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Understanding > Astronomical calculations > Calendars VIII


The Computus

  YEAR (between 325 and 2500) :  





The computus is used to set the time for ecclesiastical purposes, in particular to calculate the date of Easter. 


The current definition of the date of Easter is that defined in 325 at the Council of Nicaea. "Easter is the Sunday following the fourteenth day of the Moon reaching this age on March 21 or immediately after". The fourteenth day of the Moon being the day of the full moon and March 21 being the date of the spring equinox, this definition is often translated as follows: Easter is the first Sunday following the first full Moon of Spring. This second definition is misleading because it suggests that the date of Easter is the result of an astronomical calculations based on the determination of the Spring equinox and of the first full moon after the equinox. In reality it is not so, the calculation of the date of Easter is done with a perpetual calendar using a fictitious average Moon (Ecclesiastical Moon ). This method of calculation is named Ecclesiastical Computus .
There are two ecclesiastical computus: the Julian one in use until 1582 and the Gregorian one in use since 1583. The Gregorian computus corrects imperfections the Julian computus. The Julian computus has two elements: the dominical letter and the golden numberr. The Gregorian computus has also two elements: the dominical letter and the epact. Sometimes it also provides for the Julian computus an epact (the Julian epact) directly related to the golden number.
More generally, we named Julian Easter the date of Easter calculated with the Julian computus and Gregorian Easterthe date of Easter calculated with the Gregorian computus. 


- dominical letter : from January 1, one associates to the days of the year the 7 letters A,B,C,D,E,F,G, followed by A,B,C, and so on... In the case of leap years this association is made in two steps: until February 29, which is associated to letter D, and from March 1, which is also associated to letter D. The dominical letter is the one associated to the Sundays. For leap years, there will be two dominical letters for the year, the first one valid until February 29 and the second one valid from March 1. 
- Epact :  during the Middle Age, in the Julian computus, before the Gregorian reform of the calculation of the date of Easter, the julian epact is the age of the Moon at eve of Januarty 1 (December 31); in the Gregorian computus, so after the Gregorian reform of 1582, the epact is the age of the Moon on January 1, minus one unit. It is this definition which is used in the results above.
The age of the Moon is equal to one for each new moon. In these computus, let us remind that it is not the true Moon which is used but a fictitious average Moon named the Ecclesiastical Moon.
- Solar cycle (1 to 28) : rank of the year in a 28-year cycle, (coming back of the days of the week at the same dates in the Julian calendar). 
- Golden number (1 to 19) : rank of the year in the Meton cycle of 235 lunations. The Golden number is used in the Julian computus of the calculation of the Easter date and it is replaced by the epactin the Gregorian computus. 
- Roman indiction (1 to 15) : rank of the year in a 15-year cycle, without any astronomical meaning, this element is not used in the calculation of the Easter date. 


For years prior to the Gregorian reform, is given: the Julian date of Easter in the Julian calendar, then the date of Passover in the Jewish calendar and in the Julian calendar.
For post-reform years (after 1582): we give the date of Gregorian Easter in the Gregorian calendar, it is the date used by the Catholic Church since 1583, and the date of the Julian Easter, in the Julian calendar and in the Gregorian calendar, this date is still used today by some Orthodox churches and finally the date of Passover in the Jewish calendar and in the Gregorian calendar.


This program calculates the dates of Easter from the year 325, when the definition of the date of Easter was defined by the Council of Nicaea. It uses the ecclesiastical computus developed by Dionysius Exiguus in the year 525 AD. This computus is based on a fictitious average Moon following the Metonic cycle. In this computus, we find the same dates of Easter every 532 years (19 x 28 product of the Metonic cycle by the solar cycle). This computus has been used uniformly by the entire Christian community only from the second half of the eighteen century. The values ​​found for the years prior to this time are purely indicative and can depend on the different regions and on the considered Christian communities, in disagreement with the actual dates celebrations.
Same, the Jewish calendar in its current form dates of the end of IVth century, but it has actually been in use throughout the Jewish community only many centuries after its creation (about the VIIIth century). So the results obtained for the years prior to this time are purely indicative.

For historical data for these periods one should consult historical sources and not just the results provided by this program.

Credit : P. Rocher/G. Satre/IMCCE/CNRS

click here to have more explanations about the determination of the Easter date.