Literature on the Islamic Calendar (chronological)

• Sylvestre de Sacy, A.I., “Mémoire sur divers événemens de l’histoire des Arabes avant Mahomet”, Mémoires de littérature, tirés des registres de l’Académie royale des inscriptions et belles-lettres, 48 (1808), 484-762.
• Navoni, Giovanni-Battista, “Rouz-namé, ou calendrier perpétuel des Turcs, avec les remarques et des exemples sur la manière de compter les lunaisons, et avec des tables pour trouver la correspondance des dates entre l’ère turque et l’ère vulgaire”, Fundgruben des Orients, 4 (1814), 38-67, 127-153 & 253-277 – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 1-92.
• Ideler, Christian Ludwig, “Ueber die Vergleichung der muhammedanischen und christlichen Zeitrechnung”, Fundgruben des Orients, 4 (1814), 299-308 – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main:Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 93-102.
• Ideler, Christian Ludwig, “Ueber die Zeitrechnung der Araber”, Abhandlungen der Königlichen Akademie der Wissenschaften in Berlin 1812/13 (Berlin, 1816), Historisch-philologische Klasse, 97-120 [Akademiebibliothek link] – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 103-126.
• Ideler, Christian Ludwig, “Ueber die Zeitrechnung der Perser”, Abhandlungen der Königlichen Akademie der Wissenschaften in Berlin 1814/15 (Berlin: ???, 1818), Historisch-philologische Klasse, 259-289 [Akademiebibliothek link] – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 127-157.
• Ideler, Christian Ludwig, “Ueber die bei den morgenländischen Völkern gebräuchlichen Formen des julianischen Jahrs”, Abhandlungen der Königlichen Akademie der Wissenschaften in Berlin 1816/17 (Berlin: ???, 1819), Historisch-philologische Klasse, 215-262 [Akademiebibliothek link] – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 159-206.
• von Zach, Franz Xaver Freiherr, “Ueber den Kalender der Türken”, Hertha: Zeitschrift für Erd-, Völker- und Staatenkunde, 2 (1825), 64-69 – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 234-239.
• Sedillot, J.-J., Traité des instruments astronomiques des arabes [...] (Paris: ???, 1834/35).
• Caussin de Perceval, Armand-Pierre, Essai sur l’histoire des arabes avant l’islamisme, pendant l’epoque de Mahomet, et jusqu’à la réduction de toutes les tribus sous la loi musulmane (Paris: Firmin Didot frères, 1847/48), 3 vols. [cf. in particular vol. 1, pp. 283-???].
• Caussin de Perceval, Armand-Pierre, “Mémoire sur le calendrier arabe avant l’islamisme”, Journal asiatique, ou recueil de mémoires, d’extraits et de notices relatifs à l’histoire, à la philosophie, aux langues et à la littérature des peuples orientaux, sér. 4, 1 (1843), 342-379 [Gallica link] – English translation [by L. Nobiron], “Notes on the Arab Calendar Before Islam”, Islamic Culture, 21 (1947), 135-153.
• Mahmoud Pacha al-Falaki [= Maḥmūd Effendī], “Mémoire sur le calendrier arabe avant l’islamisme, et sur la naissance et l’âge du prophète Mohammad”, Journal asiatique, ou recueil de mémoires, d’extraits et de notices relatifs à l’histoire, à la philosophie, aux langues et à la littérature des peuples orientaux, sér. 5, 11 (1858), 109-192 [Gallica link] – reprinted in Mémoires couronnés et mémoires des savants étrangers, publiées par l’Académie royale des sciences, des lettres et des beaux-arts de Belgique, 30 (1861), Classe des lettres, 1-45, and in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 251-336.
• Sprenger, Aloys, “Ueber den Kalender der Araber vor Mohammad”, Zeitschrift der Deutschen Morgenländischen Gesellschaft, 13 (1859), 134-175 [MENAdoc link].
• Lane, Edward William, An Account of the Manners and Customs of the Modern Egyptians, written in Egypt during the Years 1833, -34 and -35, partly from Notes made during a Former Visit to that Country in the Years 1825, -26, -27 and -28 (London: John Murray, 1860), 5th ed. – reprinted in 2003 by The American University in Cairo Press (Cairo/New York) – in particular chapters IX & XXIV-XXVI.
• Muir, William, The Life of Mahomet, with Introductory Chapters on the Original Sources for the Biographies of Mahomet, and on the Pre-Islamite History of Arabia (London: Smith, Elder & Co., 1861), 4 vols. – many later editions.
• Sachau, C. Edward, The Chronology of Ancient Nations: An English Version of the Arabic Text of the Athâr-ul-Bâkiya of Albîrûnî, or “Vestiges of the Past,” Collected and Reduced to Writing by the Author in AH 390-1, AD 1000 (London: William H. Allen & Co., 1879) [Gallica link / MENAdoc link] – reprinted by Minerva Verlag (Frankfurt am Main, 1984) and in F. Sezgin, Publications of the Institute for the History of Arabic-Islamic Science: Islamic Mathematics and Astronomy, Volume 31 (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998).
• Mukhtar Pasha, Ghazi Ahmed, Islah at-taqwim (Cairo: ???, 1890) [text in Turkish with an Arabic translation by Sefiq Bay Mansur Yegen] – also published in a French translation [by Osman Nouri Efendi] as La réforme du calendrier (Leiden: E.J. Brill, 1893) [Internet Archive link].
• Kropf, Lewis, L. & Lane-Poole, Stanley, “The Mohammadan Calendar”, The English Historical Review, 13 (1898), 700-703 [JSTOR link].
• Hadji Khan, With the Pilgrims to Mecca: The Great Pilgrimage of A.H. 1319; A.D. 1902 (London/New York: John Lane, 1905) [Internet Archive link / other link].
• Ginzel, Friedrich Karl, Handbuch der mathematischen und technischen Chronologie (Leipzig: J.C. Hinrichs’sche Buchhandlung, 1906), vol. 1, pp. 238-274 – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies II (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 65]), pp. 113-150.
