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Ancient Chronology Calculators

Calculators Coded by Jefferson Williams combined with External Calculators not coded by JW

Julian Day

Julian Day Calculations allow you to figure out the day of the week.


Day Month Year Local
Specify E or W
1 - East
2 - West
Julian Day
(12 hour UT)
Julian Day

Hover over underlined variables for pop up explanations. The calculator above computes Julian Day and day of the week for the Julian and Gregorian calendars and is valid from noon 1 January 4713 BCE until present. In these calendars, a new day begins at midnight. Lunar and lunisolar local calendars (e.g., Islamic, Hebrew, Syriac, and Coptic Liturgical Calendars) start their day at night fall and solar calendars (e.g., Coptic Civil Calendar) start their day at sunrise. Make adjustments to the day of the week accordingly (see illustration below).

Days of the Week in different calendars Days of the Week in different calendars

illustration by Jefferson Williams


Meeus, J. (1991). Astronomical algorithms. Richmond, Virginia USA, Willmann-Bell Inc., pages 60-65

timeprophecy.com - makes a nice detailed calculation of JD, Day of Week, Moonrise, Moonset, Sunrise, Sunset, etc. and is seamlessly valid for Julian and Gregorian calendar time periods

fourmilab computes JD - fourmilab computes Julian Day at UT zero hour (not 12). It has seperate entry forms for the Julian and Gregorian Calendars.


Algorithmic Notes

  • The Julian Day starts at 0.0 at noon on 1 January 4713 BCE (-4712 in astronomical years)
Meeus (1991:59-62) notes that
The Julian Day number or, more simply, the Julian Day (JD) is a continuous count of days and fractions thereof from the beginning of the year —4712. By tradition, the Julian Day begins at Greenwich mean noon, that is, at 12h Universal Time. If the JD corresponds to an instant measured in the uniform scale of Dynamical Time, the expression Julian Ephemeris Day (JDE) is often used. For example,

1977 April 26.4 UT = JD 2443 259.9
1977 April 26.4 TD = JDE 2443 259.9
In the methods described below, the Gregorian calendar reform is taken into account. Thus, the day following 1582 October 4 (Julian calendar) is 1582 October 15 (Gregorian calendar).

The Gregorian calendar was not at once officially adopted by all countries. This should be kept in mind when making historical research. In Great Britain, for instance, the change was made as late as in 1752, and in Turkey not before 1927.


There is a disagreement between astronomers and historians about how to count the years preceding the year 1. In this book, the "B.C." years are counted astronomically. Thus, the year before the year +1 is the year zero, and -the year preceding the latter is the year —1. The year which the historians call 585 B.C. is actually the year —584. (Do not use the mention "B.C." when using negative years! " —584 B.C.", for instance, is incorrect.) [JW: This is accounted for in the Calculator so one should enter historical years]

The astronomical counting of the negative years is the only one suitable for arithmetical purposes. For example, in the historical practice of counting, the rule of divisibility by 4 revealing the Julian leap years no longer exists; these years are, indeed, 1, 5, 9, 13, ... B.C. In the astronomical sequence, however, these leap years are called 0, -4, -8, —12 , and the rule of divisibility by 4 subsists.


take care when using the INT function for negative numbers.


The week was not modified in any way by the Gregorian reform of the Julian calendar. Thus, in 1582, Thursday October 4 was followed by Friday October 15.


When is a given year a leap year ?

In the Julian calendar, a year is a leap (or bissextile) year of 366 days if its numerical designation is divisible by 4. All other years are common years (365 days).

For instance, the years 900 and 1236 were bissextile years, while 750 and 1429 were common years.

The same rule holds in the Gregorian calendar, with the following exception : the centurial years that are not divisible by 400, such as 1700, 1800, 1900, 2100, are common years. The other century years, which are divisible by 400, are leap years, for instance 1600, 2000, and 2400.

Longitude Table

Location Approx. Longitude
Cairo 31.3
Jerusalem 35.3
Beirut 35.5
Antioch 36.2
Damascus 36.3
Edessa (Sanliurfa) 38.8
Mabbug (Manbij) 38.0
Baghdad 44.4
Tabuk 36.6
Medina 39.6
Mecca 39.8

Anno Mundi (A.M.)

