# Easter dating calculator

Contents:

There are three steps to calculating the Easter Sunday date: If you're looking further into the future, click here to see another Table A for years to A. The result is March 21, A. For example, year gave us a PFM date of March 21, and step 2 gave us a total result of 6. This accurate procedure applies to Orthodox churches, which always base their calculations on the Julian calendar and the "19 PFM dates" table. It applies from the year A. This is the current situation in These instructions show the procedure for years to A. However, this simple method continues indefinitely, because the Julian calendar always has a February 29 date in every fourth year.

The result is April 5, For example, year gave us a PFM date of April 5, and step 2 gave us a total result of 9. This date is the Julian calendar Orthodox Easter Sunday date for year If the year itself is also Julian e. April 3 in is their Orthodox Easter Sunday date for that year. For example, English Easter Sunday date for A. The Gregorian calendar omits certain February 29 dates to keep its dates aligned with the seasons and position of Earth in relation to the Sun. To convert the Julian date to the Gregorian date, it is necessary to add the number of days shown in Table F.

Step 4 must be ignored if the Easter Sunday date calculated after step 3 occurred when the Julian calendar was still in use. The example for year gives the Julian Easter Sunday date of April 10, and Table F shows that we need to add 13 days to convert it to the Gregorian calendar date of April BASIC code is fairly straightforward, and can easily be converted to other programming languages.

Some typical questions about Easter are: Q1 "When was Easter Sunday last on April 10? NEXT loops to search or count. If you have any questions regarding the information presented here, please e-mail Ron Mallen at rwmallen chariot. If you are using these dates to plan travel, meetings, or for any use requiring the expenditure of money, time, or other resources, please consult other sources to verify the dates of Easter holidays.

Mallen or anyone who owns the hardware or manages the host machines of this home page, or the Astronomical Society of South Australia, nor anyone who has contributed any information that has been used in this document, may be held financially responsible, or responsible in any way, if these dates are incorrectly calculated or applied.

The user assumes full responsibility for the consequences of using this information. The complete procedure for calculating Easter Sunday dates for all years to A. How to work out Easter Sunday dates quickly and easily for yourself. The Easter Method Calculation. The way in which Easter dating methods evolved, and provides Lists of Easter Sunday dates for the last and next years. Easter Sunday, from A. Following Sunday Step 2 result: There are four steps to calculating the Orthodox Easter Sunday date: Convert to Gregorian Calendar Year Days to Add to 10 to 11 to 12 to 13 to 14 to 15 to 16 to 17 to 18 to 19 to 20 to 21 to 22 to 23 Other examples: In principle, Easter falls on the Sunday following the full moon that follows the northern spring equinox the paschal full moon.

However, the vernal equinox and the full moon are not determined by astronomical observation. The vernal equinox is fixed to fall on 21 March previously it varied in different areas and in some areas Easter was allowed to fall before the equinox. The full moon is an ecclesiastical full moon determined by reference to a lunar calendar, which again varied in different areas.

While Easter now falls at the earliest on the 15th of the lunar month and at the latest on the 21st, in some areas it used to fall at the earliest on the 14th the day of the paschal full moon and at the latest on the 20th, or between the sixteenth and the 22nd. The last limit arises from the fact that the crucifixion was considered to have happened on the 14th the eve of the Passover and the resurrection therefore on the sixteenth.

The "computus" is the procedure of determining the first Sunday after the first ecclesiastical full moon falling on or after 21 March, and the difficulty arose from doing this over the span of centuries without accurate means of measuring the precise tropical year. The synodic month had already been measured to a high degree of accuracy. The schematic model that eventually was accepted is the Metonic cycle , which equates 19 tropical years to synodic months.

In , the Catholic Church began using 21 March under the Gregorian calendar to calculate the date of Easter, while the Eastern Churches have continued to use 21 March under the Julian calendar. The Catholic and Protestant denominations thus use an ecclesiastical full moon that occurs four, five or thirty-four days earlier than the eastern one.

The earliest and latest dates for Easter are 22 March and 25 April, [1] in the Gregorian calendar as those dates are commonly understood. However, in the Orthodox Churches, while those dates are the same, they are reckoned using the Julian calendar; therefore, on the Gregorian calendar as of the 21st century, those dates are 4 April and 8 May. Easter is the most important Christian feast, and the proper date of its celebration has been the subject of controversy as early as the meeting of Anicetus and Polycarp around According to Eusebius's Church History , quoting Polycrates of Ephesus , [2] churches in the Roman Province of Asia "always observed the day when the people put away the leaven ", namely Passover, the 14th of the lunar month of Nisan.