• Juynboll, Theodoor Willem, Handleiding tot de kennis van de Mohammedaansche wet, volgens de leer der Sjâfi‘itische school (Leiden: E.J. Brill, 1930), 4th ed.
• Hartner, Willy, “Zamān”, in: Enzyklopädie des Islam (Leiden: E.J. Brill, 1934), vol. 4, pp. 1307-1310 – reprinted in Oriens-Occidens: Ausgewählte Schriften zur Wissenschafts- und Kulturgeschichte: Festschrift zum 60. Geburtstag (Hildeheim: Georg Olms Verlagsbuchhandlung, 1968), pp. 260-263.
• Taqizadeh, Sayyid Hasan, “Various Eras and Calendars used in the Countries of Islam”, Bulletin of the School of Oriental Studies, 9 (1937/39), 903-922 [JSTOR link]; 10 (1940/42), 107-132 [JSTOR link] – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies II (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 65]), pp. 347-392.
• Sauer, M., “Mohammedanische Zeitrechnung, Festtage und Gebetszeiten”, Die Sterne, 34 (1958), 194-196.
• Mayr, Joachim, “Das türkische Finanzjahr”, Der Islam: ???, 36 (1961), 264-268 [de Gruyter link].
• Grohmann, Adolph, Mayr, Joachim & Till, Walter Curt, Arabische Chronologie (Leiden/Köln: E.J. Brill, 1966 [= Handbuch der Orientalistik, Abteilung I, Ergänzungsband II, Halbband I).
• Grunebaum, Gustave E. von, Muhammadan Festivals (London/Totowa: Curzon Press/Rowman & Littlefield, 1976), 2nd ed.
• Séguy, Marie-Rose (ed.), The Miraculous Journey of Mohammet: Mirâj Nâmeh (New York: George Braziller, 1977).
• Ilyas, Mohammad, “Progress towards a Schematic World Hijrī Calendar”, Hamdard Islamicus: Quarterly Journal of the Hamdard Foundation (Pakistan), 7 (1984), nr. 3, 61-83.
• Ilyas, Mohammad, A Modern Guide to Astronomical Calculations of Islamic Calendar, Times & Qibla (Kuala Lumpur: Berita Publishing, 1984).
• Shamsi, Fazal Ahmad, “The Date of Hijrah”, Islamic Studies: ???, 23 (1984), 189-224 [JSTOR link] & 289-323 [JSTOR link].
• Shamsi, Fazal Ahmad, “The ‛Year’ in the Qur’ān”, Islamic Studies: ???, 25 (1986), 305-324 [JSTOR link].
• Shamsi, Fazal Ahmad, “The Meaning of Nasī: An Interpretation of Verse 9:37”, Islamic Studies: ???, 26 (1987), 143-164 [JSTOR link].
• Lindner, Johannes, “Transformation von Daten der muslimischen in die christliche Zeitrechnung und umgekehrt mit programmierbaren elektronischen Taschenrechern”, Die Welt des Islams, 29 (1989), 30-40 (*).
• Ilyas, Mohammad, “Islamic Schematic Calendar: A Note on Some Useful Compendia”, Islamic Studies: ???, 31 (1992), 487-493 [JSTOR link].
• Ansari, Shahabuddin, “Towards a Unified World Islamic Calendar””, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 17 (1994), nr. 4, 99-123.
• Lindner, Johannes, “Die türkischen Finanz-(Maliye-)Jahre ab 1917”, Zeitschrift der Deutschen Morgenländischen Gesellschaft, 144 (1994), 56-59 [MENAdoc link].
• McNaughton, David L., “Eclipses during Ramadhan”, Journal of the British Astronomical Association, 105 (1995), 160 [ADS link].
• McNaughton, David L., “A Note on A Unified World Islamic Calendar”, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 18 (1995), nr. 4, 123-125.
• McNaughton, David L., “Eclipses during Ramadān”, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 19 (1996), nr. 1, 81-86.
• Ansari, Shahabuddin, “Interchanging of Christian and Hijrah Dates”, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 19 (1996), nr. 2, 89-98.
• Ilyas, Mohammad, Astronomy of Islamic Calender (Kuala Lumpur: A.S. Noordeen, 1997) [check].
• Ilyas, Mohammad, “Calendars in Islam”, in: H. Selin (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (Dordrecht/Boston/London: Kluwer Academic Publishers, 1997), pp. 171-173.
• McNaughton, David L., “A Universal Islamic Calendar”, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 20 (1997), nr. 1, 77-85.
• Dallal, Ahmad, “Calendar”, in: J.D. McAuliffe (ed.), Encyclopaedia of the Qur’ān (Leiden/Boston/Köln: Brill, 2001), vol. 1, pp. 272-273.
• Jones, Alan, “The Dotting of a Script and the Dating of an Era: The Strange Neglect of PERF 558”, Islamic Culture: ???, 72 (1998), 95-103 [Islamic Awareness link].
• Ansari, Shahabuddin, “A Note on “A Universal Islamic Calendar””, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 23 (2000), nr. 1, 71-76.
• Schimmel, Annemarie Brigitte, Das islamische Jahr: Zeiten und Feste (Munich: C.H. Beck, 2001 [= Beck’sche Reihe, nr. 1441]) – Dutch translation [by Carolijn Visschers], Het islamitische jaar: Kalender en feesten (Baarn: Ten Have, 2003).
• Rizvi, Saiyid Samd Husain, “Al-Bīrūnī’s International Lunar Calendar”, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 29 (2006), nr. 3, 83-94.
• Hanne, Eric, “Dates and Calendars”, in: J.W. Meri (ed.), Medieval Islamic Civilization: An Encyclopedia (New York/Abingdon: Routledge/Taylor & Francis Group, 2006 [= Routledge Encyclopedias of the Middle Ages, vol. 13]), vol. I, pp. 195-197.
• Shoshan, Boaz, “Festivals and Celebrations”, in: J.W. Meri (ed.), Medieval Islamic Civilization: An Encyclopedia (New York/Abingdon: Routledge/Taylor & Francis Group, 2006 [= Routledge Encyclopedias of the Middle Ages, vol. 13]), vol. I, pp. 254-257.
• Cajee, Na’eel, “Circular Calculus and Elliptical Realities: The Standardization of the Islamic Lunar Calendar in the United States”, Journal of Muslim Minority Affairs, 31 (2011), 441-462 [doi link].
• Blake, Stephen P., Time in Early Modern Islam: Calendar, Ceremony, and Chronology in the Safavid, Mughal, and Ottoman Empires (Cambridge: Cambridge University Press, 2013).
• Stowasser, Barbara Freyer, The Day Begins at Sunset: Perceptions of Time in the Islamic World (London/New York: I.B. Tauris & Co., 2014).
• Wishnitzer, Avner, Reading Clocks, Alla Turca: Time and Society in the Late Ottoman Society (Chicago/London: University of Chicago Press, 2015).

