# Paschalion

The **Paschalion** of the Orthodox Church combines the metonic and solar calendrical cycles to determine the date of Pascha for a given year. A common formula to determine the date of Pascha was created in connection with the First Ecumenical Council, held at Nicea in 325 A.D.

## Contents |

## The Nicene Formula

From 326 A.D. (the first year following the Council), Pascha has been officially defined as the first Sunday following the date of the Paschal Full Moon ("PFM") for a given year. The PFM is not, however, as commonly thought, the first full moon following the vernal equinox. Rather, the PFM is the first Ecclesiastical Full Moon ("EFM") date that follows March 20. Ecclesiastical Full Moons are calendar dates that approximate of astronomical full moons using a cycle that repeats every 19 years. March 20 is the date used for determining the PFM because it was the near the date of the vernal equinox in the early 4th century A.D., when the Paschal cycle was being developed.

Because of the inaccuracy of the Julian Calendar, Pascha is drifting later into the year for those who use the Julian Paschalion. Thus, while according to the calendar, for those using the Julian Calendar Pascha will always be sometime in March or April, it will eventually be celebrated in the northern hemisphere in the summer, the autumn, and then the winter. (For those using the Revised Julian Calendar, the calendar date of Pascha is drifting along with its astronomical position.) Additionally the Julian Ecclesiastical Full Moons are deviating further with time from the astronomical full moons: The EFM now falls 3 to 5 days after the corresponding astronomical full moon. The Gregorian Calendar, which includes its own revised Paschalion, has neither of these problems.

## The Gregorian Reform

In October 1582, the Roman Catholic Church adopted a major calendar reform designed to correct for the 10-day drift in the vernal equinox since the First Ecumenical Council. The Julian calendar then in common use was based on an average year of 365.25 days, slightly longer than the mean tropical year of 365.24219 days and the mean vernal equinox year of 365.2424 days.

The new calendar was called the Gregorian after its sponsor, Pope Gregory XIII. The reform also introduced refinements to the calculation of Pascha.

## The Rejected Proposal of 1923

A congress of Orthodox bishops meeting in 1923 under the presidency of Patriarch Meletios IV agreed to set Pascha by means of precise astronomical computations referred to the meridian of Jerusalem.[1] This proposal was, however, never implemented in any Orthodox diocese.

## East and West Today

The Roman Catholic and Protestant West eventually adopted the Gregorian Calendar for civil and ecclesiastical purposes, including the determination of Pascha. The Orthodox East, however, was not so quick to change. Even when the traditionally Orthodox countries began to adopt the Gregorian Calendar for civil purposes, the Orthodox Church retained the Julian Calendar and original Paschalion. For the sake of convenience, the date of Pascha is often transposed to the coincident date on the Gregorian Calendar for reference.

Because of the difference in calendars and formulas, Western Easter and Orthodox Pascha do not often coincide. Under current rules, they can differ from each other by 0, 1, 4, or 5 weeks. They are in separate lunations (meaning that they 4 or 5 weeks apart because their respective cycles identify different lunar months as the Paschal lunar month) in years 3, 8, 11, 14, and 19 of the 19-year cycle, and in the same lunation (0 or 1 week apart) in the other years.

## Algorithms

Many notable mathematicians have developed algorithms for determining the date of Orthodox Pascha over the centuries. This simple and elegant one was devised by the brilliant mathematician Jacques Oudin in the 1940s:

*N.B. -- In this formula MOD is the modulus function, in which the first number is divided by the second and only the remainder is returned. Further, all division is integer division, in which remainders are discarded. Thus* **22 MOD 7 = 1***but* **22 / 7 = 3**.

G =yearMOD 19 I = ((19 * G) + 15) MOD 30 J = (year+ (year/4) + I) MOD 7 L = I - J Easter Month = 3 + ((L + 40)/44) Easter Day = L + 28 - 31 * (Easter Month/4)

`Easter Month will be a number corresponding to a calendar month (e.g., 4 = April) and Easter Day will be the day of that month. Note that this returns the date of Pascha on the Julian calendar. To get the corresponding date on the Gregorian calendar, add 13 days (14 days after March 1, 2100).
`

## Online Paschalion Utility

You can find the date of Pascha and many Pascha-dependent dates (e.g., the start of Great Lent, Pentecost, etc.) through this online JavaScript Paschalion utility (works best with IE3 or Netscape 3 or above).

This site allows the user to enter a year and uses Oudin's algorithm to compute the relevant dates. Although the Orthodox (Julian-based) formulas are used, the utility returns the corresponding Gregorian calendar dates. For example, in 2006 Pascha falls on Sunday, April 10, on the Julian calendar. That date corresponds to April 23 on the Gregorian calendar.

A perpetual Paschalion utility is available here. The utility was created by Aleksandr Andreev of Duke University and calculates Pascha and associated feasts for any series of years. It also calculates the numbers used in Paschal calculations which can be found in an Orthodox Typicon.

## References

1. M. Milankovitch, "Das Ende des julianischen Kalenders und der neue Kalender der orientalischen Kirchen", *Astronomische Nachrichten* 220, 379-384(1924).

## See also

## External links

- Concerning the Date of Pascha and the 1st Ecumenical Council, by Archbishop Peter (L'Huillier) of New York
- The Calendar Issue in the Orthodox Church, by John Parsells (PDF)
- Frequently Asked Questions about Calendars by Claus Tondering (everything you ever wanted to know)
- Calendar and Easter Topics