the number of days in each month by using the traditional mnemonic verses:

Thirty days hath September,
April, June, and November.
All the rest have thirty-one,
excepting February alone,
which hath twenty-eight.
Leap year cometh one year in four,
in which February hath one day more.

A language-independent alternative was used in many countries. This 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 while the space represents a short month of 28 or 29 days such February any month of 31 days.

The connection between the hands is not counted therefore the two index knuckles represent the months of July and August. This method also works by starting the sequence on the right hand’s little knuckle and continue towards to the left. You can also use just one hand after counting the fourth knuckle as July. Then start again counting the first knuckle as August. A similar mnemonic can be found on a piano keyboard by starting on the key F for January, moving up the keyboard in semitones, the black notes give the short months and the white notes are the long ones.

The Origins of English Naming used by the Gregorian Calendar:

January: Janus (Roman god of gates, doorways, beginnings, and endings)
February: Februus (Etruscan god of death) Februarius (mensis) (Latin for the month of purification (rituals) it is said to be a Sabine word, the last month of ancient pre-450 BC Roman calendar). It is related to fever.
March: Mars (Roman god of war)
April: Modern scholars associate the name with an ancient root meaning other, i.e., the second month of a year beginning in March.
May: Maia Maiestas (Roman goddess)
June: Juno (Roman goddess, wife of Jupiter)
July: Julius Caesar (Roman dictator) (month was formerly named Quintilis, the fifth month of the calendar of Romulus)
August: Augustus (first Roman emperor) (month was formerly named Sextilis, the sixth month of Romulus)
September: septem (Latin for seven, the seventh month of Romulus)
October: octo (Latin for eight, the eighth month of Romulus)
November: novem (Latin for nine, the ninth month of Romulus)
December: decem (Latin for ten, the tenth month of Romulus)

Weeks in the Gregorian Calendar

In connection with the system of months, there is also 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, since it may have some irregularities in the Gregorian system. When the Gregorian calendar was adopted by most countries worldwide, the weekly cycle had continued to be uninterrupted. Therefore, using the originally proposed adoption date of , Thursday, October 4, 1582, would be followed by Friday 15 October of the Julian Calendar.

Distribution of dates by day of the week

Since the 400-year cycle of the Gregorian calendar consisted of a whole number of weeks, every cycle has a fixed distribution of weekdays among the calendar dates. It then becomes possible that this distribution is not even.

Since there are 97 leap years in every 400 years in the Gregorian Calendar, there is an average of 136?7 for every starting weekday in every cycle. This already shows that the frequency is not the same for every weekday, probably because of the effects of the common centennial years of 1700, 1800, 1900, 2100, 2200 and so on.

The absence of an extra day in such years may cause the following leap years of 1704, 1804, 1904, 2104 and so on to be able to begin on the same day of the week as the leap year twelve years of 1692, 1792, 1892, 2092 and so on. Similarly, the leap year, eight years after a common centennial years begin on the same day of the week as the leap year immediately before the common centennial. Thus, those days of the week wherein such leap years begin and gain an extra year or two in every cycle. In ever cycle there are:

  • 15 leap years starting on Sunday
  • 13 leap years starting on Monday
  • 14 leap years starting on Tuesday
  • 14 leap years starting on Wednesday
  • 13 leap years starting on Thursday
  • 15 leap years starting on Friday
  • 13 leap years starting on Saturday

Note that as a cycle, this pattern is proportional to the low Saturday value.
A leap year beginning on Sunday means the next year does not start on Monday, therefore, more leap years beginning on Sunday means lesser years starting on Monday and more. Thus, the pattern of number of years starting on each day is inverted and shifted by one weekday such as 58, 56, 58, 57, 57, 58, 56, which are symmetrical against the high Sunday value. The number of common years beginning on each day is found by subtraction such as 43, 43, 44, 43, 44, 43, 43.

