Revised Julian calendar

The Revised Julian calendar, also known as the Milanković calendar, or, less formally, new calendar, is a calendar proposed by the Serbian scientist Milutin Milanković in 1923, which effectively discontinued the 340 years of divergence between the naming of dates sanctioned by those Eastern Orthodox churches adopting it and the Gregorian calendar that has come to predominate worldwide. This calendar was intended to replace the ecclesiastical calendar based on the Julian calendar hitherto in use by all of the Eastern Orthodox Church. The Revised Julian calendar temporarily (approximately between the years 1600 and 2800) aligns its dates with the Gregorian calendar proclaimed in 1582 by Pope Gregory XIII for adoption by the Christian world.[1] The calendar has been adopted by the Orthodox churches of Constantinople, Albania, Alexandria, Antioch, Bulgaria, Cyprus, Greece, Poland, and Romania.

The Revised Julian calendar has the same months and month lengths as the Julian calendar, but, in the Revised Julian calendar, years evenly divisible by 100 are not leap years, except that years with remainders of 200 or 600 when divided by 900 remain leap years.[2]


der on
by 900
Is a
Is a
Julian is
same as
1000 100
1100 200
1200 300
1300 400
1400 500
1500 600
1600 700
1700 800
1800 0
1900 100
2000 200
2100 300
2200 400
2300 500
2400 600
2500 700
2600 800
2700 0
2800 100
2900 200
3000 300
3100 400
3200 500
3300 600
3400 700
3500 800
3600 0
3700 100
3800 200
3900 300
4000 400

A committee composed of members of the Greek government and Greek Orthodox Church was set up to look into the question of calendar reform. It reported in January 1923.[3] It recommended a switch (for civil purposes only) to the "political calendar" devised in 1785 and advocated by Maksim Trpković.[4] Trpković advocated this calendar in preference to the Gregorian because of its greater accuracy and also because the vernal equinox would generally fall on 21 March, the date allocated to it by the church. In the Gregorian, it generally falls on 20 March. As in the Gregorian, end-century years are generally not leap years, but years that give remainder 0 or 400 on division by 900 were to be leap years. The changeover went into effect on 17 February/1 March.

After the promulgation of the royal decree, the Ecumenical Patriarch, Patriarch Meletius IV of Constantinople, issued an encyclical on 3 February recommending the calendar's adoption by Orthodox churches. The matter came up for discussion at a "Pan-Orthodox" Congress of Constantinople, which deliberated in May and June. Subsequently it was adopted by several of the autocephalous Orthodox churches. The synod was chaired by the controversial patriarch and representatives were present from the churches of Cyprus, Greece, Romania and Serbia. There were no representatives of the other members of the original Orthodox Pentarchy (the Patriarchates of Jerusalem, Antioch, and Alexandria) or from the largest Orthodox church, the Russian Orthodox Church.[5]

Discussion was lengthy because although Serbia officially supported the political calendar, Milanković (an astronomical delegate to the synod representing the Kingdom of Serbs, Croats and Slovenes) pressed for the adoption of his own version, in which the centennial leap years would be those giving remainder 200 or 600 when divided by 900 and the equinox would generally fall on 20 March (as in the Gregorian). Under the official proposal the equinox would sometimes fall on 22 March. This might make Easter fall outside its canonical limits due to the requirement that the Easter full moon follow the equinox.[6] Also his scheme maximised the time during which the political calendar and the Gregorian would run in tandem.

Milanković's arguments won the day. In its decision the conference noted that "the difference between the length of the political year of the new calendar and the Gregorian is so small that only after 877 years it is observed difference of dates." The same decision provided that the coming 1 October should be called 14 October, thus dropping thirteen days. It then adopted the leap year rule of Milanković.[7][8] The political calendar was preferred over the Gregorian because its mean year was within two seconds of the then current length of the mean tropical year.[8] The present vernal equinox year, however, is about 12 seconds longer, in terms of mean solar days.

The synod also proposed the adoption of an astronomical rule for Easter: Easter was to be the Sunday after the midnight-to-midnight day at the meridian of the Church of the Holy Sepulchre in Jerusalem (35°13′47.2″ E or UT+2h20m55s for the small dome) during which the first full moon after the vernal equinox occurs. Although the instant of the full moon must occur after the instant of the vernal equinox, it may occur on the same day. If the full moon occurs on a Sunday, Easter is the following Sunday. Churches that adopted this calendar did so on varying dates. However, all Eastern Orthodox churches continue to use the Julian calendar to determine the date of Easter (except for the Finnish Orthodox Church and the Estonian Orthodox Church, which now use the Gregorian Easter).


The following are Gregorian minus Revised Julian date differences, calculated for the beginning of March in each century year, which is where differences arise or disappear, until 10000 AD. These are exact arithmetic calculations, not depending on any astronomy. A negative difference means that the proleptic Revised Julian calendar was behind the proleptic Gregorian calendar. The Revised Julian calendar is the same as the Gregorian calendar from 1 March 1600 to 28 February 2800. A positive difference means that the Revised Julian calendar will be ahead of the Gregorian calendar, which will first occur on 1 March 2800:

Gregorian minus Revised Julian date differences

In 900 Julian years there are ​9004 = 225 leap days. The Revised Julian leap rule omits seven of nine century leap years, leaving 225−7 = 218 leap days per 900-year cycle. Thus the calendar mean year is 365 + ​218900 days, but this is actually a double-cycle that reduces to 365 + ​109450 = 365.242 days, or exactly 365 days 5 hours 48 minutes 48 seconds, which is exactly 24 seconds shorter than the Gregorian mean year of 365.2425 days, so in the long term on average the Revised Julian calendar pulls ahead of the Gregorian calendar by one day in 3600 years.

The number of days per Revised Julian cycle = 900 × 365 + 218 = 328,718 days. Taking mod 7 leaves a remainder of 5, so like the Julian calendar, but unlike the Gregorian calendar, the Revised Julian calendar cycle does not contain a whole number of weeks. Therefore, a full repetition of the Revised Julian leap cycle with respect to the seven-day weekly cycle is seven times the cycle length = 7 × 900 = 6300 years.