The rest of the Christian world at that time, according to Eusebius, held to "the view which still prevails," of fixing Easter on Sunday. Eusebius does not say how the Sunday was decided. Other documents from the 3rd and 4th centuries reveal that the customary practice was for Christians to consult their Jewish neighbors to determine when the week of Passover would fall, and to set Easter on the Sunday that fell within that week. By the end of the 3rd century some Christians had become dissatisfied with what they perceived as the disorderly state of the Jewish calendar.

The chief complaint was that the Jewish practice sometimes set the 14th of Nisan before the spring equinox. This is implied by Dionysius, Bishop of Alexandria , in the mid-3rd century, who stated that "at no time other than the spring equinox is it legitimate to celebrate Easter" Eusebius, Church History 7. And it was explicitly stated by Peter, bishop of Alexandria that "the men of the present day now celebrate [Passover] before the [spring] equinox Jews in one city might have a method for reckoning the Week of Unleavened Bread different from that used by the Jews of another city.

But these experiments themselves led to controversy, since some Christians held that the customary practice of holding Easter during the Jewish festival of Unleavened Bread should be continued, even if the Jewish computations were in error from the Christian point of view. At the First Council of Nicaea in , it was agreed that the Christians should observe a common date, independent from the Jewish method. The council ignored the fact that the Christian vernal equinox was a day rather than an astronomical instant, that the Christian 14 Nisan was a different day than the Jewish 14 Nisan , and that Alexandria and Rome used different Easter tables.

Because of the divergence of these tables it was usual to negotiate a common date when discrepancies arose. It took several centuries before a common method was accepted throughout Christendom. The process of working out the details generated still further controversies.

The method from Alexandria became authoritative. In its developed form it was based on the epacts of a reckoned moon according to the year Metonic cycle. Such a cycle was first proposed by Bishop Anatolius of Laodicea in present-day Syria , c. In Constantinople, several computists were active over the centuries after Anatolius and after the Nicaean Council , but their Easter dates coincided with those of the Alexandrians.

The Alexandrian computus was converted from the Alexandrian calendar into the Julian calendar in Rome by Dionysius Exiguus , though only for 95 years.

Dionysius introduced the Christian Era counting years from the Incarnation of Christ when he published new Easter tables in Dionysius's tables replaced earlier methods used by the Church of Rome. The earliest known Roman tables were devised in by Hippolytus of Rome based on eight-year cycles. Then year tables were introduced in Rome by Augustalis near the end of the 3rd century. These old tables were used in Northumbria until , and by isolated monasteries as late as A modified year cycle was adopted in Rome during the first half of the 4th century.

Victorius of Aquitaine tried to adapt the Alexandrian method to Roman rules in in the form of a year table, but he introduced serious errors. In the British Isles Dionysius' and Victorius' tables conflicted with the indigenous tables. These used an year cycle because this made the dates of Easter repeat every 84 years—but an error made the full moons fall progressively too early.

Add the fact that Easter could fall, at earliest, on the fourteenth day of the lunar month and often Eanfleda , who followed the Roman system, fasted on Palm Sunday at the same time that her husband Oswy , king of Northumbria, fasted on her Easter Sunday. Bede records that, "There happened an eclipse of the sun on the third of May, about ten o'clock in the morning. This was done to conceal the inaccuracy that had accumulated in the new cycle since it was originally constructed.

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## Calculate the Date of Easter Sunday

The Dionysian reckoning was fully described by Bede in The Gregorian Easter has been used since by the Roman Catholic Church and was adopted by most Protestant churches between and German Protestant states used an astronomical Easter based on the Rudolphine Tables of Johannes Kepler between and , while Sweden used it from to This astronomical Easter was one week before the Gregorian Easter in , , , , etc.

The Easter cycle groups days into lunar months, which are either 29 or 30 days long. There is an exception. The month ending in March normally has thirty days, but if 29 February of a leap year falls within it, it contains There are 12 synodic months in a lunar year, totaling either or days. The lunar year is about 11 days shorter than the calendar year, which is either or days long. These days by which the solar year exceeds the lunar year are called epacts Greek: Whenever the epact reaches or exceeds 30, an extra intercalary month or embolismic month of 30 days must be inserted into the lunar calendar: Wheatly [24] provides the detail:.