A.M. – Anno Mundi. This calendar was used by several of the Byzantine authors including Theophanes and Anastasius Bibliothecarius. The calendar is based on the Julian calendar however the year does not begin on 1 January and the starting day, month, and year of this calendar was a point of contention as it was based on an estimate for the start of "creation" (among other things) as interpreted through the Septuagint - a Greek translation of the Old Testament. An ongoing several hundred year long theological debate over when Biblical "creation" began led to multiple versions of the A.M. calendar. The earlier Byzantine sources used the Alexandrian version (A.M.a) or “Alexandrian era” of this calendar which has a starting date of 25 March 5492 BCE or, according to Bickerman (1980), 25 March 5493 BCE. Earthquake catalogers Guidoboni et al (1994) and Ambraseys (2009) assume a starting date of 25 March 5492 BCE and that is what I use. As explained by Grumel (1958:219)

The Alexandrian era of Panodorus began in 5493 BCE [and] the Alexandrian era of Annianos began in 5492 BCE. The Alexandrian Era of Annianos is what is commonly called the Alexandrian era.
Another reckoning system, used for example by Megas Chronographos, is the Byzantine version (A.M.Byz) which has a starting date of 1 September 5509 BCE (Bickerman, 1980:73-74). Yet another reckoning system is a variant suggested in Chronicon Paschale which was composed in ~630 CE. The starting date for this system is 21 March, 5507 BCE. In the Anno Mundi calendar system used by the Byzantine authors, the day followed the Roman civil custom of beginning the calendarical day at midnight. When hours are indicated they mark time since dawn. Hence, if daybreak began at 6 am, the 4th hour would correspond to 10 am (Rautman, 2007:3).

Calendaric Inconsistencies of Individual Authors

Author Inconsistencies
Theophanes Theophanes used the Alexandrian version of the Anno Mundi calendar even though it was out of favor at the time and would be obsolete by the 9th century CE. He did so because his Chronicle was a continuation of George Syncellus Chronicle which itself used the Alexandrian version of the Anno Mundi calendar. Proudfoot (1974:374) noted that the problem of whether Theophanes regarded the year as commencing on March 25 according to the Alexandrian world-year or on September 1 according to the Byzantine indiction cycle has not been resolved with [] clarity.
Theophanes Grumel (1934:407), Proudfoot (1974:373-374), and others have pointed out that Theophanes A.M.a in the years A.M.a 6102-6206 and A.M.a 6218-6265 are frequently a year too low. The indictions, however, are thought by many more likely to be correct.

Grumel's (1934:398-402) synchronisms
Synchronism Explanation
MA Theophanes’s indictions begin in March - the start date for A.M.a
MB Theophanes’s indictions begin in September after the March starting date for A.M.a
Note: Outside of Egypt, Indictions began in 1 September
Grumel's (1934:398-402) synchronisms by time period
Synchronism Years A.M.a (approx.) Date Range CE Historical Markers
MA ? - 6102 ? - 5 Oct. 610 until the end of the reign of Phocas (ruled 23 Nov. 602 – 5 Oct. 610 CE)
MB 6102 - 6206 5 Oct. 610 - 3 June 713 starting with the reign of Heraclius (ruled 5 Oct. 610 – 11 Feb. 641 CE) and ending right before the start of the reign of Anastasios II (aka Artemios) (ruled from 4 June 713 – 4 June 715 CE)
MA 6206 - 6220 4 June 713 CE - 24 March 728 starting with the reign of Anastasios II (aka Artemios) (ruled from 4 June 713 – 4 June 715 CE) until A.M.a 6220
MB 6221 - 6266 1 Sept. 728 - 31 Aug. 774 A.M.a6221 - 6266
MA 6267 - ? 25 March 774 - ? A.M.a6267 - ?
Martin (1930:12-13) states the following:
The indiction runs from Sept. 1st, the Alexandrian A.M. from March 25th, but Theophanes probably dates the latter for calendar purposes from Sept. 1st2, to correspond with the Indiction.
In two periods (607-714 and 726-774) the A.M. and the indictions do not correspond 3. It was formerly supposed that the Indictions were most likely to be correct, and therefore they must be made the foundation for a true chronology. But a suggestion was made by Bury (Later Roman Empire, II, p. 425). and worked out by Hubert (Byzant. Zeitschrift, VI, pp. 491 sqq.), that in 726 Leo III raised double taxes and put two indictions in one year, while in 774 or 775, Constantine remitted a year's taxation and spread one indiction over two years. This suggestion has been generally accepted. On the other hand, it is purely conjectural. Ginis (Das Promulgationsjahr d. Isuar. Ecloge. Byz. Zeitsch., XXIV, pp. 346 sqq.) would trace the error to Theophanes having confused the April of Indiction 10 (Sept. 1st, 726, to Aug. 31st, 727), with April of the 10th regnal year of Leo (March 25th, 725, to March 24th, 726). E.W. Brooks (Byz. Zeitsch., VIII, pp. 82 sqq.) explains the error by differences in the chronological systems of the sources used by Theophanes.