The epoch of the Julian calendar was on the Saturday before the Monday that was the epoch of the Gregorian calendar. In other words, Gregorian 1 January 1 AD = Julian 3 January 1 AD. The Revised Julian reform not only changed the leap rule but also made the epoch the same as that of the Gregorian calendar. This seems to have been carried out implicitly, and even scientific articles make no mention of it.[9] Nevertheless, it is impossible to implement calendrical calculations and calendar date conversion software without appreciating this detail and taking the 2-day shift into account. If the original Julian calendar epoch is mistakenly used in such calculations then there is no way to reproduce the currently accepted dating of the Revised Julian calendar, which yields no difference between Gregorian and Revised Julian dates in the 21st century.

March equinox

The following is a scatter plot of actual astronomical northward equinox moments as numerically integrated by SOLEX 11[10][11] using DE421 mode[12] with extended (80-bit) floating point precision, high integration order (18th order), and forced solar mass loss[13] ("forced" means taken into account at all times). SOLEX can automatically search for northern hemisphere spring equinox moments by finding when the solar declination crosses the celestial equator northward, and then it outputs that data as the Terrestrial Time day and fraction of day relative to 1 January 2000 at noon (J2000.0 epoch). The progressive tidal slowing of the Earth rotation rate was accounted for by subtracting ΔT as calculated by the Espenak-Meeus polynomial set recommended at the NASA Eclipses web site[14] to obtain the J2000.0-relative Universal Time moments, which were then properly converted to Revised Julian dates and Jerusalem local apparent time, taking local apparent midnight as the beginning of each calendar day. The year range of the chart was limited to dates before the year 4400 AD—by then ΔT is expected to accumulate to about six hours, with an uncertainty of less than ​2 12 hours.[15]


The chart shows that the long-term equinox drift of the Revised Julian calendar is quite satisfactory, at least until 4400 AD. The medium-term wobble spans about two days because, like the Gregorian calendar, the leap years of the Revised Julian calendar are not smoothly spread: they occur mostly at intervals of four years but there are occasional eight-year gaps (at 7 out of 9 century years). Evidently each of the authorities responsible for the Gregorian and Revised Julian calendars, respectively, accepted a modest amount of medium-term equinox wobble for the sake of traditionally perceived leap rule mental arithmetic simplicity. Therefore, the wobble is essentially a curiosity that is of no practical or ritual concern.


The new calendar has been adopted by Orthodox churches as follows:

  • 1923: Estonia (accepted the Gregorian calendar, including the Gregorian Paschalion, but in 1945 joined the Moscow Patriarchate and reverted to Julian; after re-establishing in 1996, the Estonian Apostolic Orthodox Church adopted the Revised Julian calendar in 2012)
  • 1923: Finland (uses the Gregorian calendar, including the Gregorian Paschalion)
  • 10/23 March 1924: Constantinople, Cyprus and Greece
  • 1/14 October 1924: Poland (Very few parishes changed - on 2/15 June 2014 the Church switched back, but individual parishes may use the Revised Julian calendar if they wish)
  • 1/14 October 1924: Romania
  • 1/14 October 1928: Alexandria and Antioch
  • The Albanian Orthodox Church became autocephalous on 12 April 1937
  • 7/20 December 1968: Bulgaria [16]

Adopting churches are known as New calendarists. The new calendar has not been adopted by the Orthodox churches of Jerusalem, Russia, Serbia (including the uncanonical Macedonian Orthodox Church), Georgia, Mount Athos and the Greek Old Calendarists. Although Milanković stated that the Russian Orthodox Church adopted the new calendar in 1923, the present church continues to use the Julian calendar for both its fixed festivals and for Easter. A solution to this conundrum is to hypothesize that it was accepted only by the short-lived schismatic Renovationist Church, which had seized church buildings with the support of the Soviet government while Patriarch Tikhon was under house arrest. After his release, on 15 July 1923, he declared that all Renovationist decrees were without grace, presumably including its acceptance of the new calendar.[17]


The basic justification for the new calendar is the known errors of the Julian calendar, which will in the course of time lead to a situation in which those following the Julian calendar will be reckoning the month of December (and the feast of Christ's Nativity) during the heat of summer, August and its feasts during the deep cold of winter, Easter during the autumn season, and the November feasts in the springtime. This would conflict with the Church's historic practice of celebrating Christ's birth on 25 December, a date chosen for a number of reasons.[18] One of the reasons mentioned by Bennet is the time of the winter solstice, when the days begin to lengthen again as the physical sun makes its reappearance, along with the fact that Christ has traditionally been recognized by Christians as the metaphorical and spiritual sun who fulfills Malachi's prophetic words: "the sun of righteousness will shine with healing in its wings" (Malachi 4:2). The identification, based on this prophecy, of Jesus Christ as the "sun of righteousness" is found many times in writings of the early Church fathers[19] and follows from many New Testament references linking Jesus with imagery of sun and light.[19]

The defenders of the new calendar do not regard the Julian calendar as having any particular divine sanction (for more on this, see below); rather, they view the Julian calendar as a device of human technology, and thus subject to improvement or replacement just as many other devices of technology that were in use at the dawn of the Church have been replaced with newer forms of technology.

Supporters of the new calendar can also point to certain pastoral problems that are resolved by its adoption.

(1) Parishes observing the Julian calendar are faced with the problem that parishioners are supposed to continue fasting throughout western Christmas and New Year, seasons when their families and friends are likely to be feasting and celebrating New Year's, often with parties, use of liquor, etc. This situation presents obvious temptations, which are eliminated when the new calendar is adopted.

(2) Another pastoral problem is the tendency of some local American media to focus attention each year on the 7 January (N.S.) / 25 December (O.S.) celebration of Christmas, even in localities where most Orthodox parishes follow the new calendar. So too, in all likelihood, do certain non-Orthodox churches profit from the Orthodox remaining Old Style, since the 7 January observance of Christmas among the Orthodox tends to focus attention on ethnic identifications of the feast, rather than on its Christian, dogmatic significance; which, in turn, tends to foster the impression in the public mind that for the Orthodox, the feast of Christ's Nativity is centered on the observance of the Julian date of that feast, rather than on the commemoration of Christ's birth. Such a focus appears to the defenders of the Revised Julian calendar and to many non-Orthodox as well, as a practice that is charming and quaint, but also anachronistic, unscientific and hence ultimately unreasonable and even cultish.