Accuracy of the Gregorian Calendar

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years. With an average year of 365.2425, it means the solar days are long and has an error of about one day per 3300 years with respect to the mean tropical year. The tropical year can be translated to a calendar year that averages about 26 seconds longer than the true length of the tropical year. The year 2000 had a length of 365.24219 days wherein each day consisted of 86,400 SI seconds but less than half this error with respect to the vernal equinox year of 365.24237 days, and with respect to both solstices, the Gregorian Calendar gives an average year length that is actually shorter than the actual length. By any criterion, the Gregorian calendar is substantially more accurate than the one day in 128 years error of the Julian calendar average year 365.25 days.

In the 19th century, Sir John Herschel proposed an alteration to the Gregorian calendar with 969 leap days in every 4000 years instead of the 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, it has never been officially adopted.

On timescales of thousands of years, the Gregorian calendar falls behind the seasons because the slowing down of the Earths 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 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.
Calendar Seasonal Error

Every point represents a single date in a given 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 on years of 1700, 1800, 1900, 2100, 2200, and 2300.

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

Leap seconds and other Aspects

Since 1972, some years may also contain one or more leap seconds, to account for cumulative irregularities in the Earths rotation. So far, these have always been positive and have occurred on average once every 18 months.

The day of the year is somewhat inconvenient to compute, partly because the leap day does not fall at the end of the year. But the calendar exhibits a repeating pattern for the number of days in the months March through July and August through December: 31, 30, 31, 30, 31, for a total of 153 days each. In fact, any five consecutive months not containing February contain exactly 153 days.

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. The years that are divisible by 400 begin on a Saturday. In the 400-year cycle, more months begin on a Sunday (and hence have Friday the 13th) than any other day of the week (see above under Week for a more detailed explanation of how this happens). 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 only occurs with common years when there is a dropped leap year in between.

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.

The Rata Die is the number of days from 1 January AD 1 (counting that day as day 1) in the proleptic Gregorian calendar. For May 26, 2009, it is 733553. It is 678,576 more than the Modified Julian date, and 1,721,425 less than the Julian date 2454978.

Days of the Week

Common years always begin and end on the same day of the week, since 365 is one more than a multiple of 7 (52 [number of weeks in a year] × 7 [number of days in a week] = 364). For example, 2003 began on a Wednesday and ended on a Wednesday. Leap years end on the next day of the week from which they begin. For example, 2004 began on a Thursday and ended on a Friday.

Not counting leap years, any calendar date will move to the next day of the week the following year. For example, if your birthday fell on a Tuesday in 2002, it fell on a Wednesday in 2003. Leap years make things a little more complicated. 2004 was a leap year, so calendar days of 1 March or later in the year, moved two days of the week from 2003. However, calendar days occurring before 1 March do not make the extra day of the week jump until the year following a leap year. So, if your birthday is 15 June, then it must have fallen on a Sunday in 2003 and a Tuesday in 2004. If, however, your birthday is 15 February, then it must have fallen on a Saturday in 2003, a Sunday in 2004 and a Tuesday in 2005.

In any year (even a leap year), July always begins on the same day of the week that April does. Therefore, the only difference between a July calendar page and an April calendar page in the same year is the extra day July has. The same relationship exists between September and December as well as between March and November. Add an extra day to the September page, and you’ve got December. Take a day away from the March page, and you’ve got November. In common years only, there are additional matches: October duplicates January, and March and November duplicate February in their first 28 days. In leap years only, there is a different set of additional matches: July is a duplicate of January while February is duplicated in the first 29 days of August.

English names for year numbering system

The Anno Domini (Latin for in the year of the/our Lord) system of numbering years, in which the leap year rules are written, and which is generally used together with the Gregorian calendar, is also known in English as the Common Era or Christian Era. Years before the beginning of the era are known in English as Before Christ, Before the Common Era, or Before the Christian Era. The corresponding abbreviations AD, CE, BC, and BCE are used. There is no year 0; AD 1 immediately follows 1 BC.

Naturally, since Inter gravissimas was written in Latin, it does not mandate any English language nomenclature. Two era names occur within the bull, anno Incarnationis dominicæ (in the year of the Incarnation of the Lord) for the year it was signed, and anno à Nativitate Domini nostri Jesu Christi (in the year from the Nativity of our Lord Jesus Christ) for the year it was printed. Nevertheless, anno Domini and its inflections anni Domini and annus Domini are used many times in the canons attached to the bull.