Calculator - not fully QCED

Alexandrian fully QCed, Byzantine partly QCed and Chronicon Pachale not QCed

Enter A.M. Year Specify Reckoning
1 - Alexandrian
2 - Byzantine
3 - Chronicon Paschale
Chosen Reckoning Time Span in the Julian Calendar


Indictions - An indiction (Latin: indictio, impost) was a periodic reassessment of taxation in the Roman Empire which took place every fifteen years. In Late Antiquity, this 15-year cycle began to be used to date documents and it continued to be used for this purpose in Medieval Europe. Indictions refer to an individual year in the 15 year cycle; for example, "the fourth indiction" came to mean the fourth year of the current indiction. Since the cycles themselves were not numbered, other information is needed to identify the specific year. When an ancient author supplies an indiction along with an A.M. date, the result may be greater chronological precision. For our dating purposes, indictions began in 312 CE when they were introduced by the Roman Emperor Constantine. The indiction was first used to date documents unrelated to tax collection in the mid-fourth century. By the late fourth century it was being used to date documents throughout the Mediterranean. In 537 CE, Roman Emperor Justinian decreed that all dates must include the indiction.Outside of Egypt, the year of the indiction generally began on 1 September (Bickerman, 1980:78).


Input Start Year (CE) Notes
Invalid before 312 CE
Indiction Year (CE) Indiction Time Span outside of Egypt

Regnal Years

Regnal Year Start Day Start Month Start Year (CE) Time Span in the Julian Calendar

Seleucid Era including the Syriac Calendar (A.G. - Anno Graecorum)

The Anno Graecorum (A.G.) Calendar is also known as the Seleucid Era, Chaldean, or the Macedonian Calendar. This calendar began at the start of the Seleucid Empire and was assimilated into the Babylonian calendar with Macedonian month-names sometimes substituted for the Babylonian names (Stern, 2012:238). The A.G. calendar uses the same 19 year cycle of intercalations as the Babylonian calendar. There are two start dates. The Macedonian reckoning used by court officials in the Seleucid Empire and native Greek speakers started in the Autumn of 312 BCE with the start date eventually getting fixed to 1 Oct. 312 BCE. The Babylonian reckoning used by most Semitic speaking populations has a start date of 1 Nisan in 311 BCE. Ambraseys (2009) equates this to 1 April, Guidoboni et al (1994) equate this with 2 April, and others equate it to 3 April. A version of the A.G. calendar was used by the Christian Syriac authors such as Pseudo-Dionysius of Tell Mahre and Chronicon Ad Annum 1234. Syriac writing authors would have likely used the Macedonian reckoning as this was the standard usage among these authors for the Seleucid era (Sebastian Brock, personal communication, 2021 – see also Stern, 2012:236). In the Anno Graecorum calendar system, the day starts at sundown (Sebastian Brock, personal communication, 2022).

Macedonian Months and Julian equivalent dates
Sources: Meimaris and Kritikakou (2005) and Theodossiou et al (1997)
Macedonian Month Julian Equivalent Duration (days)
Xanthikos 22 March - 20 April 29
Artemisios 21 April - 20 May 30
Daisios 21 May - 19 June 29
Panemos 20 June - 19 July 30
Loos 20 July - 18 Aug. 29
Gorpiaios 19 Aug. - 17 Sept. 30
Hyperberetaios 18 Sept. - 17 Oct. 29
Dios 18 Oct. - 16 Nov. 30
Apellaios 17 Nov. - 16 Dec. 29
Audynaios 17 Dec. - 15 Jan. 30
Peritios 16 Jan. 14 Febr. 29
Dystros 15 Febr. - 16 March 30
Epagomenai 17 March - 21 March 5


Enter A.G. Year Specify Reckoning
1 - Macedonian
2 - Babylonian
Chosen Reckoning Time Span in the Julian Calendar

Islamic (A.H. - Anno Hegirae)

A.H. – Anno Hegirae is also known as the Muslim Calendar or the Islamic lunar calendar. The start date is the Hijra - when on Friday 16 July 622 CE, Mohammed and his followers migrated from Mecca to Medina. The calendar consists of 12 alternating months of 30 and 29 days. Although the original calendar determined the start of each month based on astronomical observation of the first visible crescent after a new moon, a fixed tabular calendar was developed in the 8th century CE. In the tabular calendar, a day is added to the final (12th) month during leap years making it 30 days long instead of 29. Leap days are added every 2-3 years in a 30 year cycle which is subject to local variation. The most common distribution is on the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th, and 29th year of each 30-year cycle (timeanddate.com). The Islamic day begins at sundown.