(3) Some Orthodox themselves may unwittingly reinforce this impression by ignorance of their own faith and by a consequential exclusive, or excessive, focus on the calendar issue: it has been observed, anecdotally, that some Russians cannot cite any difference in belief or practice between their faith and the faith of western Christians, except for the 13-day calendar difference.

Against the new calendar, the argument is made that inasmuch as the use of the Julian calendar was implicit in the decision of the First Ecumenical Council at Nicaea (325), no authority less than an Ecumenical Council may change this decision. However, the fact is that that Council made no decision or decree at all concerning the Julian calendar. Its silence constituted an implicit acceptance not of the Julian calendar, but of the civil calendar, which happened to be, at that time, the Julian calendar (the explicit decision of Nicaea being concerned, rather, with the date of Easter). By virtue of this, defenders of the new calendar argue that no decision by an Ecumenical Council was or is necessary today in order to revise (not abandon) the Julian calendar; and further, that by making the revision, the Church stays with the spirit of Nicaea I by keeping with the civil calendar in all its essentials—while conversely, failure to keep with the civil calendar could be seen as a departure from the spirit of Nicaea I in this respect. Lastly, it is argued that since the adoption of the new calendar evidently involves no change in or departure from the theological or the ethical teachings of Orthodox Christianity, but rather amounts to a merely disciplinary or administrative change—a clock correction of sorts—the authority to enact that change falls within the competency of contemporary, local episcopal authority. Implicit acceptance of this line of reasoning, or something very close to it, underlies the decision to adopt the new calendar by those Orthodox churches that have done so.

It follows that, in general, the defenders of the new calendar hold the view that in localities where the Church's episcopal authority has elected to adopt the new calendar, but where some have broken communion with those implementing this change, it is those who have broken communion who have in fact introduced the disunity, rather than the new calendar itself or those who have adopted it — although most would agree that attempts at various times to mandate the use of the new calendar through compulsion, have magnified the disunity.

To the objection that the new calendar has created problems by adjusting only the fixed calendar, while leaving all of the commemorations in the moveable cycle on the original Julian calendar, the obvious answer, of course, is that the 1923 Synod, which adopted the new calendar, did in fact change the moveable calendar as well, and that calendar problems introduced as a result of the adoption of the (fixed) new calendar alone, would not have existed had the corrections to the moveable calendar also been implemented.

According to the defenders of the new calendar, the argument that the 25 December (N.S.) observance of Christmas is a purely secular observance and is therefore an unsuitable time for Orthodox Christians to celebrate Christ's Nativity, is plainly inaccurate, since the 25 December observances of Christ's birth among western Christians (and today, among many Orthodox Christians) obviously occur overwhelmingly in places of worship and involve hymns, prayers, scripture readings, religious dramas, liturgical concerts, and the like. Defenders of the new calendar further note that, to the extent that 25 December is a secular observance in the western world, 7 January (i.e., 25 December O.S.) appears to be becoming one as well, in Orthodox countries that continue to follow the old calendar. In Russia, for example, 7 January is no longer a spiritual holiday for Orthodox Christians alone, but has now become a national (hence secular) holiday for all Russians, including non-Orthodox Christians, people of other religions, and nonbelievers. Where this will lead in the end remains to be seen.

Among other arguments by defenders of the new calendar are those made on the basis of truth (notwithstanding that the detractors of that calendar make the claim that the Old Style date, 7 January / 25 December, is the true celebration of Christ's Nativity). Arguments from truth can take two forms: (1) If a calendar is a system for reckoning time based on the motions of astronomical bodies—specifically the movements of Sun and Moon, in the case of the church calendar—and if precision or accuracy is understood as one aspect of truth, then a calendar that is more accurate and precise with respect to the motions of those bodies must be regarded as truer than one that is less precise. In this regard, some of those who champion the old calendar as truth (rather than for pastoral reasons, as seems to be the case with the national churches that adhere to it) may appear, to those following the new calendar, as the defenders of a fiction. (2) Some defenders of the new calendar argue that the celebration, in any way or form, of two feasts of Christ's Nativity within the same liturgical year is not possible, since according to the faith there is only one celebration of that feast in a given year. On this basis, they argue that those who prefer to observe a "secular" feast of the Nativity on 25 December and a "religious" one on 7 January, err in respect of the truth that there is but one feast of the Nativity each year.


While the new calendar has been adopted by many of the smaller national churches, a majority of Orthodox Christians continue to adhere to the traditional Julian calendar, and there has been much acrimony between the two parties over the decades since the change, leading sometimes even to violence, especially in Greece.

Critics see the change in calendar as an unwarranted innovation, influenced by Western society. They say that no sound theological reason has been given for changing the calendar, that the only reasons advanced are social. The proposal for change was introduced by Meletios Metaxakis, a patriarch whose canonical status has been disputed and who is alleged to have been a Freemason,[20][21][22] which is forbidden by the Orthodox Church.[23]

The argument is also made that since the use of the Julian calendar was implicit in the decision of the First Ecumenical Council at Nicaea (325), which standardized the calculation of the date of Easter, no authority less than an Ecumenical Council may change it. It is further argued that the adoption of the new calendar in some countries and not in others has broken the liturgical unity of the Eastern Orthodox churches, undoing the decision made by the council of bishops at Nicaea to decree that all local churches celebrate Easter on the same day. The emperor Constantine, writing to the bishops absent from the Council to notify them of the decision, argued, "Think, then, how unseemly it is, that on the same day some should be fasting whilst others are seated at a banquet".[24]

Liturgical objections to the new calendar stem from the fact that it adjusts only those liturgical celebrations that occur on fixed calendar dates, leaving all of the commemorations on the moveable cycle on the original Julian calendar. This upsets the harmony and balance of the liturgical year. (This would not have been a problem if the recommendations of the 1923 synod to use an astronomical rule to reckon the date of Easter, as outlined above, had not been rejected.) This disruption is most noticeable during Great Lent. Certain feast days are designed to fall during Lent, such as the feast of the Forty Martyrs of Sebaste. The Feast of the Annunciation is also intended to fall either before Easter or during Bright Week. Sometimes, Annunciation will fall on the day of Easter itself, a very special concurrence known as Kyrio-Pascha, with special liturgical practices appointed for such an occurrence. However, under the new calendar, Kyrio-Pascha becomes an impossibility. The Apostles' Fast displays the most difficult aspect of the new calendar. The fast begins on the moveable cycle and ends on the fixed date of 29 June; since the new calendar is 13 days ahead of the traditional Julian calendar, the Apostles' Fast is 13 days shorter for those who follow the new calendar, and some years it is completely abrogated. Furthermore, critics of the new calendar point out the advantage to celebrating Nativity separately from the secular observances of Christmas and New Year, which are associated with partying and alcohol consumption.