Conversion Tables or Algorithms based on the Tabular Islamic Calendar

Type I [Intercalary years 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29]

• Greaves, John, Epochæ Celebriores, Astronomis, Historicis, Chronologis, Chataiorum, Syro-Græcorum, Arabum, Persarum, Chorasmiorum, usitatæ ex traditione Ulug Beigi, Indiæ citra extráque Gangem Principis (London: James Flesher, 1650) [Google Books link] [2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29; epoch = 15 July 622 CE].
• Pococke, Edward,
• Beverage, William, Institutionum chronologicarum libri II. Unà cum totidem arithmetices chronologicæ libellis. Editio altera, priori emendatior (London: Samuel Roycroft, 1705), pp. 70-85, 159-160 & 177-179 – epoch: 15/16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29 [Internet Archive link].
• Wolff, Christian, Elementa Matheseos Universæ: Tomus Quartus, qui Geographiam cum Hydrographia, Chronologiam, Gnomonicam, Pyrotechniam, Architecturam Militarem atque Civilem complectitur. Editio nova; priori multo auctior et correctior (Geneva: Pellissari & Soc, 1738), pp. 103, 117 & 146-150 [Internet Archive link] [epoch: 16 July 622; astronomers adopt 15 July].
• Ciccolini, Lodovico, “Calendrier des turcs”, Correspondance astronomique, géographique, hydrographique et statistique, 11 (1824), 552-567 [Google books] [epoch = 16 July 622].
• von Littrow, Joseph Johann, Calendariographie, oder Anleitung, alle Arten Kalender zu verfertigen (Vienna: J.G. Heubner, 1828), pp. 88-112 [Google books] [epoch = 16 July 622].
• von Zach, Franz Xaver Freiherr, “Calendrier des turcs”, Correspondance astronomique, géographique, hydrographique et statistique, 12 (1825), 3-53 [Google books] [epoch = 16 July 622; astronomers adopt 15 July 622].
• Ciccolini, Lodovico, “Sur la conversion de l’ère de l’hégire”, Correspondance astronomique, géographique, hydrographique et statistique, 12 (1825), 348-362 [Google books].
• Kulik, Jakob Philipp, Der tausendjährige Kalender: Ein nützliches Handbuch für Historiographen, Diplomatiker, Archivare, Richter, Advokaten, Landgeistliche, und überhaupt für Jene, welche die in den alten Manuskripten, Geschichtbüchern, und Urkunden vorkommenden chronologischen Daten zu bestimmen haben. Zweite verbesserte, und mit einem Kalender der Juden und Türken vermehrte Auflage (Prague: Kronberger und Weber, 1834) [E-RARA link] – table: 0 AH to 1800 AH; epoch: ?? July 622 CE; intercalary years: 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29 – first published in 1831.
• Sédillot, Louis Pierre Eugène Amélie, Manuel de chronologie universelle, comprenant des notions préliminaires sur la chronologie mathématique et technique, un tableau synchronique de l’histoire universelle, des tables chronologiques et généalogiques pour les états anciens et modernes (Paris: ???, 18??), vol. 1, pp. 11-12 & 21; vol. 2, pp. 340-??? – intercalary years: 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29.
• Biot, Eduard, “Résumé de chronologie astronomique”, Mémoires de l’Académie des Sciences de l’Institut de France, 22 (1850), 209-523 [in particular pp. 454-476] [Gallica link] [epoch: 15 July 622 CE; provides correction for when the 16th year is intercalary].

