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01 Apr

Calculating Easter: Irish Computus to the Carolingian Renaissance

A bearded Christ with long hair sits, a red book in his left hand, with eagles either side of his head, a cross over him, surrounded by interlaced borders

In his Historia Ecclesiastica (Ecclesiastical History of the English Nation, c. 731 AD) Bede noted that the Irish (Scots) and Britons had differed from the rest of the Western Church regarding Easter: “they did not keep Easter Sunday at the proper time, but from the fourteenth to the twentieth moon; which computation is contained in a revolution of eighty-four years” 1

This might suggest the Irish were at fault. Yet, for the past centuries and into the Carolingian Renaissance Irish scholars were at the forefront of “computus”, the development of the ecclesiastical calendar, most particularly the date of Easter. To do this correctly required observation of the moon, and facility at mathematics. “What Irish scholars of the seventh century achieved, therefore, was a comprehensive understanding of Easter reckoning, which was to become the unanimously accepted system for the calculation of Easter, from the ninth century onwards, for the rest of the Middle Ages and in the Orthodox Church to the present day”2.

The question of when to celebrate Easter had been contentious from the 2nd century. At that time Christians in Asia fasted before the celebration of “the Lord’s Passover” on “the fourteenth day of the moon, on which day the Jews were commanded to sacrifice the lamb” ie. the day before Passover. However Christians elsewhere ended their fast on the celebration of the Resurrection. Eventually it was agreed that the Resurrection was the feast that should end the fast and that it should be celebrated on the first Sunday after Passover3

This 2nd century dispute was followed by one in the 4th century, arguing that the Jewish calculation of Passover had slipped into error. The First Council of Nicaea (325) decided that all Christians should celebrate Easter on the same day, and that the Christians should calculate the day for themselves4 However the actual calculation of the date was not laid out, and over time different methods developed.

Easter in Ireland

Illuminated text of “Erat autem hora tertia” (“now it was the third hour”) from the 1990 facsimile of the Book of Kells.

In Irish, as in most European languages, the word for Easter (“Cásc”) derives from the Latin “Pascha”, which also relates to Passover. The alteration of the leading “P” in “Pascha” to “C” in “Cásc” suggests the word was adopted early, before the Irish got used to the exotic “P” sound that was not originally present in Irish 5 The first mention of Easter in the Annals of Ulster is dated 451AD – this early mention is not surprising since it has been suggested that the first annals were compiled in the 8th century from marginal notes made to Easter tables in the 6th and 7th centuries6.

The first calculation for Easter used in Ireland was the Latercus. This was developed in Southern France, one of the few sites where chronological studies had continued after the fall of the Roman Empire. It was created as a replacement for the Supputatio Romana, a method which had become clearly out of sync with the visible moon phases, probably by Sulpicius Severus. This computus was most likely brought to Ireland around the time of Palladius. It was certainly the only method in use by the 6th century7

The details of this method were believed lost, until the discovery by Dáibhí Ó Cróinín of an Irish 84-year Easter table (for AD 438-521) in a tenth-century manuscript now in Padua and, with Daniel McCarthy, the method was recreated8.

Developing computus

This is not to say that the Latercus was the only Easter calculation that the Irish were aware of. When the Irish peregrini (religious exiles) went to Gaul, they found that they were celebrating Easter to a different calendar to the locals, who used the Victorian reckoning. Columbanus, the most famous peregrinus who left Ireland c. 590, took a combative approach. He wrote to Pope Gregory the Great complaining of Gaulish bishops harassing his monks over their dating of Easter. He argued that the learned men of Ireland had already examined and rejected the Victorian reckoning as ludicrous, and a modern novelty compared to the Latercus’ 84 year cycle9.

The Victorian reckoning had been made mandatory in Gaul by the synod of Orléans in 541. This reckoning had been developed in Southern France around the same time as the Latercus, by Victorius of Aquitane at the request of Pope Leo. The failings of the Supputatio Romana had meant variants of a third reckoning, the Alexandrian (ascribed falsely to Cyril of Alexandria, with the original version yielding tables covering 437-531) had been used. However difficulties arose when Easter was calculated to fall after 21st April, which was unacceptable to Rome. Victorius of Aquitaine was commissioned to create a new reckoning avoiding these issues. The tables were issued in 457AD, but neither matched the lunar cycles as well as the Alexandrian, and compounded the confusion by giving mis-calculated Alexandrian dates for Easter in the Easter tables10 So Columbanus had grounds for his criticisms of the Victorian.