Critics also point out that proponents of the new calendar tend to use worldly rather than spiritual justification for changing the calendar: wanting to "party with everyone else" at Christmas; concern that the gradual shift in the Julian calendar will somehow negatively affect the celebration of feasts that are linked to the seasons of the year. However, opponents counter that the seasons are reversed in the southern hemisphere, where the liturgical celebrations are no less valid. The validity of this argument is questionable, since the feasts of the Orthodox Church were not changed no matter where they were celebrated, and Orthodox services were held in the southern hemisphere with little issue centuries before the introduction of the new calendar.

Proponents also argue that the new calendar is somehow more "scientific", but opponents argue that science is not the primary concern of the Church; rather, the Church is concerned with other-worldliness, with being "in the world, but not of it", fixing the attention of the faithful on eternity. Scientifically speaking, neither the Gregorian calendar nor the new calendar is absolutely precise. This is because the solar year cannot be evenly divided into 24-hour segments. So any public calendar is imprecise; it is simply an agreed-upon designation of days.

From a spiritual perspective, Old Calendarists also point to a number of miraculous occurrences that occur on the old calendar exclusively, such as the "descent of the cloud on the mount" on the feast of the Transfiguration. After the calendar change was instituted, the followers of the old calendar in Greece apparently witnessed the appearance of a cross in the sky, visible to thousands on the feast of the Exaltation of the Holy Cross, 1925, of which eyewitness accounts were recorded.[25]

For such special events, if the original Julian date and year is known then the option always exists to calculate what was the proleptic Revised Julian date of that event and then observe its anniversary on that day, if that could be socially and ritually accepted.

Revised Julian calendrical calculations

The calendrical arithmetic discussed here is adapted from Gregorian and Julian calendar arithmetic published by Dershowitz and Reingold, although those authors explicitly ignored the Revised Julian calendar.[26] Their book, referred to hereinafter as CC3, should be consulted for methods to handle BC dates and the traditional omission of a year zero, both of which are ignored here. They define the MOD operator as x MOD y = x − y × floor(x / y), because that expression is valid for negative and floating point operands, returning the remainder from dividing x by y while discarding the quotient.[27] Expressions like floor(x / y) return the quotient from dividing x by y while discarding the remainder.

Leap rule

isLeapYear = (year MOD 4 = 0)

IF isLeapYear THEN

IF year MOD 100 = 0 THEN
Century = (year / 100) MOD 9
isLeapYear = (Century=2) OR (Century=6)


Fixed days

Calendrical calculations are made consistent and straightforward for arithmetic operations if dates are first converted to an ordinal number of days relative to an agreed-upon epoch, in this case the Revised Julian epoch, which was the same as the Gregorian epoch. To find the difference between any two Revised Julian dates, convert both to ordinal day counts and simply subtract. To find a past or future date, convert a given date to an ordinal day count, subtract or add the desired number of days, then convert the result to a Revised Julian date.

The arithmetic given here will not "crash" if an invalid date is given. To verify that a given date is a valid Revised Julian date, convert it to an ordinal day count and then back to a Revised Julian date—if the final date differs from the given date then the given date is invalid. This method should also be used to validate any implementation of calendrical arithmetic, by iteratively checking thousands of random and sequential dates for such errors.

To convert a Revised Julian date to any other calendar, first convert it to an ordinal day count, and then all that is needed is a function to convert the ordinal days count to that calendar. To convert a date from any other calendar to a Revised Julian date, first convert that calendar date to an ordinal day count, then convert ordinal days to the Revised Julian date.

The following constant defined midnight at the start of Revised Julian date Monday, 1 January 1 AD as the beginning of the first ordinal day. This moment was Julian day number 1721425.5.

RJepoch = 1

CC3 outlines functions for Gregorian and Julian calendar conversions,[28] as well as many other calendars, always calculating in terms of the ordinal day number, which they call the "fixed date" or rata die (RD), assigning the number 1 to the Gregorian calendar epoch. The arithmetic herein, by using the same ordinal day numbering epoch, is fully compatible with all CC3 functions for calendrical calculations and date inter-conversions.

One can assign a different integer to the Revised Julian epoch, for the purpose of numbering ordinal days relative to some other epoch, but if you do so then one must take the epoch difference into account when using any CC3 calendar functions and when converting an ordinal day number to a weekday number.

Optionally the ordinal day number can include a fractional component to represent the time as the elapsed fraction of a day. The ordinal day number of the J2000 moment (1 January 2000 noon) was 730120.5.

Revised Julian to fixed days

Convert a year, month, and day to the corresponding fixed day number:

PriorYear = year − 1
FixedDays = RJepoch + 365 × PriorYear + floor(PriorYear / 4) + floor((367 × month − 362) / 12) + day − 1

If month is after February then subtract 1 day for a leap year or subtract 2 days for a common year:

IF month > 2 THEN
IF isLeapYear(year) THEN
FixedDays = FixedDays − 1
FixedDays = FixedDays − 2

Finally subtract a day for each prior century year (most of which are non-leap) and then add back in the number of prior century leap years:

PriorCenturies = floor(PriorYear / 100)
FixedDays = FixedDaysPriorCenturies + floor((2 × PriorCenturies + 6) / 9)

Fixed days to Revised Julian

Convert an ordinal day number to the corresponding Revised Julian year, month, and day, starting by removing any fractional time-of-day portion:

Days = floor(FixedDays) − RJepoch + 1
PriorCenturies = floor(Days / 36524)
RemainingDays = Days − 36524 × PriorCenturies - floor((2 × PriorCenturies + 6) / 9)
PriorSubcycles = floor(RemainingDays / 1461)
RemainingDays = RemainingDays MOD 1461
PriorSubcycleYears = floor(RemainingDays / 365)
year = 100 × PriorCenturies + 4 × PriorSubcycles + PriorSubcycleYears
RemainingDays = RemainingDays MOD 365
IF RemainingDays = 0 THEN
This is either the 365th day of a common year, or the 365th or 366th day of a leap year. Either way, we have to decrement the year because we went one year too far:
year = year − 1
IF isLeapYear(year) AND PriorSubcycles=0 THEN RemainingDays=366 ELSE RemainingDays=365
PriorDays = RemainingDays − 1
IF isLeapYear(year) THEN correction = 1 ELSE correction = 0
IF PriorDays < (31+28+correction) THEN correction = 0 ELSE correction = 2 − correction
Month = floor((12 × (PriorDays + correction) + 373) / 367)

Finally, calculate the day number within the month by subtracting the Fixed days count for the start of the month from the originally given Fixed days count, and then add one day:

Day = FixedDays - RevisedJulianToFixed(year, month, 1) + 1

Fixed days to weekday number

Convert the ordinal number of days since the Revised Julian epoch to a weekday number (Sunday=1 through Saturday = 7):

WeekdayNumber = (floor(FixedDays) − RJepoch + 1) MOD 7 + 1

Don't be tempted to omit subtracting the RJepoch just because it is offset by adding +1. As written, this expression is robust even if you assign a value other than one to the epoch.


  1. ^ "Gregorian Calendar". Encyclopædia Britannica. Retrieved 20 April 2010.
  2. ^ "The Revised Julian Calendar". Time and Date. Retrieved 25 December 2017.
  3. ^ Holy Trinity Monastery (1996). The Orthodox Church Calendar. p. 27. ISBN 9780884650621. The Church of Greece accepted the New Calendar on March 1, 1924. Archbishop Chrysostomos (Papadopoulos) of Athens must have forgotten the words he wrote while still an Archimandrite in a report given to the Greek government by the five member commission on the question of calendar reform in January, 1923: …
  4. ^ Maksim Trpković, Reforma kalendara, Belgrade 1900.
  5. ^ Cassian, Hieromonk (1998). A Scientific Examination of the Orthodox Church Calendar. Center for Traditionalist Orthodox Studies. pp. 51–52. ISBN 978-0-911165-31-9.
  6. ^ The Romanian church adopted the new calendar on the date specified by the conference. As the Julian Easter continued to be observed, in 1926 it would have fallen outside the canonical limits. The church decreed that the Gregorian Easter would be observed instead, which led to dissent. The same thing happened in 1929. This time there was civil disorder and churches were barricaded. The experiment was not repeated.
  7. ^ Milankovitch, M. (1924). "Das Ende des julianischen Kalenders und der neue Kalender der orientalischen Kirchen". Astronomische Nachrichten (in German). 220 (5279): 379–384. Bibcode:1924AN....220..379M. doi:10.1002/asna.19232202303.
  8. ^ a b Shields, Miriam Nancy (1924). "The new calendar of the Eastern churches". Popular Astronomy. 32: 407–411. Bibcode:1924PA.....32..407S. This is a translation of the paper by Milankovitch in Astronomische Nachrichten.
  9. ^ Dimitrijević, M.S. & Theodossiou, E. (2002). "The calendar of the Greek Orthodox Church" (PDF). Astronomical & Astrophysical Transactions. 21 (1): 145–147. doi:10.1080/10556790215577.
  10. ^ Vitagliano, Aldo (1997). "Numerical integration for the real time production of fundamental ephemerides over a wide time span" (PDF). Celestial Mechanics and Dynamical Astronomy. 66 (3): 293–308. Bibcode:1996CeMDA..66..293V. doi:10.1007/bf00049383. Archived from the original (PDF) on 22 July 2011.
  11. ^ "The SOLEX home page". Archived from the original on 3 April 2011.
  12. ^ Folkner, W. M.; Williams, J. G. & Boggs, D. H. (31 March 2008). "The Planetary and Lunar Ephemeris DE 421" (PDF). Jet Propulsion Laboratory, California Institute of Technology, Memorandum. IOM 343R-08-003. Archived from the original (PDF) on 2 May 2013.
  13. ^ Noerdlinger, Peter D. (2008). "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System". arXiv:0801.3807 [astro-ph].
  14. ^ "Eclipses Delta T web site". NASA. Gives the Espenak-Meeus polynomial expressions for Delta T.
  15. ^ "Uncertainty in Delta T (ΔT)".
  16. ^ Clogg 2002, pp. 8–9.
  17. ^ Koestel 2012, p. 157.
  18. ^ Bennett, David. "Choosing the Date of Christmas: Why is Christmas Celebrated on December 25?".
  19. ^ a b Murdock, D.M.; Acharya S. "Jesus as the Sun Throughout History".
  20. ^ The Orthodox Church Calendar: In Defense of the Julian Calendar. Jordanville, NY: Holy Trinity Monastery. 1996. p. 11. ISBN 978-0884650621.
  21. ^ ΕΠΙΦΑΝΕΙΣ ΕΛΛΗΝΕΣ ΕΛΕΥΘΕΡΟΤΕΚΤΟΝΕΣ (in Greek). Grand Lodge of Greece. Archived from the original on 10 February 2009. Retrieved 16 February 2010. Contains the name of the Patriarch in question Meletios Metaxakis, "Alexandrian and Ecumenical Patriarch," listed on its website.
  22. ^ "Meletios Metaxakis".
  23. ^ "Freemasonry: Official Statement of the Church of Greece (1933)".
  24. ^ Eusebius. "On the Keeping of Easter". Vita Const. Lib. iii., 18–20. Retrieved 4 June 2007.
  25. ^ "The Appearance of the Sign of the Cross Near Athens in 1925".
  26. ^ Dershowitz, Nachum; Reingold, Edward M. (2008). Calendrical Calculations (3rd ed.). Cambridge University Press. p. 47, footnote 3. Archived from the original on 12 July 2008.
  27. ^ Dershowitz, Nachum; Reingold, Edward M. (2008). Calendrical Calculations (3rd ed.). Cambridge University Press. p. 18, equation 1.15. Archived from the original on 12 July 2008.
  28. ^ For example, see "alt-fixed-from-gregorian" in Dershowitz, Nachum; Reingold, Edward M. "Errata" (PDF). Calendrical Calculations: The Millennium Edition (2nd ed.). Cambridge University Press. erratum 106, equation 2.25.