Type II [Intercalary years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29]

• Christmann, Jacob, Muhamedis Alfragani arabis chronologica et astronomica elementa, e Palatinæ bibliothecæ veteribus libris versa, expleta, & scholiis expolita. Additus est commentarius, qui rationem calendarii Romani, Ægyptiaci, Arabici, Persici, Syriaci & Hebræi explicat, & intervalla præcipuarum ærarum ita declarat, ut ab Olympiadibus & Urbe condita usque ad nostram memoriam, per annos Nabonasari, Iulij Cæsaris & Christi, certa temporum series constare possit (Frankfurt am Main: Andreae Wecheli heredes, Claudium Marnium & Ioann. Aubrium, 1590), pp. 7-16 & 194-211 [E-RARA link] [epoch: 16 July 622 CE; astronomers adopt 15 July 622 CE] – reprinted in 1618.
• Mulerius, Nicolaus, Iudæorum Annus Lunæ-Solaris et Turc-Arabum Annus merê Lunaris: Recens uterque è suis fontibus deductus, & cum anno Romano facili methodo connexus (Groningen: Johannes Sassius, 1630), preface & pp. 69-79 [E-RARA link / Internet Archive link] [epoch: 16 July 622 CE].
•  l’Art de vérifier les dates des faits historiques, des chartes, des chroniques et autres anciens monumens, depuis la naissance de Notre-Seigneur, par le moyen d’une table chronologique, où l’on trouve les Olympiades, les années de Jésus-Christ, des Eres d’Alexandrie & de Constantinople, de l’Ere de Séleucides, de l’Ere Césaréenne d’Antioche, de l’Ere d’Espagne, de l’Ere des Martyrs, de l’Hégire, les Indictions, le Cycle Pascal, les Cycles Solaire & Lunaire, le Terme Pascal, les Pâques de chaque année & les Epactes. Avec deux calendriers perpétuels, la chronologie historique des Conciles, des Papes, des quatre Patriarches d’Orient, des Empereurs Romains, Grecs, des Califes, des Rois des Parthes, des Perses, des Huns, des Vandales, des Goths, des Lombards, des Bulgares, de Jérusalem, de Chypre, des Princes d’Antioche, des Comptes de Tripoli, des Sultans d’Iconium, d’Alep, de Damas, des Empereurs Ottomans, des Schahs de Perse, des Grands-Maîtres de Malte, du Temple, de l’Ordre Teutonique, des Empereurs François, Allemands, des six Electeurs Laiques de l’Empire, des Rois de Hongrie, de Pologne, de Danemarck, de Suede, des Czars de Russie, des Rois de France, des grands Vassaux de cette Couronne, des Rois d’Angleterre, d’Ecosse, d’Espagne, de Portugal, des Souverains d’Italie, &c. Nouvelle édition, revue, corrigée & augmentée, par un religieux Bénédictin de la Congrégation de S. Maur (Paris: G. Desprez, 1770), pp. xviii-xix, 13-38 & 392 [Bizkaia link] [intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29; epoch:16 July 622 CE – astronomers adopt 15 July].
• Marsden, William, “On the Era of the Mahometans, called the Hejerà”, Philosophical Transactions of the Royal Society of London, 78 (1788), 414-432 [JSTOR link] [epoch = 16 July 622].
• Warren, John, Kala Sankalita: A Collection of Memoirs on the Various Modes according to which the Nations of the Southern Parts of India divide Time, to which are added, Three General Tables, wherein may be found by mere inspection the Beginning, Character, and Roots of the Tamul, Tellinga, and Mahommedan Civil Years, concurring, viz. the two former with the European Years of the XVIIth, XVIIIth and XIXth Centuries, and the latter with those from A.D. 622 (A.H. 1) to 1900 (Madras: College Press, 1825) [Google Books link] [epoch: 15/16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29] [check].
• Prinsep, James, Useful Tables, forming an Appendix to the Journal of the Asiatic Society. Part the Second: Chronological and Genealogical Tables of Ancient and Modern India, including a Chronological Table of the Principal Events of British Connection with India (Calcutta: Baptist Mission Press, 1836), pp. 13-14 & 56-64 [Internet Archive link] – table: 1 AH to 1318 AH; epoch: 16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29.
• Francoeur, Louis-Benjamin, “Sur le calendrier des mahométans”, Connaissance des Temps ou des Mouvements Célestes, à l’usage des astronomes et des navigateurs, pour l’an 1844 (Paris: Bachelier, 1841), Additions, pp. 111-122 [Gallica link] [epoch: 16 July 622 CE].
• Wüstenfeld, Ferdinand, Vergleichungs-Tabellen der Muhammedanischen und Christlichen Zeitrechnung, nach dem ersten Tage jedes Muhammedanischen Monats berechnet (Leipzig: F.A. Brockhaus, 1854) [Google Books link] – tables for 1 AH to 1300 AH – reprinted with errata in 1903 [Internet Archive link].
• Patell, Cowasjee Sorabjee, Chronology, containing Corresponding Dates of the Different Eras used by Christians, Jews, Greeks, Hindus, Mohamedans, Parsees, Chinese, Japanese, &c. (London: Trübner and Co., 1866), pp. 34-35, 50-53, 60, 78 & General Table I [Google Books link] [tables: 1 AH to 1421 AH; epoch: 16 July 622 CE [astronomers 15 July 622 CE]; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29].
• Cunningham, Alexander, Book of Indian Eras, with Tables for Calculating Indian Dates (Calcutta: Thacker, Spink & Co., 1883), pp. 66-70 & 118-134 – epoch: 16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29 [Internet Archive link].
• Mahler, Eduard, Fortsetzung der Wüstenfeld’schen Vergleichungs-Tabellen der Muhammedanischen und Christlichen Zeitrechnung (von 1300 bis 1500 der Hedschra) (Leipzig: F.A. Brockhaus, 1887) [Internet Archive link [2nd part]].
• Burnaby, Sherrad Beaumont, Elements of the Jewish and Muhammadan Calendars with Rules and Tables and Explanatory Notes on the Julian and Gregorian Calendars (London: George Bell & Son, 1901) [Internet Archive link] [epoch: 16 July, 622].
• Mahler, Eduard, Wüstenfeld-Mahler’sche Vergleichungs-Tabellen der mohammedanischen und christlichen Zeitrechnung: Zweite Auflage. Im Auftrage der DMG. neu redigiert sowie mit einem Anhange: “Das türkische Sonnenjahr” erweitert und auf deren Kosten herausgegeben (Leipzig: Deutsche Morgenländische Gesellschaft, 1926) [table: 1 AH to 1500 AH; epoch: 16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29] [Internet Archive link].
• Cappelli, Adriano, Cronologia, Cronografia e Calendario Perpetuo dal principio dell’Êra Cristiana ai giorni nostri: Tavole cronologico-sincrone e quadri sinottici per verificare le date storiche. Seconda edizione interamente rifatta ed ampliata (Milan: Ulrico Hoepli, 1930), pp. 22 & 169-176 [table: 1 to 1421 AH; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29; epoch: 16 July 622].
• Haig, Wolseley, Comparative Tables of Muhammadan and Christian Dates: Enabling One to Find the Exact Equivalent of any Day in any Month from the Beginning of the Muhammedan Era (London: Luzac and Co., 1932) [tables: 1 AH to 1421 AH; epoch: 16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29].
• Zinner, Ernst, “Die Tafeln von Toledo (Tabulae Toletanae)”, Osiris, 1 (1936), 747-774 [JSTOR link].
• Ocaña Jiménez, Manuel, Tablas de conversión de datas islámicas y cristianas y viceversa: Fundamentadas en nuevas fórmulas de coordinación y compulsa (Madrid/Granada: Consejo Superior de Investigaciones Científicas, 1946) [Internet Archive link] – from 1 AH to 1650 AH; intercalary years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29; epoch 16 July 622 CE – an updated edition was published as: Nuevas tablas de conversión de datas islámicas y cristianas y viceversa: Estructuradas para concordar, día por día, años completos (Madrid: Instituto Hispano-árabe de Cultura, 1981).
• Unat, Faik Reşit, Hicrî Tarihleri Milâdî Tarihe çevirme Kılavuzu (Ankara: Maarif Matbaası, 1943) [Internet Archive link of the 6th (1988) edition] [epoch = 16 July 622; based on Wüstenfeld?].
• Mayr, Joachim & Spuler, Bertold, Wüstenfeld-Mahler’sche Vergleichungs-Tabellen zur muslimischen und iranischen Zeitrechnung mit Tafeln zur Umrechnung orient-christlicher ären (Wiesbaden: Deutsche Morgenländische Gesellschaft, 1961), 3rd ed.
• Freeman-Grenville, Greville Stewart Parker, The Muslim and Christian Calendars, being Tables for the Conversion of Muslim and Christian Dates from the Hijra to the Year A.D. 2000 (London [etc.]: Oxford University Press, 1963) – tables: 1 to 1421 AH; epoch: 16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29.
• Toomer, G.J., “A Survey of the Toledan Tables”, Osiris, 15 (1968), 5-174 [JSTOR link].
• Tsybulsky, Vladimir Vasiljewich, Calendars of Middle East Countries: Conversion Tables and Explanatory Notes (Moscow: Nauka Publishing House/Central Department of Oriental Literature, 1979) – tables: 1 AH to 1421 AH; epoch: 16 July 622 CE; intercalary years: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29 – the original Russian edition was published in 1976.
• Meeus, Jean, Astronomical Tables of the Sun, Moon and the Planets (Richmond: Willmann-Bell, 1995), pp. ???-??? [epoch = ?? July 622 CE].
• Meeus, Jean, Astronomical Algorithms (Richmond: Willmann-Bell, 1998), 2nd ed., pp. 71-76 [epoch: 16 July 622 CE].