Comparing the three reckonings, the Victorian and Dionysian (a variant of the Alexandrian) gave the same date most of the time, while the Latercus gave radically different answers.

Lunar limits
for Easter Sunday
Earliest Easter
Full Moon
21 March20 March20 March
Julian Calendar
limits for
Easter Sunday
26 March-23 April22 March-24 April 22 March-25 April
Lunar Cycle84 years19 years19 years

Table 1:comparison of methods of reckoning Easter11.

The southern Irish churches received a letter from Pope Honorius I circa 629 asking them “not to think that their small number, at the furthest ends of the earth, were wiser than all the ancient and modern churches of Christ thoughout the world” and to reconsider their Pascal calculations. The leading clerics met at Mag Léne and sent a delegation to Rome to confirm what reckoning was used there. On their return the clerics decided to adopt Alexandrian reckoning, using in practice the Victorian tables or a combination of Victorian and Dionysian12.

That decision was criticised by Ségéne, abbot of Iona and the reply to him from Cummain provides us with extensive evidence of the computational resources available in the south of Ireland. Cummain was able to cite ten different Pascal cycles in his reply to Ségéne, and from his range of references had virtually the same collection of computistical works as was available in Spain in the 6th century, supplemented with Irish works. Some of these were at best dubious, such as the episola Cyrilli, a version of a real letter from Cyril of Alexandria doctored to approve of the 19-year cycle, and the Liber Anatolii, a key document debated at the Synod of Whitby, which contained a genuine extract from Anatolius with the Latercus criteria inserted (25 March (equinox) and 14-20 lunar limits)13.

Manuscript page

Page from the Munich Computus – the first words are “Victorius & Latercus”
Munich, Bayerische Staatsbibliothek CLM 14456

Ireland was famous as a centre for Latin grammar (see Literacy and Learning post); it was also a centre for teaching computus. The computistical textbook was an insular innovation. A manuscript found in Brussels contains a computus created as a school-text (de ratione conpuntandi), in dialogue form, “dealing intimately with problems like lunar and solar calculations, the technicalities of cycles and the mechanics of Easter tables.” It also draws on authorities from Augustine to Isodore of Seville, and based on the contents was probably a production of the circle around Cummain. This is the most sophisticated text; other Irish textbooks include the Munich Computus (text from c 718-9) and the Computus Einsidlensis (text from c. 700) 14.

Existing manuscripts also show the development of Victorian tables in Ireland. One table now in Paris (700-771) uses the Victorian data but in the format used for Latercus, including data on the Lenten fast and omitting Victorius’ “Greek” dates. Instead, there is evidence of the Victorian and Dionysian dates being compared directly 15.

Towards conformity

Ruins of Whitby Abbey, and its reflection in a pond.

The ruins of Whitby Abbey, when the Synod of Whitby was held. Mike Peel/Wikimedia (CC-BY-SA-4.0).

The learned arguments continued, but over time the Irish and British moved away from the old reckoning. After the southern Irish move in 613, the Synod of Whitby in 664 saw a Northumbrian switch from the Irish reckoning to the Dionysian. The north of Ireland stood firm until Adamnán, abbot of Iona, switched his support to the Dionysian from the Latercus towards the end of the 7th century. (Iona did not change at this time however.) The agreement by the northern Irish to use the new reckoning was formalised in the Synod of Birr in 697. Ironically, this led to further controversy, since some in the south of Ireland clung to the Victorian reckoning. The Picts changed over in 710, and Iona and its dependencies were finally persuaded to change to the new reckoning in 71516