External links

Adrian and Natalia of Nicomedia

Saint Adrian (also known as Hadrian) or Adrian of Nicomedia (died 4 March 306) was a Herculian Guard of the Roman Emperor Galerius Maximian. After becoming a convert to Christianity with his wife Natalia, Adrian was martyred at Nicomedia.

Bulgarian budnik

Budnik (transliterated), (Bulgarian: Бъдник), refers to a log brought into the house and placed on the fire on the evening of Christmas Eve, a central tradition in Slavic Christmas celebrations in Bulgaria, Bosnia and Herzegovina, Croatia, Serbia, and Montenegro, much like a yule log in other European traditions (in the Bulgarian, Croatian, and Serbian languages, the name for Christmas Eve is derived from the term badnjak or budnik) as well as the Bulgarian name for Christmas Eve (bg:Бъдни вечер). The tree from which the log is cut, preferably a young and straight oak, is ceremonially felled early on the morning of Christmas Eve. The felling, preparation, bringing in, and laying on the fire, are surrounded by elaborate rituals, with many regional variations.

Bulgaria's Orthodox Church turned to the Revised Julian calendar in 1968. Since then, Bulgaria has celebrated Christmas on December 25, therefore, most celebrate Christmas Eve (Budni Vecher) on December 24.

Common year

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar, (like the earlier Julian calendar), employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

The common year of 365 days has 52 weeks and one day, hence a common year always begins and ends on the same day of the week (for example, January 1 and December 31 fell on a Sunday in 2017) and the year following a common year will start on the subsequent day of the week. In common years, February has four weeks, so March will begin on the same day of the week. November will also begin on this day.

In the Gregorian calendar, 303 of every 400 years are common years. By comparison, in the Julian calendar, 300 out of every 400 years are common years, and in the Revised Julian calendar (used by Greece) 682 out of every 900 years are common years.

Determination of the day of the week

The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables.

A typical application is to calculate the day of the week on which someone was born or a specific event occurred.

Dominical letter

Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter (or pair of letters for leap years) depending on which day of the week the year starts on.

Dominical letters are derived from the Roman practice of marking the repeating sequence of eight letters A–H (commencing with A on 1 January) on stone calendars to indicate each day's position in the eight-day market week (nundinae). The word is derived from the number nine due to their practice of inclusive counting. After the introduction of Christianity a similar sequence of seven letters A–G was added alongside, again commencing with 1 January. The dominical letter marks the Sundays. Nowadays they are used primarily as part of the computus, which is the method of calculating the date of Easter.

A common year is assigned a single dominical letter, indicating which lettered days are Sundays in that particular year (hence the name, from Latin dominica for Sunday). Thus, 2017 is A, indicating that all A days are Sunday, and by inference, 1 January 2017 is a Sunday. Leap years are given two letters, the first valid for January 1 – February 28 (or February 24, see below), the second for the remainder of the year.

In leap years, the leap day may or may not have a dominical letter. In the Catholic version it does, but in the 1662 and subsequent Anglican versions it does not. The Catholic version causes February to have 29 days by doubling the sixth day before 1 March, inclusive, because 24 February in a common year is marked "duplex", thus both halves of the doubled day have a dominical letter of F. The Anglican version adds a day to February that did not exist in common years, 29 February, thus it does not have a dominical letter of its own.In either case, all other dates have the same dominical letter every year, but the days of the dominical letters change within a leap year before and after the intercalary day, 24 February or 29 February.

Eastern Orthodox liturgical calendar

The Eastern Orthodox Liturgical Calendar describes and dictates the rhythm of the life of the Eastern Orthodox Church. Passages of Holy Scripture, saints and events for commemoration are associated with each date, as are many times special rules for fasting or feasting that correspond to the day of the week or time of year in relationship to the major feast days.

There are two types of feasts in the Orthodox Church calendar: fixed and movable. Fixed feasts occur on the same calendar day every year, whereas movable feasts change each year. The moveable feasts are generally relative to Pascha (Easter), and so the cycle of moveable feasts is referred to as the Paschal cycle.

Greek Old Calendarists

Greek Old Calendarists (Greek: Έλληνες Ορθόδοξοι Παλαιοημερολογίτες), also Genuine Orthodox Christians (GOC; Γνήσιοι Ορθόδοξοι Χριστιανοί), are groups of Old Calendarist Orthodox Christians that remained committed to the traditional Orthodox practice and are not in communion with many other Orthodox churches such as the Orthodox Church of Greece, the Patriarchate of Constantinople, or the Church of Cyprus. The split began with a disagreement over the abandonment of the traditional church calendar (also called the Julian calendar) in preference to the adoption of the Revised Julian calendar which is similar to the papal Gregorian calendar but will pull ahead by one day in the year 2800 and over other liturgical reforms that were introduced.

Leap year

A leap year (also known as an intercalary year or bissextile year) is a calendar year containing one additional day (or, in the case of lunisolar calendars, a month) added to keep the calendar year synchronized with the astronomical or seasonal year. Because seasons and astronomical events do not repeat in a whole number of days, calendars that have the same number of days in each year drift over time with respect to the event that the year is supposed to track. By inserting (also called intercalating) an additional day or month into the year, the drift can be corrected. A year that is not a leap year is called a common year.

For example, in the Gregorian calendar, each leap year has 366 days instead of 365, by extending February to 29 days rather than the common 28. These extra days occur in years which are multiples of four (with the exception of centennial years not divisible by 400). Similarly, in the lunisolar Hebrew calendar, Adar Aleph, a 13th lunar month, is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Bahá'í Calendar, a leap day is added when needed to ensure that the following year begins on the vernal equinox.

The name "leap year" probably comes from the fact that while a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, the day of the week in the 12 months following the leap day (from March 1 through February 28 of the following year) will advance two days due to the extra day (thus "leaping over" one of the days in the week). For example, Christmas Day (December 25) fell on a Sunday in 2016, Monday in 2017, and Tuesday in 2018, then will fall on Wednesday in 2019 but then "leaps" over Thursday to fall on a Friday in 2020.