Type III [Intercalary years 2, 5, 8, 10, 13, 16, 19, 21, 24, 27 & 29]

• Scaliger, Joseph Justus, Opus novum de emendatione temporum in octo libros tributum (Paris: Robert Stephanus, 1583), pp. 94-104, 354-356, 378 & 415-416 – intercalary years: 2, 5, 8, 10, 13, 16, 19, 21, 24, 27 & 29 [BSB link].
• Riccioli, Giovanni Baptista, Chronologiæ Reformatæ et ad certas conclusiones redactæ (Bologna: Haeredis Dominici Barberij, 1659), pp. 53-60 [= lib. I, cap. xxiv].
• Riccioli, Giovanni Baptista, Astronomiæ Reformatæ tomi duo, quorum prior Observationes, Hypotheses, et Fundamenta Tabularum, posterior præcepta pro usu Tabularum Astronomicarum, et ipsas Tabulas Astronomicas CII. continet (Bologna: Haeredis Victorij Benatij, 1665), vol. 2, p. 9 & tab. 20-21 [epoch: 16 July 622 CE; intercalary years: 2, 5, 8, 10, 13, 16, 19, 21, 24, 27 & 29 [or 30]].
• Jervis, Thomas Best, The Expediency and Facility of establishing the Metrological and Monetary Systems throughout India, on a Scientific and Permanent Basis, grounded on an Analytical Review of the Weights, Measures, and Coins of India, and their Relative Quantities with respect to such as subsist at Present, or have hitherto subsisted in all Past Ages throughout the World: In Connexion with which, the Measures of Time, on Elementary Principles of Technical Chronology of Eastern Nations, are investigated, explained, and now for the First Time referred to their Proper Originals (Bombay: American Mission Press, 1834) [Google Books link] [check].

Type ?? [Intercalary years 2, 5, 8, 10, 13, 16, 18, 21, 24, 26 & 29]

• Sauvaire, H. & de Rey Pailhade, J., “Sur une mère d’astrolabe arabe du XIIIe siècle (609 de l’hégire) portant un calendrier perpétuel avec correspondance musulmane et chrétienne: Traduction et interprétation”, Journal asiatique, ou recueil de mémoires, d’extraits et de notices relatifs à l’histoire, à la philosphie, aux langues et à la littérature des peuples orientaux, série 9, 1 (1893), 5-76 & 185-231 [Gallica link].

[as yet unplaced]