Thus the lunar month took the name of the Julian month in which it ended. The nineteen-year Metonic cycle assumes that 19 tropical years are as long as synodic months.

So after 19 years the lunations should fall the same way in the solar years, and the epacts should repeat. So after 19 years, the epact must be corrected by one day for the cycle to repeat.

## A Perpetual Easter and Passover Calculator

This is the so-called saltus lunae "leap of the moon. The Julian calendar handles it by reducing the length of the lunar month that begins on 1 July in the last year of the cycle to 29 days. This makes three successive day months. The extra months commenced on 3 December year 2 , 2 September year 5 , 6 March year 8 , 4 December year 10 , 2 November year 13 , 2 August year 16 , and 5 March year That is, the remainder of the year number Y in the Christian era when divided by 19, plus one.

The paschal or Easter-month is the first one in the year to have its fourteenth day its formal full moon on or after 21 March. Easter is the Sunday after its 14th day or, saying the same thing, the Sunday within its third week.

The paschal lunar month always begins on a date in the day period from 8 March to 5 April inclusive. Its fourteenth day, therefore, always falls on a date between 21 March and 18 April inclusive, and the following Sunday then necessarily falls on a date in the range 22 March to 25 April inclusive. In the solar calendar Easter is called a moveable feast since its date varies within a day range. But in the lunar calendar, Easter is always the third Sunday in the paschal lunar month, and is no more "moveable" than any holiday that is fixed to a particular day of the week and week within a month.

As reforming the computus was the primary motivation for the introduction of the Gregorian calendar in , a corresponding computus methodology was introduced alongside the calendar. Easter Sunday is the Sunday following the paschal full moon date. The paschal full moon date is the ecclesiastical full moon date following 20 March.

The Gregorian method derives paschal full moon dates by determining the epact for each year. The first day of a lunar month is considered the day of the first appearance of the crescent moon. The 14th day is considered the day of the full moon. Historically the paschal full moon date for a year was found from its sequence number in the Metonic cycle, called the golden number , which cycle repeats the lunar phase on a certain date every 19 years. This method was abandoned in the Gregorian reform because the tabular dates go out of sync with reality after about two centuries, but from the epact method a simplified table can be constructed that has a validity of one to three centuries.

The above table is valid from to inclusive. From the table, paschal full moon for golden number 6 is 18 April. From week table 18 April is Sunday. Easter Sunday is the following Sunday, 25 April. The epacts are used to find the dates of the new moon in the following way: Write down a table of all days of the year the leap day is ignored. However, in every second such period count only 29 days and label the date with xxv 25 also with xxiv Treat the 13th period last eleven days as long, therefore, and assign the labels "xxv" and "xxiv" to sequential dates 26 and 27 December respectively.

Finally, in addition, add the label "25" to the dates that have "xxv" in the day periods; but in day periods which have "xxiv" together with "xxv" add the label "25" to the date with "xxvi". The distribution of the lengths of the months and the length of the epact cycles is such that each civil calendar month starts and ends with the same epact label, except for February and for the epact labels "xxv" and "25" in July and August.

This table is called the calendarium. The ecclesiastical new moons for any year are those dates when the epact for the year is entered. If the epact for the year is for instance 27, then there is an ecclesiastical new moon on every date in that year that has the epact label "xxvii" Also label all the dates in the table with letters "A" to "G", starting from 1 January, and repeat to the end of the year. If, for instance, the first Sunday of the year is on 5 January, which has letter "E", then every date with the letter "E" is a Sunday that year.

Then "E" is called the dominical letter for that year from Latin: The dominical letter cycles backward one position every year. However, in leap years after 24 February the Sundays fall on the previous letter of the cycle, so leap years have two dominical letters: In practice, for the purpose of calculating Easter, this need not be done for all days of the year. For the epacts, March comes out exactly the same as January, so one need not calculate January or February.

You need the epacts only from 8 March to 5 April. This gives rise to the following table:. If the epact is 27 xxvii , an ecclesiastical new moon falls on every date labeled xxvii. The ecclesiastical full moon falls 13 days later. From the table above, this gives a new moon on 4 March and 3 April, and so a full moon on 17 March and 16 April. Then Easter Day is the first Sunday after the first ecclesiastical full moon on or after 21 March.