from fourmilab

Coptic (A.M. - Anno Martyrum)

The Coptic Calendar is also known as the Alexandrian Calendar. The Coptic Calendar is coordinated with the Julian Calendar and, since the 4th century CE, used a starting year (Year 1) from 29 August 284 CE to 28 August 285 CE. A year consists of 13 months where the first 12 months have 30 days each followed an epagomenal month which has 5 days during normal years and 6 days during leap years. This version of the Coptic calendar is frequently called the Era of Martyrs and is frequently abbreviated as A.M. (Anno Martyrum). Coptic Leap Years are coordinated with Julian leap years however the coptic leap day is added on the last day of the coptic year rather than on 29 February. If a Coptic year will encompass a Julian Leap year (i.e. a year where there will be a February 29), the coptic year will start on 30 August instead of 29 August as 29 August in the previous Coptic year will be a leap day. In years such as this, the coptic day will be a day ahead of the Julian Calendar until 29 February. Thus, for example while 21 Tuba normally corresponds to 16 January, in a Julian Leap Year it will correspond to 17 January. The Coptic day begins at sunrise in the civil calendar and sunset in the liturgical version (Claremont Coptic Encyclopedia).


The Hebrew Calendar is also known as the Jewish Calendar or HaLuah HaIvri (הַלּוּחַ הָעִבְרִי) in Hebrew. The Hebrew Calendar is a lunisolar calendar influenced by the Ancient Babylonian Calendar which has undergone revisions over time. Initially, this calendar was based on sightings of the first crescent after the new moon. After the destruction of the 2nd temple in 70 CE and throughout the diaspora, the calendar was subject to local variations. By the 4th century CE, a calendar had emerged which was increasingly based on predicted lunar cycles. Sometime before the 8th century, a fixed 19 year Metonic cycle of intercalations similar to the Babylonian cycle was adopted and by the early 10th century, the rabbinic calendar had become like the fixed and predictable calendar that is used today. (Stern, 2012:334-335), The structure of the Hebrew Calendar is one of 12 months with an additional intercalary month added in years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle along with a complicated set of rules (Reingold and Dershowitz, 2018:Section 8.1). The modern Hebrew Calendar is also characterized by a change in the start date of the calendar from the destruction of the second Temple in 70 CE to the start of “creation” like the Anno Mundi Calendar of the Byzantines. In the Hebrew Calendar, the day begins at sundown.

Modern Hebrew Calendar Rules from Stern (2001:191-193)