• Calvisius, Sethus, Opus Chronologicum, ex autoritate potissimùm Sacræ Scripturæ et Historicorum fide dignissimorum, ad motum luminarium cœlestium, tempora & annos distinguentium, secundùm characteres Chronologicos contextum, trecentis ferê Eclipsibus annotatis confirmatum, & deductum usq[uam] nostra tempora. Cui præmissa est Isagoge Chronologica, in quâ cùm Tempus Astronomicum de numerandis motibus Luminarium cœlestium, & eorundem Eclipsibus; tum diversæ diversorum in omnibus Epochis annorum quantitates & formæ dilucidè explicantur, characteres infallibiles ostenduntur, & quid in unaquaq[ue] Epocha verum falsumvé sic, ex veris fundamentis Chronologicis apertè demonstratur. Editio altera & auctior & correctior (Frankfurt an der Oder: Johannes Thiem, 1620), pp. 90-93 – epoch: 15 July 622 CE; intercalary years: 2, 5, 8, 11, 13, 16, 19, 21, 24, 27 & 29 [E-RARA link].
• Kepler, Johannes, Tabulæ Rudolphinæ, quibus Astronomicæ Scientiæ, temporum longinquitate collapsæ Restauratio continetur; a Phœnice illo Astronomorum Tychone, Ex Illustri & Generosa Braheorum in Regno Daniæ familiá oriundo Equite [...] (Ulm: Jonas Saurius, 1627), pp. 47-49 & table 39 [??? link] [epoch: 16 July 622 CE; intercalary years: 2, 5, 8, 11, 13, 16, 19, 21, 24, 27 & 30].
• Petau, Dennis, De Doctrina Temporum (Paris: ???, 1627), pp. ???-??? [= lib. VII, cap. 22].
• d’Herbelot de Molainville, Barthélemy, Bibliothèque orientale, ou dictionaire universel contenant generalement tout ce qui regarde la connoissance des peuples de l’orient (Paris: Compagnie des Libraires, 1697), pp. 444-445 & 857 [Gallica link].
• Strauchius, G., Breviarium Chronologicum, Being a Treatise Describing the Terms and Most Celebrated Characters, Periods and Epocha’s us’d in Chronology, by which that Useful Science may easily be attained to (London: A. Bosvile & P. Gilburne, 1699), pp. 473-474 [EEBO link].
• Bernoulli, ???.
• Petau, Dennis, Rationarium temporum, editio novissima (Venice: Laurentium Basilium, 1733), vol. 2, pp. 22, 50 & 268 [Bizkaia link] [epoch = 16 July 622].
• Langlet du Dufresnoy, Nicolas, Chronological Tables of Universal History, Sacred and Profane, Ecclesiastical and Civil; from the Creation of the World, to the Year One thousand Seven hundred and Forty-three. With a Preliminary Discourse on the Short Method of Studying History; and a Catalogue of Books necessary for that Purpose; with some Remarks on them (London: A. Millar [etc.], 1762), vol. 1, pp. xci-xciii & 305-320 [ECCO link].
• Playfair, James, A System of Chronology: containing, I. An explanation of the principles of this science; together with an account of the most remarkable epochs, aeras and periods, the dates and extent of which are ascertained. II. A chronological history, which exhibits a connected view of the time, mode, and circumstances of the origin, progress, decline, and fall of every considerable kingdom, from the earliest period to the present. III. A list of several eclipses before the Christian aera, observed by astronomers, or recorded by historians and of all eclipses from A.D. 1, to A.D. 1900 [...] IV. A chronological list of councils [...] V. Chronological tables and charts from B.C. 2300 to A.D. 1784, adapted to a scale and ascertaining the duration of the lives and reigns of the most eminent personages in all ages. VI. A list of remarkable events and occurrences relating to every kingdom and nation [...] with the dates of many celestial phaenomena. VII. Supplemental tables [...] VIII. A copious biographical index (Edinburgh: W. Creech, 1784) [ECCO link].
• Soliman-el-Haraīri & Cotelle, Henri, “Concordance entre le calendrier musulman et le calendrier chrétien”, Journal asiatique, ou recueil de mémoires, d’extraits et de notices relatifs à l’histoire, à la philosophie, aux langues et à la littérature des peuples orientaux, sér. 4, 10 (1847), 249-258 [Gallica link] – reprinted in F. Sezgin, Calendars and Chronology in the Islamic World: Texts and Studies I (Frankfurt am Main: Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998 [= Publications of the Institute for the History of Arabic-Islamic Science, Islamic Mathematics and Astronomy, nr. 64]), pp. 241-250.
• von Gumpach, Johannes, Practical Tables for the Reduction of Mahometan Dates to the Christian Kalendar, Computed for the Use of Astronomers, Chronologers, Historians, Diplomatists, Political and Consular Agents, Merchants, Travellers and Sojourners in the East, and Others, with an Introduction including some Special Remarks on the Turkish Kalendar (London: Madden, 1856) [Internet Archive link] [check].
• Martin, René, Mémoire sur le calendrier musulman et sur le calendrier hébraïque. Première partie: Sur le calendrier musulman et rectification des formules du P. Pétau, de Nicolas Muler, de Ciccolini et du baron de Zach (Paris: Mallet-Bachelier, 1857) [Google Books link] – the second part, on the Jewish calendar, was published in 1863.
• Brown, Charles Philip, Carnatic Chronology: The Hindu and Mahomedan Methods of Reckoning Time Explained. With Essays on the Systems, Symbols used for Numerals, a New Titular Method of Memory, Historical Records, and Other Subjects (London: Bernard Quaritch, 1863) [Internet Archive link] [check].
• Schram, Robert Gustav, “Hilfstafeln für Chronologie”, Denkschriften der mathematisch-naturwissenschaftliche Classe der kaiserlichen Akademie der Wissenschaften zu Wien, 45 (1883), 289-360 [Internet Archive link].
