This was first published on the WWW 1995 June 25 by Marcos J. Montes.
This version was created 2001 July 31 by Marcos J. Montes.
Reviewed in Rettig on Reference Newsletter for October, 1995.
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Calculation of the
Ecclesiastical Calendar

Resources and Acknowledgements | Links to this page | Related Links | DISCLAIMER
Please enter a year after A.D. 325 (see text below).
Ecclesiastical Calendar for which year: A.D.
Orthodox - New Calendarists
Orthodox - Old Calendarists
Western
Here is a list of Orthodox Easter dates listed in the Julian Calendar or the Gregorian Calendar, 1875-2124.
Here is a list of Western Easter dates AD 1875-2124.
Here is a list of years with the same Julian date or Gregorian date of Orthodox Easter, AD 1875-2124.
Here is a list of years with the same date of Western Easter, AD 1875-2124.
Here is a Table of the frequency of the difference between the dates of Orthodox and Western Easter, AD 1583 to AD 3000.

Introduction

This program calculates: I have summarized some information on the Orthodox Ecclesiastical Calendar and an algorithm by Gauss to calculate the date of the Orthodox Easter.

Easter Calculations

History

Prior to AD325, churches in different regions celebrated Easter on different dates, not always on Sundays. The Council of Nicea (AD 325) clarified this a bit by stating that Easter would be celebrated on Sundays. Still a number of methods were used until a method defined by Dionyisius Exiguus was adopted in about AD 532. This was not widely accepted until it was described and defended by the Venerable Bede in his De temporum ratione (AD 725). [Thanks to Jim Morrison (70451.2106@compuserve.com) for the previous four sentences.]

Aloisius Lilius (d. 1576) devised the system that would become the basis of the Gregorian Calendar, as well as the tables that would be used to determine the date of Easter. Christoph Clavius modified the tables slightly, and was one of the prime defenders of the Gregorian calendar. The tables used to determine the date of Easter (in the West) since AD 1583 are these modified tables of Clavius. All algorithms for calculating the date of Easter since then are based on these tables.

Easter is the Sunday after the Paschal Full Moon. The Paschal Full Moon may occur from March 21 through April 18, inclusive. Thus the date of Easter is from March 22 through April 25, inclusive. The date of the Paschal full moon is determined from tables, and it may differ from the date of the the actual full moon by up to two days. This definition, along with tables, etc. may be found in "The Explanatory Supplement to the Astronomical Ephemeris and American Ephemeris and Nautical Almanac". This definition that uses tables instead of actual observations of the full moon is useful and necessary since the the full moon may occur on different (local, not UT) dates depending where you are in the world. If the date of Easter was based on local observations, then it would be possible for different parts of the world to celebrate Easter on different dates in the same year.

To further confuse the issue, many countries did not start using the Gregorian calendar in October 1582, so Easter in those countries was celebrated at times different than is listed here UNTIL they began using the Gregorian calendar. And some countries that switched to the Gregorian calendar used a different definition of Easter for some time (parts of Germany and Sweden used tables based on the observations of Tycho Brahe to determine Easter for many years after the Gregorian calendar was adopted in those locations). A reasonably comprehensive list of when nations started to use the Gregorian Calendar may be found in reference (1) and in the Calendar FAQ.

An interesting upshot of the algorithm is that the cycle of Easter dates (in the Gregorian Calendar) repeats every 5,700,000 years - and no sooner! (See the Calendar FAQ for why the period has this particular length.) Using the algorithms, I have calculated the distribution of the Gregorian Easter dates over various periods of time. You may view the frequency of the date of Easter over one complete 5,700,000 year cycle, or over the first complete 400 year Gregorian Calendar cycle, or over a more contemporary timespan of 1875 to 2124.

Algorithms

The algorithm used to calculate the date of Easter in the Western tradition (after 1582) is from Practical Astronomy with your Calculator by Peter Duffett-Smith and he got it from "Butcher's Ecclesiastical Calendar" (1876); apparently the algorithm was first published anonomously in Nature in 1876. This particular algorithm uses just integer math. The algorithm is valid for all years in the Gregorian calendar, that is October 1582 and onwards. Carter's algorithm is a more simple method for calculating the date of Easter and it is valid only from 1900 until 2099. Doggett's modification of Oudin's algorithm is easy to use and is valid after AD 1583. Mallen's method is another general, easy to use method. Some published methods do not for work for all years, and the method at this link from the 11th Edition Encyclopedia Brittanica unfortunately fails in some cases. There is a useful collection of articles gleaned from the soc.religion.christian newsgroup discussions that contains some history, as well as explanation of the algorithms used by both the Orthodox and Western churches that has been collected as an Easter-Date FAQ; it has both some C code and an amazing Bourne shell script for calculating the date of Easter. Finally, there is a simple algorithm due to Gauss for calculating the date of the Orthodox Easter.

A few other useful algorithms are also listed on my American Secular Holidays Page. This includes algorithms for determining dates such as "The Second Sunday in May".

Future Validity of All Algorithms of Determining the Date of Easter

There are many reasons to expect that all methods of determining the date of Easter will not be valid in the far future. The prime physical reason is that the length of the day is increasing, thus the number of days in a year is slowly decreasing. The current rate of increase in the length of the day implies that the Gregorian calendar will need to neglect a leap year sometime in the 4th or 5th millenium.