4.4.1 The Present-Day Rabbinic Calendar: An Outline

  1. The conjunction (molad) is calculated on the basis of two values
    1. the mean lunation (duration of the lunar month) of 29 days, 12 hours, and 793 parts (there are 1080 parts to an hour).
    2. molad of Tishre year 1 (of the era of creation, i.e. the first Tishre in ‘history’), which is given as 2nd day (Monday), 5 hours (of the 24-hour period beginning in the evening), 204 parts, or in its Hebrew acronym: (BaHaRaD). This corresponds to Sunday, 6 October 3761 BCE at 23 hours, 11 minutes, and 20 seconds (assuming the day begins at 18 hours). The molad of Tishre year 1 functions as an epoch (reference point). Any subsequent molad can be worked out by adding the right number of lunations to this epoch. As an alternative to BaHaRaD, the molad of the following Tishre (year 2) can also be used. This molad is 6th day (Friday), 14 hours, no parts (acronym: WeYaD).The fact that this epoch is a round figure (with no parts of the hour) suggests that this was the original epoch to have been in use.
  2. The month begins, apriori, on the day of the molad. Sometimes it is postponed by one or more days, because of the rules that follow (iii–iv), which are hence known as ‘postponement’ rules.
  3. Rosh ha-Shanah, 1 Tishre, cannot occur on Sunday, Wednesday, on Friday. This rule is known by its Hebrew mnemonic: (lo ADURosh). If the molad of Tishre occurs on any of these days, the 1st of the month must be postponed.
  4. If the molad of Tishre occurs on or after the 18th hour (i.e. midday), the 1st of the month must be postponed. (footnote: If the following day is either Sunday, Wednesday, or Friday, Rosh ha-Shanah must be postponed till the day after, hence a postponement of two days.) This is known as molad zaqen (‘late conjunction’).
  5. The calendar consists of a fixed alternation of 29 and 30 day months: there are always 30 days in Nisan, 29 days in Iyyar, etc. Only the months of Marḥeshwan and Kislew are subject to variation: they can be ‘regular’ (i. e. 29–30), ‘full’ (i.e. 30–30), or ‘defective’ (i.e. 29–29) . This variation makes it possible for rules (iii) and (iv) to be observed, i.e. for the subsequent Rosh ha-Shanah(s) (sometimes more than one year ahead) not to occur on the wrong days. This variation also makes it possible to compensate for the discrepancy between the mean lunation under rule (i)(a) and the average month length of 29½ days resulting from a pure alternation of 29- and 30-day months.
  6. The intercalation is based on a fixed 19-year cycle, which starts at year 1 (from the creation) and within which the following seven years are intercalated: 3, 6, 8, 11, 14, 17, 19. Intercalation consists of an additional 30-day month, which is inserted before Adar and called ‘first Adar’
From the late Geonic period until the present day, a number of tables and algorithms have been designed and formulated on the basis of these fundamental principles, so as to facilitate the calendar calculation and remove unnecessary complications. Among the earliest of these algorithms were the cycle attributed to R. Naḥshon (gaon of Sura, 871–9), and the table known as (‘four gates’ or ‘four parts’ table) which was already in existence and apparently widespread in R. Saadya's time. The ‘four parts table’ represents the earliest formulation of the normative rabbinic calendar, with which it corresponds down to the finest detail. All it requires is knowledge of the molad and of the cycle of intercalations; on this basis, calendar dates can be worked out with the greatest of ease.


from fourmilab. This converter uses modern Hebrew Calendar rules

Era of Province Arabia

The Era of Province Arabia (also called Bostran era, the era of Bostra, the Arabian era, or Provincial era) was a calendar era (year numbering) with an epoch (start date) corresponding to 22 March 106 AD. It was the official era of the Roman province of Arabia Petraea, introduced to replace dating by regnal years after the Roman annexation of the Nabataean Kingdom. It is named after the city of Bostra, which became the headquarters of the Sixth Legion stationed in the province.


Enter Year of Province Arabia Time Span in the Julian Calendar

Olympiads (Ol.)

The Era of the Olympiads was widely used in ancient texts and is based on the Greek Olympiads which were held every four years. The start date of this calendar is accepted by most modern scholars as 1 July 776 BCE (Finegan, 1998:93). Olympiads (abbreviated Ol.) are four years apart with 4 cycles specifying years within the Olympiad.


Enter Olympiad Year Enter Olympiad Cycle (1-4) Time Span in the Julian Calendar

Melkite Era of the Incarnation

Treiger (2015) describes this as follows:

6. The Melkite Era of the Incarnation

The honor of discovering the Melkite era of the Incarnation (AInc), in use from the eleventh to the fourteenth century, belongs to Samir Khalil Samir (Samir 1987). By looking at Melkite colophons where dates “to the divine Incarnation” (li-l-taǧassud al-ilāhī) are given alongside dates according to other eras, he discovered that AInc dates are 8-9 years ahead of AD dates. The conversion key is as follows:

1 January–31 August: AInc–8 = AD;
1 September–31 December: AInc–9 = AD.


Samir, Samir Khalil. “L’ère de l’Incarnation dans les manuscrits arabes melkites du 11e au 14esiècle.” Orientalia Christiana Periodica 53 (1987): 193-201

Calculator - Not QCed

Enter Melkite Year Time Span in the Julian Calendar

Year of the Incarnation (aka Divine Incarnation Year)

The year of the Incarnation was occassionally used by Theophanes and Anastasius Bibliothecarius (when copying from Theophanes ?). It has a start date of 9 CE (Martin, 1930:12).

Calculator - Not QCed

Enter Incarnation Year Time Span in the Julian Calendar

Astronomical Calculators
Calculator - Sunrise and Sunset

from Clear Sky Tonight - appears to use Julian Calendar prior to 1582 CE

Calculator - New Moon

from Clear Sky Tonight - appears to use Julian Calendar prior to 1582 CE

Calculator - Moonrise and Moonset

from Clear Sky Tonight - appears to use Julian Calendar prior to 1582 CE

Solar Eclipses

from imcee - in French - excellent. Other Calculators at imcee

Lunar Eclipses

from imcee - in French - excellent. Other Calculators at imcee

Miscellaneous References