• Mas Latrie, Louis de, Trésor de chronologie, d’histoire et de géographie pour l’étude et l’emploi des documents du moyen age (Paris: Librairie Victor Palmé, 1889), cols. 41-46 [Gallica link] & 549-622 [Gallica link] [follows Wüstenfeld].
• Lacoine, Émile, Tables de concordance des dates des calendriers arabe, copte, grégorien, israélite, julien, républicain, etc., établies d’après une nouvelle méthode (Paris: Librairie Polytechnique Baudry et Cie, 1891) [Internet Archive link].
• Sewell, Robert, Dīksit, Śankara Bālakrisna & Schram, Robert Gustav, The Indian Calendar with Tables for the Conversion of Hindu and Muhammadan into A.D. Dates, and vice versâ, with Tables of Eclipses visible in India (London: Swan Sonnenschein & Co., 1896) [Internet Archive link] [2, 5, 7, 10, 13, 15/16, 18, 21, 24, 26 & 29, or, according to Thomas Best Jervis, 2, 5, 8, 10, 13, 16, 19, 21, 24, 27 & 29].
• Schram, Robert Gustav, Kalendariographische und chronologische Tafeln (Leipzig: J.C. Hinrichs’sche Buchhandlung, 1908) [??? link].
• Delaporte, Louis-Joseph, La chronographie d’Élie bar-Šinaya, métropolitain de Nisibe, traduite pour la première fois d’après le manuscrit Add. 7197 du Musée Britannique (Paris: Librairie Honoré Champion, 1910 [= Bibliothèque de l’École des Hautes Études, Sciences historiques et philologiques, fasc. 181]) [Internet Archive link].
• Svami-Kunnu Pillai, Lewis Dominic, Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-Records, B.C. 1 to A.D. 2000 (Madras: Grant & Co., 1911).
• Svami-Kunnu Pillai, Lewis Dominic, An Indian Ephemeris, A.D. 1800 to A.D. 2000; Showing, for Every Day in the Year for Two Hundred Years the Ending Moments of Tithis and Nakshatras with the English, Tamil, Malayalam and Muhammadan Equivalents; and for Every Ten Days, from A.D. 1800 to A.D. 2000, the Geocentric Longitudes of Planets, mainly according to the Sûrya Siddhânta; also the Years in Different Eras, A.D., Hijra, Śaka, Vikrama, Kaliyuga, Kollam, etc., and Tables for Ascertaining Local Time, with Full Instructions for casting Lagna & Horoscopes, and Tables of Hindu Fasts, Feasts and Festivals, and Solar and Lunar Eclipses (Madras: Government Press, 1915).
• Svami-Kunnu Pillai, Lewis Dominic, An Indian Ephemeris, A.D. 700 to A.D. 1799; Showing, the Daily Solar and Lunar Reckoning according to the Principal Systems current in India, with their English Equivalents, also the Ending Moments of Tithis and Nakshatras and the Years in different Eras, A.D., Hijra, Saka, Vikrama, Kaliyuga, Kollam, etc., with a Perpetual Planetary Almanac and other Auxiliary Tables (Madras: Government Press, 1922), 6 vols.
• Arvanitakis, G.L., “Note sur le calendrier musulman”, Bulletin de l’Institut d’Égypte, 16 (1934), 111-114.
• Neugebauer, Paul Victor, “Hilfstafeln zur technischen Chronologie: Teil III. Die Zeitrechnung der Mohamedaner. Die Festrechnung des Mittelalters und der Neuzeit”, Astronomische Nachrichten, 261 (1937), 461-524 [nr. 6264] [ADS link] – tables for types I & II.
• Ocaña Jiménez, Manuel, “Notas sobre cronología hispano-musulmana”, Al-Andalus, 8 (1943), 333-381.
• Cattenoz, Henri Georges, Tables de concordance des ères chrétienne et hégirienne (???: ???, 1945) – reprinted by Les Éditions Techniques Nord-Africaines (Rabat/Casablanca) in 1954 [also in 1952?] (2nd ed.) and 1961 (3rd ed.).
• Grumel, Victor, Traité d’études Byzantines: I. La chronologie (Paris: Presses Universitaires de France, 1958 [= Bibliothèque Byzantine]).
• Pingree, David Edwin, “The Fragments of the Works of Al-Fazārī”, Journal of Near Eastern Studies, 29 (1970), 103-123 [JSTOR link] [intercalary years according to Yahya/al-Khwārizmī: 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29; intercalary years according to Habash: 3, 6, 8, 11, 13, 16, 19, 21, 24, 27 & 30].
• Gossler, Marcus, “Basisformeln zur programmierten Umrechnung einiger astronomischer Kalendertypen”, Astronomische Nachrichten, 301 (1980), 191-194 [ADS link] – algorithms for types I & II.
• Ubieto Artur, Antonio-Paulo, Tablas teóricas de equivalencia diaria entre los calendarios islámico y cristiano / Theoretical Tables of Daily Equivalence between the Islamic and Christian Calendars (Zaragoza: Anubar, 1984), 2 vols. – tables for 1 AH to 1500 AH.
• Hatcher, D.A., “Generalized Equations for Julian Day Numbers and Calendar Dates”, Quarterly Journal of the Royal Astronomical Society, 26 (1985), 151-155 [ADS link].
• Birashk, Ahmad, A Comparative Calendar of the Iranian, Muslim Lunar, and Christian Eras for Three Thousand Years (1260 B.H. – 2000 A.H. / 639 B.C. – 2621 A.D.) (Costa Mesa: Mazda Publishers, 1993).
• Freeman-Grenville, Greville Stewart Parker, The Islamic and Christian Calendars A.D. 622-2222 (A.H. 1-1650): A Complete Guide for Converting Christian and Islamic Dates and Dates of Festivals (Reading: Garnet Publications, 1995), 3rd. ed.
• Neugebauer, Otto E. – works Abu Shaker.
• Ansari, Shahabuddin & Jinnah, M.M., Interchanging Muslim and Christian Era Dates: A Handbook of Precisely Synchronizing Hijrah Era dates with the Christian Era Dates and vice verca from 60 B.H. to 2100 A.H. (564 A.D. to 2659 A.D.), together with to Ascertain the Day of the Week of any pre-Hijrah, post-Hijrah, Julian and Gregorian Calendar Dates (Kanpur/Delhi: Islam Research Centre/B.R. Publ. Co., 2007).

