# Calculation of Orthodox Easter Sunday in the Julian calendar

Not only does the Orthodox Church use the old Julian calendar, but other chronological cycles of the year to calculate the calendar date for Easter Sunday (and Passover) as well. Of course, the final date of Easter Sunday coincides with the western calculation of Easter Sunday in the Julian calendar (see the page Calculating Easter Sunday in the Julian calendar). The principle of the calculation is the same: first, we calculate the date of the first spring ecclesiastical full moon, and then the following Sunday is Easter Sunday. In the following calculations, only integers (whole numbers) are counted, with the character '%' (modulo) indicating that only the remainder after division is sought (e.g. 23/5 = 4 and 23 % 5 = 3).

To start with, we need to convert the given year to the year in the Byzantine calendar (in English, this means “from the creation of the world”, while in Russian it’s лето от сотворения мира nebo i лето от Адама). According to the Orthodox Church, the world was created on 1 September, year 1 of the Byzantine era. Sometimes, two values for the Orthodox calendar year’s foundations are given, with some calendars listing home many days until 1 September (Julian calendar) and how many days since 1 September (in brackets). In the case of Easter, we’re only interested in the first value. The leap year system is the same as it is for the Julian calendar. The conversion to the Byzantine date is then made by simply adding the constant 5508 to our year:

creation_of_world = year + 5508

In year 1 of the Byzantine era, three Orthodox calendar cycles (Russian: круг Луны, круг Солнцу, индикт) had a value of 1. By simply dividing by the length of the selected cycle and finding the remainder after this division, we obtain the value of the cycle. If the resulting value is 0, then this 0 is adjusted to a value equal to the cycle length. The first cycle is the lunar cycle (Russian: Kруг Луны), which is the equivalent of our Golden Number with the same 19-year long duration. It only one needs to be shifted by three years, which makes for an easy calculation:

lunar_cycle = (creation_of_world - 1) % 19 + 1

For the sake of comparison, below is a table with the values of the Golden Number and the Kруг Луны. Unlike the Golden Number cycle, where the lunar leap (Latin: saltus lunae) is performed at the end of the cycle, the same leap (Russian: скачок Луны) is performed at the end of the 16th year of their lunar cycle. The table shows that although the monthly leap is performed at different values in both cycles, they are in fact, timed out the same.

 Golden Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Lunar cycle 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

From the value of the lunar cycle, we then calculate the foundation (Russian: основание), which indicates the age of the moon on 1 March. If the lunar cycle is larger than 16, a minor correction is required due to the monthly leap:

foundation = (11 × lunar_cycle + 3) % 30
if lunar_cycle is greater than 16, foundation = foundation + 1

If we already know the lunar phase on 1 March, by subtracting 30 from it, we get the March date of the New Moon (Russian: мартовское новолуние), and by adding 14 to that we’ll get the date of the half moon (Russian: мартовское полнолуние). From here, it’s necessary to apply a special rule: in order to compare the calculated phases of the Moon with the actual phases of the moon during the time of the Council of Nicaea, three more days need to be added. If what we get for the final date of the full moon (Russian: пасхальное полнолуние) is before 21 March (i.e. before the date declared by the church as the beginning of spring) we choose the next full moon, which can be obtained by simply adding the entire length of a lunation (30 days). Everything can be summarized in a fairly simple calculation:

ecclesiastical_full_moon = 47 - foundation
if the ecclesiastical_full_moon is less than 21, then ecclesiastical_full_moon = ecclesiastical_full_moon + 30

The result is the March date of the first spring ecclesiastical full moon. If the number exceeds 31, for example the number 33, then subtract 31 and set it as an April date (i.e. 2 April in this example). Another Orthodox foundation of the year is the epact (Russian: епакта), the value of which shows the March date that falls on the twentieth day of the lunar month (this coincides with the end of the Passover celebration). For example, if the lunar cycle (Orthodox counterpart to the Golden Number) is equal to 1, then the half moon is equal to 14, which will put the ecclesiastical new moon on 1 March, thus making the lunar cycle 14 days old. In 6 more days (7 March) the Moon will be 20 days old, which means that the epact has a value of 7. This Orthodox epact (do not confuse it with the Gregorian epact) is obtained from the half moon by simply taking 21 and subtracting the half moon date. If we get a number less than 1, we add 30. However, this epact is not needed for this calculation of Easter Sunday. The term “correct date” (Russian: исправная дата) is defined as the date in a given year before which Passover is not possible, can be found throughout the sources. In essence, it is the date of the ecclesiastical full moon plus one day.

Now we can make a simple table, for each value of the lunar cycle foundational elements in the Orthodox calculation. The half moon increases regularly by 11, and if the value is greater than 30 we subtract 30. After 16 years of the lunar cycle, a monthly leap is made (this is highlighted in the table) and the value of the half moon increases by 12. Similarly, the epact decreases again by 11 (for the monthly leap of 12), and if the result is less than 1, add 30.