This definition uses "on or after 21 March" to avoid ambiguity with historic meaning of the word "after". In modern language, this phrase simply means "after 20 March". The definition of "on or after 21 March" is frequently incorrectly abbreviated to "after 21 March" in published and web-based articles, resulting in incorrect Easter dates.

In the example, this paschal full moon is on 16 April. If the dominical letter is E, then Easter day is on 20 April. The label " 25 " as distinct from "xxv" is used as follows: Within a Metonic cycle, years that are 11 years apart have epacts that differ by one day. A month beginning on a date having labels xxiv and xxv impacted together has either 29 or 30 days. If the epacts 24 and 25 both occur within one Metonic cycle, then the new and full moons would fall on the same dates for these two years.

This is possible for the real moon [31] but is inelegant in a schematic lunar calendar; the dates should repeat only after 19 years. To avoid this, in years that have epacts 25 and with a Golden Number larger than 11, the reckoned new moon falls on the date with the label 25 rather than xxv. Where the labels 25 and xxv are together, there is no problem since they are the same.

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This does not move the problem to the pair "25" and "xxvi", because the earliest epact 26 could appear would be in year 23 of the cycle, which lasts only 19 years: The Gregorian calendar has a correction to the tropical year by dropping three leap days in years always in a century year. This is a correction to the length of the tropical year, but should have no effect on the Metonic relation between years and lunations.

Therefore, the epact is compensated for this partially—see epact by subtracting one in these century years. This is the so-called solar correction or "solar equation" "equation" being used in its medieval sense of "correction". However, 19 uncorrected Julian years are a little longer than lunations. The difference accumulates to one day in about years. Therefore, in the Gregorian calendar, the epact gets corrected by adding 1 eight times in 2, Gregorian years, always in a century year: The first one was applied in , the next is in , and will be applied every years except for an interval of years between and , which starts a new cycle.

The solar and lunar corrections work in opposite directions, and in some century years for example, and they cancel each other. The result is that the Gregorian lunar calendar uses an epact table that is valid for a period of from to years.

The epact table listed above is valid for the period to Every second lunar month has only 29 days, so one day must have two of the 30 epact labels assigned to it. According to Dionysius in his introductory letter to Petronius , the Nicene council, on the authority of Eusebius , established that the first month of the ecclesiastical lunar year the paschal month should start between 8 March and 5 April inclusive, and the 14th day fall between 21 March and 18 April inclusive, thus spanning a period of only 29 days.

A new moon on 7 March, which has epact label "xxiv", has its 14th day full moon on 20 March, which is too early not following 20 March. So years with an epact of "xxiv", if the lunar month beginning on 7 March had 30 days, would have their paschal new moon on 6 April, which is too late: In the Julian calendar the latest date of Easter was 25 April, and the Gregorian reform maintained that limit. So the paschal full moon must fall no later than 18 April and the new moon on 5 April, which has epact label "xxv".

Then epact "xxv" must be treated differently, as explained in the paragraph above. As a consequence, 19 April is the date on which Easter falls most frequently in the Gregorian calendar: The relation between lunar and solar calendar dates is made independent of the leap day scheme for the solar year. Basically the Gregorian calendar still uses the Julian calendar with a leap day every four years, so a Metonic cycle of 19 years has 6, or 6, days with five or four leap days. By not labeling and counting the leap day with an epact number, but having the next new moon fall on the same calendar date as without the leap day, the current lunation gets extended by a day, [32] and the lunations cover as many days as the 19 years.

A consequence is that the reckoned age of the moon may be off by a day, and also that the lunations that contain the leap day may be 31 days long, which would never happen if the real moon were followed short-term inaccuracies. This is the price for a regular fit to the solar calendar. From the perspective of those who might wish to use the Gregorian Easter cycle as a calendar for the entire year, there are some flaws in the Gregorian lunar calendar [33] although they have no effect on the paschal month and the date of Easter:.

See epact for a discussion. So the Gregorian Easter dates repeat in exactly the same order only after 5,, years, 70,, lunations, or 2,,, days; the mean lunation length is then However, the calendar must already have been adjusted after some millennia because of changes in the length of the tropical year, the synodic month, and the day. This raises the question why the Gregorian lunar calendar has separate solar and lunar corrections, which sometimes cancel each other.

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