Conversion Tables or Algorithms based on the Visibility of the Lunar Crescent

• Ilyas, Muhammad, Astronomy of Islamic Times for the Twenty-First Century (London/New York: Mansell Publ., 1988).
• Reingold, Edward M. & Dershowitz, Nachum, Calendrical Calculations: The Millennium Edition (Cambridge: Cambridge University Press, 2001), chapter 6.
• Reingold, Edward M. & Dershowitz, Nachum, Calendrical Tabulations 1900-2200 (Cambridge: Cambridge University Press, 2002).
• Ahmed, Fadhl N.M., 2000 Years Civil Hijri Comparative Calendar (Lexington: ???, 2012) [Internet Archive link].

Relevant Entries in The Encyclopaedia of Islam: New Edition (Leiden: E.J. Brill, 1960-2004).

• “‘Īd/‘Īd al-Adhā/‘Īd al-Fitr”, vol. 3 (1971), pp. 1007-1008 [Eugen Mittwoch].
• “Mi‘rādj”, vol. 7 (1993), pp. 97-105 [various authors].
• “Ramaḍān”, vol. 8 (1995), pp. 417-418 [Martin M. Plessner].
• “Sawm”, vol. 9 (1997), pp. 94-95 [Cornelis Christiaan Berg].
• “Ta’rīkh”, vol. 10 (2000), pp. 257-271 [François C. de Blois & Benno van Dalen].