Table of Contents

• Introduction
• Lunisolar cycles
• Old Roman Calendar
• Julian calendar
• The Council of Nicaea in 325
• The Roman Dating System
• Calendar eras
• Different beginnings for the new year
• The Martyrology
• Dies caniculares
• Dies egyptiaci
• Gregorian calendar reform
• Reception of the Gregorian Calendar
• When Easter is celebrated
• Calculation of Easter Sunday in the Julian calendar
• Calculation of Orthodox Easter Sunday in the Julian calendar
• Calculation of Easter Sunday in the Gregorian calendar
• Calculation of Easter Sunday online
• Calendarium gregorianum
• Table of dates for the Easter holidays
• Distribution of Easter Sundays in the Gregorian Calendar
• Graph distribution of Easter Sunday depending on the epact
• The difference between Easter Sunday in the Julian and Gregorian calendars
• The Easter Paradox
• Chronological Cycles
• Golden number
• Epacts
• Solar cycle
• Dominical letter
• Indiction
• Gaussian algorithm for calculating Easter Sunday
• Carter's algorithm for calculating Easter Sunday
• Tabula Paschalis Nova Reformata
• Tabula Noviluniorum
• French Republican calendar

Solar cycle

To calculate Easter in the Julian calendar, it is first necessary to know the dates on which Sunday would fall in a given year. To do this, a solar cycle (Latin: circulus solaris, cyclus solaris) needs to be constructed. This solar cycle is composed of a continuously numbered series of 28 years, where all the years that form an identical match in week order are marked. In short, if two years start and end on different days of the week, they are not perfect matches. Now, this can only be done with the Julian calendar, not the Gregorian calendar, due to the inaccessibility of its centenary years—because of this, it’s pointless to use a solar cycle on a Gregorian calendar.

An ordinary year has 52 weeks, and an extra day if the year began on a Monday. It then follows that the next year begins on a Tuesday, and so on, and so forth. In this way, seven years would be enough calendar dates to cycle back to the same day of the week. However, by inserting leap years every fourth year (as in the Julian calendar), the date of the new week’s start is shifted by two days in the following year. Ultimately, this causes the whole cycle to last even longer, bringing the length up to 28 years (7 × 4).

Each value of the solar cycle in the Julian calendar can be assigned a Dominical letter—once again, in the Gregorian calendar this does not apply.

The beginning of the first cycle was set to the year 9 BC (which was supposed to be a leap year), because it began on a Monday. The French classicist, Josephus Justus Scaliger, asserted that the beginning of the first cycle was the year 328, which was the first leap year after the Council of Nicaea. Bear in mind that only integers are counted; the '%' character (modulo) indicates that the modulo, or the remainder, is the only thing we’re interested in. In this case, the remainder can be as large as 27.

Below you can find a table of solar cycle values ​​from the Year 0 (according to astronomical years) on to 5599. It is quite easy to use. Simply find the century in the column and the year in the row. The number you’re looking for will be at the intersection. So, for example, if we are interested in finding the value of the solar cycle for the year 1348, we’d find 1300 in the column and 48 in the row, then follow each to their intersection. In this example, the solar year for 1348 is 13.