By the time Bede was writing his famous and widely used computus De temporum ratione (On the Reckoning of Time) in 725, the three systems were still in use, the Victorian among southern Irish holdouts, the Latercus in England and Wales, and the Dionysian everywhere else. In doing so, Bede drew on Irish learning, in a compilation known as the Sirmond manuscript, now held in the Bodleian Library (Bodley 309). The exemplar of book 1 of this manuscript was compiled in Ireland before 718, and that of book 2 is also Irish, of around the same period. The manuscript shows that Bede got his information on the Dionysian, not from Rome, but from Ireland17

So did the creator of the oldest surviving 8th century Dionysian Easter table, Willibrord (658-739). He was educated in the Dionysian system first by Wilfrid (advocate for the system at Whitby in 664) then in Ireland by Ecgberht at the monastery of Ráth Máelsigi. English-born, Ecgberht spent much of his life in Ireland. He was present at Birr when the Northern Irish accepted the Dionysian reckoning and convinced Iona to finally move to the new reckoning in 715 when he was abbot there. He died in Iona on April 24 729, on the first Easter Sunday according to the Dionysian reckoning accepted and celebrated by all on Iona, according to Bede18.

Willibrord brought his learning on a mission to Frisia, simultaneously bringing expert knowledge of the Dionysian system (the Franks were still users of the Victorian system, and knowledge of the AD dating system. The move from the Victorian to the Dionysian resulted in Frankish scholars asking the same questions in the first half of the eighth century as the Irish had a century earlier. The Irish text De comparatione epacturum Dionysii et Victorii from 689 which compared the two systems was central in the early debate, with textbooks developed in Ireland enabling instruction in the system when it was full adopted19.

Along with Willibrord’s achievements, these books formed the basis of Frankish scientific knowledge. They remained influential into the 9th century, becoming gradually replaced by Bede’s works and Frankish contributions. Arguably this was the basis on which the Carolingian Renaissance was built, a renaissance during which computus continued to develop, including contributions from scholars such as Dicuil and Eriugena.

The Dionysian system (as described by Bede) remains in use in most Eastern Churches, including the vast majority of Eastern Orthodox Churches and Non-Chalcedonian Churches. It was replaced by the Gregorian Easter in 1583 in the Roman Catholic Church and thereafter by most of Protestant churches. The simplicity of the definition defies the complexity of the calculation: “the 1st Sunday after the 1st Full (Paschal) Moon after the fixed Vernal Equinox on March 21st.”

A bearded Christ with long hair sits, a red book in his left hand, with eagles either side of his head, a cross over him, surrounded by interlaced bordersFeatured Image: Detail of “Christ Enthroned” from the Book of Kells, Folio 32v. Wikimedia, Public Domain.

Further Reading

Peter Lynch (2016) “Ireland’s important role in calculating when Easter falls” IrishTimes
(17 Mar 2016)

Dáibhí Ó Cróinín (2017) “How the Irish helped to create Easter Sunday” on RTE: Brainstorm (31 Mar 2018)

Sarah Bond (2018) “Anno Domini: Computational Analysis, Antisemitism, and the Early Christian Debate Over Easter” on Society for Classical Studies (blog). Also on Sarah Bond’s own blog with additional pictures.

James Palmer (2015) “Bede, Misdirection, and the Synod of Whitby” on Merovingian World (blog)

Daniel McCarthy and Dáibhí Ó Cróinín (1987) “The ‘lost’ Irish 84-year Easter table rediscovered” Peritia , 6–7 (1987–1988), pp. 227–242 (online).

Daniel McCarthy(1993) “Easter Principles and a Fifth-Century Lunar Cycle used in the British Isles”, Journal for the History of Astronomy, 24, pp. 204–224 (online).

Daithi Ó Cróinín (1982) “A Seventh-Century Irish Computus from the Circle of Cummianus” Proceedings of the Royal Irish Academy, Vol. 82C, pp. 405-430.

Jacopo Bisagni and Immo Warntjes (2008) ‘The Early Old Irish material in
the newly discovered Computus Einsidlensis (c. AD 700)’ Ériu, 58 :77-105. (pdf NUIG)


Fifth century Easter table (“lost Irish 84-year Easter table): MS Padova, Biblioteca Antoniana, scaff. I, 27.