The length of a day is also occasionally changed by the insertion of leap seconds into Coordinated Universal Time (UTC), owing to the variability of Earth's rotational period. Unlike leap days, leap seconds are not introduced on a regular schedule, since the variability in the length of the day is not entirely predictable.

List of Serbian inventions and discoveries

Serbian inventions and discoveries are objects, processes or techniques invented or discovered by Serbian people.

List of Serbian inventors and discoverers

This is a List of Serbian inventors and discoverers, working locally or overseas. The list comprises people from Serbia and ethnic Serb people.

Milutin Milanković

Milutin Milanković (Serbian Cyrillic: Милутин Миланковић [milǔtin milǎːnkɔʋitɕ]; 28 May 1879 – 12 December 1958) was a Serbian mathematician, astronomer, climatologist, geophysicist, civil engineer and popularizer of science.

Milanković gave two fundamental contributions to global science. The first contribution is the "Canon of the Earth’s Insolation", which characterizes the climates of all the planets of the Solar system. The second contribution is the explanation of Earth's long-term climate changes caused by changes in the position of the Earth in comparison to the Sun, now known as Milankovitch cycles. This explained the ice ages occurring in the geological past of the Earth, as well as the climate changes on the Earth which can be expected in the future.

He founded planetary climatology by calculating temperatures of the upper layers of the Earth's atmosphere as well as the temperature conditions on planets of the inner Solar system, Mercury, Venus, Mars, and the Moon, as well as the depth of the atmosphere of the outer planets. He demonstrated the interrelatedness of celestial mechanics and the Earth sciences, and enabled consistent transition from celestial mechanics to the Earth sciences and transformation of descriptive sciences into exact ones.

Nativity Fast

The Nativity Fast is a period of abstinence and penance practiced by the Eastern Orthodox, Oriental Orthodox, and Eastern Catholic Churches, in preparation for the Nativity of Jesus (December 25). The corresponding Western season of preparation for Christmas, which also has been called the Nativity Fast and St. Martin's Lent, has taken the name of Advent. The Eastern fast runs for 40 days instead of four (Roman rite) or six weeks (Ambrosian rite) and thematically focuses on proclamation and glorification of the Incarnation of God, whereas the Western Advent focuses on the two comings (or advents) of Jesus Christ: his birth and his Second Coming or Parousia.

The Byzantine fast is observed from November 15 to December 24, inclusively. These dates apply to those Orthodox Churches which use the Revised Julian calendar, which currently matches the Gregorian calendar. For those Eastern Orthodox Churches which still follow the Julian calendar (Greek Orthodox Patriarchate of Jerusalem, Russian Orthodox Church, Serbian Orthodox Church, Polish Orthodox Church, Georgian Orthodox Church, Ukrainian Orthodox Church, Macedonian Orthodox Church, and Mount Athos), the Winter Lent does not begin until November 28 (Gregorian) which coincides with November 15 on the Julian calendar. The Ancient Church of the East fasts dawn til dusk from the 1st December until the 25th of December on the Gregorian calendar.

Sometimes the fast is called Philip's Fast (or the Philippian Fast), as it traditionally begins on the day following the Feast of St. Philip the Apostle (November 14). Some churches, such as the Melkite Greek Catholic Church, have abbreviated the fast to start on December 10, following the Feast of the Conception by Saint Anne of the Most Holy Theotokos.

New calendarists

The new calendarists are those Eastern Orthodox churches that adopted the Revised Julian calendar, namely the Orthodox churches of Constantinople, Alexandria, Antioch, Bulgaria, Greece, Cyprus, Romania, Poland, Czech and Slovak Orthodox Church, Albania, the Estonian Apostolic Orthodox Church and most of the Orthodox Church in America. The term is used to distinguish them from those who use the "old calendar" (the Julian calendar), most of whom are in communion with the new calendarists, but a few of whom are not.(Clogg 2002, pp. 8-9)

Old Calendarists

An Old Calendarist is any Eastern Orthodox Christian who uses the historic Julian calendar (called the "Old Style Calendar", "Church Calendar" or "Old Calendar"), proposed by the Roman statesman Julius Caesar, and whose church body is not in communion with the Eastern Orthodox churches that use the New Calendar.

The "Old Calendarists" are to be distinguished from Eastern Orthodox Christians or Eastern Orthodox Church bodies which are on the Old Calendar. The latter use the historic Julian calendar cited above, but are in communion with the Eastern Orthodox Churches that use the New Calendar (the Revised Julian calendar). Thus, to be "Old Calendarist" or "Old Calendar" is not the same thing as being "on the Old Calendar". The Russian Orthodox Church, for instance, is not Old Calendarist (or Old Calendar), but it is on the Old Calendar. There are a great many Eastern Orthodox Christians who are (or who belong to Churches that are) on the Old Calendar, but far fewer in number are the Eastern Orthodox Christians who are Old Calendar or Old Calendarist. It also should not be confused with the Oriental Orthodox churches, all of which are either on the Old Calendar or use their own calendar, but who are not in communion with either the Old Calendarists or mainstream Eastern Orthodoxy, although they are currently engaged in ecumenical dialogue with the latter. Nevertheless, inside the Armenian Apostolic Church, the Armenian Patriarchate of Jerusalem uses the Old Calendar in contrast to rest of the Armenian Church, which adopted the Gregorian Calendar while no member of the Armenian churches are using today the Armenian calendar. The Indian Orthodox Church uses the Gregorian calendar along with their autonomous Syriac Orthodox counterparts in India, the Malankara Jacobite Syriac Orthodox Church, in contrast to the rest of the Syriac Church which uses its own calendar. The Ancient Church of the East (Julian Calendar) emerged as the result of a schism when Patriarch Shimun XXI Eshai introduced the Gregorian Calendar into the Assyrian Church of the East.

