# Paschalion

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[[Image:Pascha.jpg|right|Great and Holy Pascha]] | [[Image:Pascha.jpg|right|Great and Holy Pascha]] | ||

− | The '''Paschalion''' of the [[Orthodox Church]] combines the metonic | + | 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. |

== The Nicene Formula == | == The Nicene Formula == | ||

− | From | + | 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. EFMs are calendar dates that approximate the cycle of astronomical full moons (usually falling within 1-3 days of an astronomical full moon), which repeats every 19 years. March 20 is the date used for determining the PFM because it was the vernal equinox in 325 A.D., the year the EFM cycle was determined by astronomers. |

== The Gregorian Reform == | == 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 | + | 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 actual solar mean year of 365.24219 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 new calendar was called the Gregorian after its sponsor, Pope Gregory XIII. The reform also introduced refinements to the calculation of Pascha. | ||

== East and West Today == | == East and West Today == | ||

− | The Roman Catholic and Protestant West eventually adopted the Gregorian Calendar for civil | + | 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 | + | Because of the difference in calendars and formulas, Western Easter and Orthodox Pascha do not often coincide. Generally, Orthodox Pascha follows Western Easter by between 1 and 5 weeks. |

== Algorithms == | == Algorithms == | ||

− | Many notable mathematicians have developed algorithms for determining the date of Orthodox Pascha over the centuries. This simple | + | 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 | + | ''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'' <tt>'''22 MOD 7 = 1'''</tt> ''but'' <tt>'''22 / 7 = 3'''. |

− | G = ''year'' MOD | + | G = ''year'' MOD 19 |

+ | I = ((19 * G) + 15) MOD 30 | ||

+ | J = (''year'' + (''year''/4) + I) MOD 7 | ||

+ | L = I - J | ||

Easter Month = 3 + ((L + 40)/44) | Easter Month = 3 + ((L + 40)/44) | ||

− | Easter Day = L + | + | Easter Day = L + 28 - 31 * (Easter Month/4) |

− | + | </tt>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 == | == 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 [http://www.websamba.com/dismissal/paschalion.htm Paschalion utility] (works best with IE3 or Netscape | + | 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 [http://www.websamba.com/dismissal/paschalion.htm Paschalion utility] (works best with IE3 or Netscape 3 or above). |

− | This site allows the user to enter | + | 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 2005 Pascha falls on Sunday, April 18, on the Julian calendar. That date corresponds to May 1 on the Gregorian calendar. |

== External Links == | == External Links == |

## Revision as of 05:09, April 21, 2005

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. EFMs are calendar dates that approximate the cycle of astronomical full moons (usually falling within 1-3 days of an astronomical full moon), which repeats every 19 years. March 20 is the date used for determining the PFM because it was the vernal equinox in 325 A.D., the year the EFM cycle was determined by astronomers.

## 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 actual solar mean year of 365.24219 days.

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

## 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. Generally, Orthodox Pascha follows Western Easter by between 1 and 5 weeks.

## 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 2005 Pascha falls on Sunday, April 18, on the Julian calendar. That date corresponds to May 1 on the Gregorian calendar.

## External Links

- Frequently Asked Questions about Calendars by Claus Tondering (everything you ever wanted to know)
- Calendar and Easter Topics
- The Calendar Issue in the Orthodox Church, by John Parsells (PDF)