Seventh century computus (de ratione conpuntandi): de Brussels, KBR, ms. 5413-22 (olim G 40) fols: 77v-107v.

Computus Einsidlensis: Einsiedeln Stiftsbibliothek Codex 321 (647)

Munich Computus: Munich Bayerische Staatsbibliothek Clm 14456, fol. 8r-46r.

“Sirmond manuscript”: Bodleian Bodley 309.


  1. Bede (2011) “Ecclesiastical History of the English Nation: Book II” in Medieval Sourcebook online at Fordham University. See chapter II for quote, chapter 4 for confirmation that the Scots (Irish) and Britons used the same calculation.
  2. Immo Warntjes (2013) “Seventh-century Ireland: the cradle of medieval science?” in Mary Kelly and Charles Doherty (eds) Music and the Stars, Four Courts Press, pp. 44–72. Quote on p. 52.
  3. Philip Schaff (ed.) (1886-1900/2005) “Eusebius Pamphilius: Church History, Life of Constantine, Oration in Praise of Constantine” on Christian Classics Ethereal Library (NPNF2-01). See Chapter XXIII.—The Question then agitated concerning the Passover, Chapter XXIV.—The Disagreement in Asia, Chapter XXV.—How All came to an Agreement respecting the Passover.
  4. Philip Schaff (ed.) (1886-1900/2005) “Theodoret, Jerome, Gennadius, & Rufinus: Historical Writings” on Christian Classics Ethereal Library (NPNF2-03). See Chapter IX.—The Epistle of the Emperor Constantine, concerning the matters transacted at the Council, addressed to those Bishops who were not present.
  5. eDIL s.v. Cásc or dil.ie/8309.
  6. “The Annals of Ulster” in CELT: The Corpus of Electronic Texts (UCC CELT). Dáibhí Ó Cróinín (1983) ‘Irish annals from Easter tables’, Peritia 2, pp. 74-86.
  7. Immo Warntjes (2016) “Computus as scientific thought in Ireland and the early medieval West” in Roy Flechner and Sven Meeder (eds) Irish in early medieval Europe, New York: Palgrave Macmillan, pp. 158–178. See pp. 159-162.
  8. Daniel McCarthy and Dáibhí Ó Cróinín (1987) “The ‘lost’ Irish 84-year Easter table rediscovered” Peritia , 6–7 (1987–1988), pp. 227–242 (online). Daniel McCarthy(1993) “Easter Principles and a Fifth-Century Lunar Cycle used in the British Isles”, Journal for the History of Astronomy, 24, pp. 204–224 (online).
  9. Warntjes (2016), pp. 160-2. Faith Wallis (1999) “Introduction” in Bede (1999) The Reckoning of Time, Liverpool University Press, p. lvi
  10. Wallis (1999), pp. xlviii – lii.
  11. based on table in Warntjes (2016), p. 160, with lunar cycles added.
  12. Daithi Ó Cróinín (1982) “A Seventh-Century Irish Computus from the Circle of Cummianus” Proceedings of the Royal Irish Academy, Vol. 82C, pp. 405-430. See pp. 405-6. Wallis (1999), p. lx.
  13. Ó Cróinín (1982), pp. 405-6. Wallis (1999), p. lx, pp. lvi-lvii. Bede considered that the document was genuine but corrupted; an original version of the passage used in the Liber Anatolii gave criteria of 22 March and limits of 15-21.
  14. Ó Cróinín (1982), pp. 406-7. Quote on p. 407. Warntjes (2016), pp. 168-9
  15. Warntjes (2016), pp. 165
  16. Immo Warntjes (2015) “‘Victorius vs Dionysius: the Irish Easter controversy of AD 689’” in Pádraic Moran & Immo Warntjes (eds.), Early medieval Ireland and Europe: chronology, contacts, scholarship, Turnhout, pp. 40–96. Wallis (1999), p. lxiii.
  17. Wallis (1999), pp. lxxii-lxxix.
  18. Warntjes (2016), pp. 166-169. Bede (2011) “Ecclesiastical History of the English Nation: Book V” in Medieval Sourcebook online at Fordham University. See chapter XXII
  19. Warntjes (2016), pp. 166-169.

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