The epacts (from the Greek epaktai hèmerai "added days") - in the narrower sense the annual pacts - is an indicator used in the Julian and Gregorian calendars for the calendar year. In the Gregorian calendar it is the number of days from the last new light of the moon in the old year to January 1st of the new year, or the age ( moon age ) of the moon, which began in December, on December 31st. The epact is assigned to the new year as a key figure. In the Julian calendar and according to Beda Venerabilis († 735; De Temporum Ratione , 725), the Julian epact is defined as the age of the moon on March 22nd (i.e. April 11th ).
Epacts and Meton cycle
The use and calculation of the epacts are based on the positioning of the calendar lunar months within a calendar year based on the solar year with the help of the 19-year Meton cycle . The similar length of 19 solar years and 235 lunar months is used . In the Julian calendar, the small error contained in the Meton cycle has been neglected. Only 19 epacts were received (so-called Julian epacts ); the epact of the 20th year was again the same as that of the first year, and so on.
The epacts of the Julian calendar year has the following simple connection with its golden number GZ:
Epacts = ((GZ - 1) · 11) Mod 30.
Just as there are only 19 golden numbers, the calculation only leads to 19 different Julian epacts.
In the Gregorian calendar, the epacts are referred to as the Lilian epacts (after Aloisius and Antonius Lilius , scientific adviser to Pope Gregory XIII and spiritual author of the Gregorian calendar reform ). In them the small error of the Meton cycle and the somewhat too long length of the Julian calendar year are occasionally corrected (at the earliest after 100 years). The lunar calendar dates are shifted one day to earlier or later (in total to later). Over a long period of time, 30 different epacts are obtained, as many as a calendar lunar month has a maximum of 30 days. The so-called Gregorian epacts as groups of 19 epacts (corresponds to the Julian epacts) are always unchangeable for at least 100 years before they are shifted together by one unit. In sum, the epact shift causes a decrease in their values and the age of the moon. If the value falls below zero, 30 units are added (adding a leap lunar month), and the epact becomes 29.
The epacts of the Gregorian calendar year is not only related to its golden number GZ in the following, in comparison to that of the Julian calendar year more complex:
Epacts = (27 + 11 · GZ - century value + Int (century value / 4) + Int (century value / 3) ) Mod 30
The two integer components contain the Gregorian corrections mentioned above:
Sun equation : - Century value + Int (century
value / 4) Moon equation : Int (century value / 3).
The century value is understood here as the first two digits of the century, i.e. Int (year / 100). The equation is simplified with respect to the lunar equation and is therefore only valid until AD 4199.
Epacts and Easter calculation
The epacts were used very early on, but never had the meaning they have had since the Gregorian calendar reform. In the Julian calendar, there was a fixed relationship between the epact or the age of the moon and the golden number - the primarily important parameter of the calendar year whose Easter date is to be determined.
An additional parameter is only necessary in the Gregorian calendar, because in it the date of the spring full moon - it is followed by Easter Sunday - is no longer linked to the golden number. Therefore, the year is advantageously also marked with the epact. The advantage takes effect after applying the lunar or solar equation in secular years, whereby the relationship changes. In years with the same golden number, the value of the epacts is now 1 higher (lunar equation) or 1 lower (solar equation). The technical term is: epact shift by 1.
The age of a full moon is 14 days (counting from the new light). If there is a full moon on December 31, the following year is assigned epact 14, and March 30 of this year is again full moon (March 30 is three cyclical lunar months with 30, 29 and 30 days later than December 31). For example, epact 14 was in 2010.
Epacts and spring
full moon dates for the years 2008 to 2017: Year 2008 • Epacts = 22 • Full moon on March 22nd (March 30th plus (14-22) days)
Year 2009 • Epacts = 3 • Full moon on April 10th (30th. March plus (14-3) days)
year 2010 • epacts = 14 • full moon on March 30th (March 30th plus (14-14) days)
year 2011 • epacts = 25 • full moon on April 18th (March 30th plus (14-25 + 30) days)
Year 2012 • Epacts = 6 • Full moon on April 7th (March 30th plus (14-6) days)
Year 2013 • Epacts = 17 • Full moon on March 27th (March 30th plus (14-17) days)
year 2014 • epacts = 29 • full moon on April 14th (March 30th plus (14-29 + 30) days)
year 2015 • epacts = 10 • full moon on April 3rd (March 30th plus (14-10) days)
Year 2016 • Epacts = 21 • Full moon on March 23 (March 30 plus (14-21) days)
Year 2017 • Epacts = 2 • Full moon on April 11 (March 30 plus (14 -2 days)
- Conversion between the Julian and Gregorian calendar
- Conversion between the Julian date and the Gregorian calendar
- Joseph Bach: The Easter calculation in old and new times. Buchdruckerei des “Elsässer”, Strasbourg 1907 ( scientific supplement to the annual reports of the Bischöflichen Gymnasium Strasbourg ,  ), p. 36, 2nd paragraph: “These epacts tell us how old the moon is at the end of a solar year , so it is at the beginning of the following year. They are therefore referred to as the epacts or moon ages of the following year. "
- Online calculation program by Nikolaus A. Bär: Calculation of the golden number and the epacts 
- also Alexandrian epacts , see Joseph Bach: The calculation of Easter in old and new times. Table with golden numbers and epacts 
- Hanns J. Prem : Manual de la antigua cronología mexicana. Ciesas, México, 2008, ISBN 978-968-496-694-9 , p. 38
- Hanns J. Prem : Manual de la antigua cronología mexicana. Ciesas, México, 2008, ISBN 978-968-496-694-9 , p. 52
An exact solution, at least from the annus correctionis 1582, is provided by the formula
Epakte = 2 + 11 · GZ + century value - Int (century value / 4) + Int ((century value -14) / 25) · 8 + Int ( maximum (((century value -14) Mod 25 ) -1.0) / 3).
- Nikolaus A. Bär: Die Epakten der Alexandriner  and Die Epakten des Beda 
- Nikolaus A. Bär: The Epacts of Lilius