Lunar cycle
(круг Луны)
foundation
(основание)
epact
(епакта)
ecclesiastical new moon
(пасхальное
новолуние)
114733
2252622
361541
417430
5282349
691238
720127
812046
912935
10232824
1141743
1215632
13262521
1471440
1518329
16292248
17111036
18222925
1931844

We already know the date for the first full moon of spring, but now it is necessary to find out when the next Sunday occurs. The equivalent of our solar cycle in the Orthodox calendar is the круг Солнцу, which also takes values from 1 to 28. Its calculation is rather simple:

solar_cycle = (creation_of_world - 1) % 28 + 1

Another Orthodox foundation for calculating its year is its 'vruceleto' (Russian: вруцелето), which determines which day of the week (день недели) falls on 1 September (the beginning of the Byzantine year). Its value is easily obtained using the following table:

vruceleto
(вруцелето)
Solar cycle
(круг Солнцу)
1171218
22131924
3381425
49152026
54102127
65111622
76172328

The value for vruceleto can also be obtained by a small calculation:

vruceleto = (solar_cycle + solar_cycle / 4 - 1) % 7 + 1

Instead of a number, the first letters (Russian: буква) of the Cyrillic alphabet (азбука) were most frequently used. Often a word was added to the letter, all in accordance with the following table:

vruceleto
(вруцелето)
letter
(буква)
1st of September
1А (аз)Sunday
2В (веди)Monday
3Г (глаголь)Tuesday
4Д (добро)Wednesday
5Е (есть)Thursday
6S (зело)Friday
7З (земля)Saturday

By following along with this calculation, we’ll find the day in March, when the first Sunday of the month, or the 'first resurrection' (Russian: первое воскресение), occurs:

if vruceleto is less than 4 first_resurrection = 4 - vruceleto
otherwise, first_resurrection = 11 - vruceleto

The result is shown in this small table:

vruceleto
(вруцелето)
first resurrection
(первое воскресенье)
13rd of March
22nd of March
31st of March
47th of March
56th of March
65th of March
74th of March

Finally, the last calculation finds the next Sunday after the first spring ecclesiastical full moon. This is a March date, so if the result is greater than 31, it is April, and in order to obtain the April date, it’s necessary to subtract from the result 31. This Sunday is what we’ve been looking for all along, and gives us Orthodox Easter Sunday (Russian: Христианская Пасха):

passover = ecclesiastical_full_moon + 7 - (ecclesiastical_full_moon - first_resurrection) % 7
if we get a number greater than 31, it’s an April date and it’is necessary to subtract 31; otherwise it’s a March date

In printed calendars, instead of the calendar date for Orthodox Easter Sunday, the 'boundary key' (Russian: ключ границ) was mentioned. It shows how many days from 21 March that Easter Sunday is. This number can take values from 1 to 35. The earliest date is Easter Sunday on 22 March, while at the value of 35, we have the latest possible date for Easter as 25 April. Each number is assigned a letter according to the table:

 1 (А) March 22 2 (Б) March 23 3 (В) March 24 4 (Г) March 25 5 (Д) March 26 6 (Е) March 27 7 (Ж) March 28 8 (Ѕ) March 29 9 (З) March 30 10 (И) March 31 11 (І) Apr 1 12 (К) Apr 2 13 (Л) Apr 3 14 (М) Apr 4 15 (Н) Apr 5 16 (О) Apr 6 17 (П) Apr 7 18 (Р) Apr 8 19 (С) Apr 9 20 (Т) Apr 10 21 (У) Apr 11 22 (Ф) Apr 12 23 (Х) Apr 13 24 (Ѿ) Apr 14 25 (Ц) Apr 15 26 (Ч) Apr 16 27 (Ш) Apr 17 28 (Щ) Apr 18 22 (Ф) Apr 12 29 (Ъ) Apr 19 30 (Ы) Apr 20 31 (Ь) Apr 21 32 (Ѣ) Apr 22 33 (Ю) Apr 23 34 (Ѫ) Apr 24 35 (Ѧ) Apr 25

Note: in some calendars, the “indiction” (Russian: индикт) was sometimes displayed, the value of which is always the same as the Western indiction. However, Easter Sunday has nothing to do with the calculation. Do not confuse this Western indiction with the term “large indiction” (Russian: великий индиктион or миротворный круг), or even more rarely as круг великой альфы), which is a cycle of 532 years. After this length of time, the calendar dates for Passover are repeated in the Julian calendar, and in the same order. In the Julian calendar, the calendar dates are repeated in the same order after 28 years (7 × 4, 7 days a week, and on every fourth year leap), which is a non-consecutive number with 19 values ​​of the lunar cycle. It is from this that we calculate the large indiction as 28 × 19 = 532. We are currently in the fifteenth cycle since year 1 of the Byzantine era. This cycle began in 1941 AD and ends in 2472 AD.

The above calculations and tables apply only to the old Julian calendar!