The Julian calendar, proposed by the pagan Roman general Julius Caesar, is commonly opposed to the Gregorian calendar introduced to Christianity by Pope Gregory XIII during the 16th century. An improved form of the Gregorian calendar, originally developed in 1785 and modified in 1923 by the Serbian astronomer Milutin Milanković, was first introduced by Greece for civil purposes only and later adopted by some Orthodox churches. In its present form it is known as the Revised Julian calendar and it will not diverge from the Gregorian until AD 2800 (see Greek Old Calendarists#History). A minority of Eastern Orthodox Christians regarded this as a surrender of the Eastern Orthodox Church to the Pope and continued following the old calendar. Some of these also broke communion with those who had adopted the new calendar, thus creating their own church, or denomination, which means in Latin "to take a new name".

This schism is the beginning of the Old Calendar Churches which suspended full communion or concelebration with other Eastern Orthodox churches ("New Calendarists") over the adoption by the latter of the Revised Julian calendar (called "New Calendar," although some churches did not specify the details of which New calendar they were adopting). This is the most common use of the term.

Those Orthodox Churches which remain in full communion with the New Calendarists and yet continue to use the Julian calendar include the Eastern Orthodox Patriarchate of Jerusalem, the Macedonian Orthodox Church, the Russian Orthodox Church, the Serbian Orthodox Church, and the Georgian Orthodox Church. (The Julian calendar is also used by the Russian Orthodox Church Outside of Russia which has reunited with the Russian Orthodox Church.) Mount Athos, subordinate to the Patriarchate of Constantinople, also follows the Julian calendar.

In recent years both Old Calendar congregations and monasteries, as well New Calendar congregations and monasteries inside the Churches on the Old Calendar have been accepted into the official churches maintaining their own Calendar. Even some Russian Old Believers groups have been accepted into the official Russian Church while keeping their own traditions.

Perpetual calendar

A perpetual calendar is a calendar valid for many years, usually designed to allow the calculation of the day of the week for a given date in the future.

For the Gregorian and Julian calendars, a perpetual calendar typically consists of one of two general variations:

14 one-year calendars, plus a table to show which one-year calendar is to be used for any given year. These one-year calendars divide evenly into two sets of seven calendars: seven for each common year (year that does not have a February 29) with each of the seven starting on a different day of the week, and seven for each leap year, again with each one starting on a different day of the week, totaling fourteen. (See Dominical letter for one common naming scheme for the 14 calendars.)

Seven (31-day) one-month calendars (or seven each of 28–31 day month lengths, for a total of 28) and one or more tables to show which calendar is used for any given month. Some perpetual calendars' tables slide against each other, so that aligning two scales with one another reveals the specific month calendar via a pointer or window mechanism.The seven calendars may be combined into one, either with 13 columns of which only seven are revealed, or with movable day-of-week names (as shown in the pocket perpetual calendar picture).

Note that such a perpetual calendar fails to indicate the dates of moveable feasts such as Easter, which are calculated based on a combination of events in the Tropical year and lunar cycles. These issues are dealt with in great detail in Computus.

An early example of a perpetual calendar for practical use is found in the manuscript GNM 3227a.

The calendar covers the period of 1390–1495 (on which grounds the manuscript is dated to c. 1389).

For each year of this period, it lists the number of weeks between Christmas day and Quinquagesima. This is the first known instance of a tabular form of perpetual calendar allowing the calculation of the moveable feasts that became popular during the 15th century.

Public holidays in Serbia

The public holidays in Serbia are defined by the Law of national and other holidays in the Republic of Serbia.

Reform of the date of Easter

A reform of the date of Easter has been proposed several times because the current system for determining the date of Easter is seen as presenting two significant problems:

Its date varies from year to year. It can fall on up to 35 different days in March and April of the respective calendar. While many Christians do not consider this to be a problem, it can cause frequent difficulties of co-ordination with civil calendars, for example academic terms. Many countries have public holidays around Easter weekend or tied to the date of Easter but spread from February to June, such as Shrove Tuesday or Ascension and Pentecost.

Many Eastern churches calculate the date of Easter using the Julian calendar, whereas some Eastern churches use the Revised Julian calendar and all Western churches and civil authorities have adopted the Gregorian reforms for all calendrical purposes. Hence in most years, Easter is celebrated on a later date in the East than in the West.There have been controversies about the "correct" date of Easter since antiquity, leading to schisms and excommunications or even executions due to heresy, but most Christian churches today agree on certain points. Easter should therefore be celebrated:

on a Sunday (according to the First Council of Nicaea in 325),

after the Northward equinox (around 20 March in the Gregorian calendar), that is in Northern Hemisphere spring,

after the nominal "Paschal" full moon.There is less agreement whether Easter also should occur:

so that Annunciation – usually celebrated 25 March, 9 months before Christmas – does not fall on any day from the Sunday before Easter to the Sunday after,

on or after the 14th day of the lunar month of Nisan,

not before Jewish Pesach. (Easter is after Christian Passover by definition.)The disagreements have been particularly about the determination of moon phases and the equinox, some still preferring astronomical observation from a certain location (usually Jerusalem, Alexandria, Rome or local), most others following nominal approximations of these in either the Hebrew, Julian or Gregorian calendar using different lookup tables and cycles in their algorithms.

Saint Menas

For the Florentine saint, see Minias of Florence.Saint Minas (also Meena, Mina, Menas, Mena, Menes, Mennas; Coptic: Ⲁⲃⲃⲁ Ⲙⲏⲛⲁ) (285 – c. 309), the Martyr and Wonder-worker, is one of the most well-known Coptic saints in the East and the West, due to the many miracles that are attributed to his intercession and prayers. Minas was an Coptic soldier in the Roman army martyred because he refused to recant his Christian faith. The common date of his commemoration is November 11, which occurs 13 days later (November 24) on the Julian calendar.

His feast day is celebrated every year on 15 Hathor in the Coptic Orthodox Church of Alexandria, which corresponds to November 24 on the Gregorian Calendar. In Eastern Orthodox Churches that follow the old style or Julian calendar, it is likewise celebrated on November 24. In the Eastern Orthodox Churches that follow the new style or Revised Julian calendar, as well as in the Catholic Church, it is celebrated on November 11.

Although Minas is recognized as a minor saint in Western churches, it is considered likely by many historians that he is celebrated in these churches under the name of Saint Christopher (i.e. the "Christ-bearer"), as one of the legends associated with Mina has him, like Christopher, carrying the Christ Child.

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