A greater likelihood is that some time in the near future the date of Easter may be fixed to a particular Sunday. At Vatican II, Pope John XXIII stated that there was nothing wrong with fixing the date of Easter. And there seems to be broad support in the World Council of Churches for a fixed celebration of Easter. According to the Encyclopaedeia Brittanica, the second Sunday in April is the most favored date. Fixing the date of Easter to a particular Sunday would still mean that Easter and the Feasts related to it would be movable, but the movement would be restricted to a span of seven dates (for example, the second Sunday in April must fall between April 8th-14th). Most of the discussion on this issue appears to have happened in the 1960's-1970's, but there is a press release from the Aleppo meeting of the World Council of Churches that discusses new proposals for fixing the date of Easter for all of Chrisitianity. The press release is dated 1997 March 24, and the basic suggestion is to use astronomical measurements of the vernal equinox and the full moon at the meridian of Jerusalem in order to determine the date of Easter. The authors of the proposal wanted this method to be adopted in the year 2001. Currently no Church has adopted this proposal. Please visit William Morris' New Easter Dates website for a comparison of Easter dates in the Gregorian and Orthodox Calendars, along withdates calculated using the Aleppo proposal, and dates calculated as the Sunday after Passover.

Feasts Related to Easter

Of interest from the reference (1) (which is a pre-Vatican II source!) are the following dates, and their relation to Easter. 

           Days Before Easter                       Days after Easter
Septuagesima         63            Rogation Sunday         35
Quinquagesima        49            Ascension               39
Ash Wednesday        46            Pentecost               49
Palm Sunday           7            Trinity Sunday          56
Good Friday           2            Corpus Christi          60
Matthew Bear (mtbear@mit.edu) was the first to inform me that Septuagesima, and Quinquagesima were in a pre-Lent season prior to Vatican II (in the Catholic church) or the 1970's (various Protestant denominations); Rogation Sunday was the Sunday before the Rogation (prayer, supplication) days before Ascension. Alex Kochergin writes that in the Eastern Orthodox perspective, Septuagesima and Quinquagesima are still celebrated- in fact, the three Sundays of Pre-Lent before Lent starts have as their Gospel Readings: the Parable of the Publican and the Pharisee, the Parable of the Prodigal Son, and Christ's reminder of the Last Judgement.

Celebrations in the Ecclesiastical Calendar Not Related to Easter

Once we have determined a date of the year and a day of the week, we can fix each date of the year to a day of the week. While my algorithm uses Easter to do this, general algorithms exist that allow the determination of the day of the week for a particular year (see the Calendar FAQ). Sundays in Advent are determined in the following straightforward method. First, the feast of Christ the King is the Sunday on or after 20 November; the First Sunday of Advent is the Sunday on or after 27 Nov.; the Second Sunday of Advent is on or after 4 Dec.; the 3rd Sunday of Advent is on or after 11 Dec.; finally, the 4th Sunday of Advent is on or after 18 Dec. The day of the week that Christmas falls on can then be easily determined.

Other Feasts that are listed by the Ecclesiastical Calendar are: The Solemnity of Mary on 1 January; Epiphany on 6 January (traditional) or the 2nd Sunday after Christmas; The Presentation of the Lord on 2 February; The Annunciation usually on 25 March; The Transfiguration of the Lord on 6 August; The Assumption of Mary on 15 August; The Birth of Virgin Mary on 8 September; The Celebration of the Holy Cross on 14 September; The Mass of the Archangels on 29 September; and All Saints' and All Souls' on 1 November and 2 November, respectively.

I still have limited the determination of these feasts to dates in the Gregorian Calendar. It is not impossible to calculate feasts for dates before then - I just have not done it. In addition, until recently some of the celebrations I list may not have been standard, defined, or celebrated on the dates currently listed. (In particular, some of the celebrations may have been celebrated on different dates before Vatican II).

Resources, Acknowledgements, and Further Reading

Folks providing links to this page (incomplete)

This list is extremely incomplete and seriously out of date. Many people have links to my pages now, and it would take up an inordinate amount of space to list all of them. I keep this section since it lists the first folks that I know about that provided links to this hierarchy of pages. Thanks to everyone who provides links to this page.

Related Links

Disclaimer

The views and writings presented here are my own, and are NOT the responsibility of Smart Net.

I have consulted many sources, and I believe that the work I have presented is correct. However, since sometimes hardware and/or software misbehave in subtle ways, and since I may, on occassion, mistype, or even accidentally use wrong or mistaken sources, the following disclaimer applies to all the pages in this hierarchy:
IF YOU ARE USING THESE DATES TO PLAN TRAVEL, MEETINGS, OR FOR ANY USE REQUIRING THE EXPENDITURE OF MONEY, TIME, OR OTHER RESOURCES, PLEASE CONSULT OTHER SOURCES TO VERIFY THE DATES OF THE VARIOUS HOLIDAYS. Neither Marcos Montes nor anyone who owns the hardware or manages the host machines of this home page, nor anyone who has contributed any information that I have used on these pages, may be held financially responsible, or responsible in any way, if these dates are wrong. The user assumes full responsibilty for the consequences of using this information.

Top | Resources and Acknowledgements | Some links to this page | Related Links | DISCLAIMER
Last updated 2001 July 31.
Copyright © 1996-2001 by Marcos J. Montes.
Marcos J. Montes
My American Calendar Page.
mmontes@no.spam.smart.net