Hebrew calendar

The Hebrew calendar (Template:Hebrew ha'luach ha'ivri) or Jewish calendar is a lunisolar calendar used by Jews. Today, the calendar is used predominantly for Jewish religious observances. It is used to determine the dates for Jewish holidays, and also to determine appropriate public reading of Torah portions, yahrzeits (dates to commemorate the death of a relative), and daily Psalm reading, among many ceremonial uses. In Israel, it is an official calendar for civil purposes and provides a framework for agriculture.

Originally the Hebrew calendar was used by Jews for all daily purposes, but following the conquest of Jerusalem by Pompey in 63 BCE (see also Iudaea province), Jews began additionally following the imperial civil calendar (which was decreed in 45 BCE) for civic matters such as the payment of taxes and dealings with government officials.

The Hebrew calendar has evolved over time. For example, until the Tannaitic period, the months were set by observation of a new crescent moon, with an additional month added every two or three years to keep Passover in the spring, again based on observation of natural events, namely the ripening of barley to reach the stage of "aviv" (nearly ripened crop). Through the Amoraic period and into the Geonic period, this system was displaced by mathematical rules. The principles and rules appear to have been settled by the time Maimonides compiled the Mishneh Torah.

Because of the roughly eleven-day difference between twelve lunar months and one solar year, the year lengths of the Hebrew calendar vary in a repeating 19-year Metonic cycle of 235 lunar months, with an intercalary lunar month added according to defined rules every two or three years, for a total of 7 times per 19 years. Seasonal references in the Hebrew calendar reflect its development in the region east of the Mediterranean and the times and climate of the Northern Hemisphere. The Hebrew calendar's year is longer by about 6 minutes and 25+²⁵/₅₇ seconds than the present-day mean solar year, so that every 224 years, the Hebrew calendar will fall a full day behind the modern fixed solar year, and about every 231 years it will fall a full day behind the Gregorian calendar year.

The present scheme of year numbers use the Anno Mundi epoch (Latin for "in the year of the world", Template:Hebrew), abbreviated AM or A.M.. Hebrew year 5769 corresponds to 30 September 2008 through 18 September 2009 according to the Gregorian calendar and the Hebrew year 5770 began at sundown on the evening of 18 September 2009 and will end on 8 September 2010.

Structure

The Jewish calendar is a lunisolar calendar, or "fixed lunar year", based on twelve lunar months of twenty-nine or thirty days, with an intercalary lunar month added seven times every nineteen years (once every two to three years) to synchronize the twelve lunar cycles with the slightly longer solar year. Each Jewish lunar month starts with the new moon. Although originally the new lunar crescent had to be observed and certified by witnesses, the timing of the new moon is now determined mathematically.

Concurrently there is a weekly cycle of seven days, mirroring the seven-day period of the Book of Genesis in which the world is created. The names for the days of the week, like those in the Creation story, are simply the day number within the week, with Shabbat being the seventh day. The Jewish day always runs from sunset to the next sunset; the formal adjustments used to specify a standard time and time zones are not relevant to the Jewish calendar.

The twelve regular months are: Nisan (30 days), Iyar (29 days), Sivan (30 days), Tammuz (29 days), Av (30 days), Elul (29 days), Tishrei (30 days), Cheshvan (29 or 30 days), Kislev (29 or 30 days), Tevet (29 days), Shevat (30 days), and Adar (29 days). In the leap years an additional month, Adar I (30 days) is added after Shevat, and the regular Adar is referred to as "Adar II".

The first month of the festival year is Nisan. 15 Nisan is the start of the festival of Pesach, corresponding to the full moon of Nisan. Pesach is a spring festival associated with the barley harvest, so the leap-month mentioned above is intercalated periodically to keep this festival in the northern hemisphere's spring season. Since the adoption of a fixed calendar, intercalations in the Hebrew calendar have been at fixed points in a 19-year cycle. Prior to this, the intercalation was determined empirically:

The year may be intercalated on three grounds: 'aviv [i.e.the ripeness of barley], fruits of trees, and the equinox. On two of these grounds it should be intercalated, but not on one of them alone.

The Bible designates Nisan, which it calls Aviv (Exodus 13:4), as the first month of the year (Exodus 12:2). At the same time, the season of the fall Festival of Booths (Sukkoth), is called "the end of the year" (Exodus 23:16). The Sabbatical year in which the land was to lie fallow, necessarily began at the time the winter barley and winter wheat would have been sown, in the fall. The Gezer calendar, an Israelite or Canaanite inscription ca. 900 BCE, also begins in the fall.

Modern practice follows the scheme described in the Mishnah: Rosh Hashanah, which means "the head of the year", and is celebrated in the month of Tishrei, is "the new year for years." This is when the numbered year changes, and most Jews today view Tishrei as the de facto beginning of the year.

Sources and history

The Tanakh contains several commandments related to the keeping of the calendar and the lunar cycle, and records changes that have taken place to the Hebrew calendar.

Day

For smaller units of time, see Measurement of hours below.

The Jewish day is of no fixed length. The Jewish day is modeled on the reference to "...there was evening and there was morning..." in the Creation story. Accordingly, it runs from sunset (start of "the evening") to the next sunset. However, some apply special rules at very high latitudes when the sun remains above or below the horizon for longer than a civil day.

There is no clock in the Jewish scheme, so that a civil clock is used. Though the civil clock incorporates local adoptions of various conventions such as time zones, standard times and daylight saving, these have no place in the Jewish scheme. The civil clock is used only as a reference point - in expressions such as: "Shabbat starts at ...". The steady progression of sunset around the world and seasonal changes results in gradual civil time changes from one day to the next based on observable astronomical phenomena (the sunset) and not on man-made laws and conventions.

Instead of the international date line convention, there are varying opinions as to where the day changes. One opinion uses the antimeridian of Jerusalem. (Jerusalem is 35°13’ east of the prime meridian, so the antimeridian is at 144°47' W, passing through eastern Alaska.) Other opinions exist as well.

Weeks

A bronze Shabbat candlestick holder made in Israel in the 1940s.

The Hebrew calendar follows a seven-day weekly cycle, which runs concurrently but independently of the monthly and annual cycles. The names for the days of the week are simply the day number within the week. In Hebrew, these names may be abbreviated using the numerical value of the Hebrew letters, for example Template:Hebrew (Day 1, or Yom Rishon (Template:Hebrew):

1. Yom rishon - Template:Hebrew (abbreviated Template:Hebrew) = "first day" = Sunday
2. Yom sheni - Template:Hebrew (abbr. Template:Hebrew) = "second day" = Monday
3. Yom shlishi - Template:Hebrew (abbr. Template:Hebrew) = "third day" = Tuesday
4. Yom reviʻi - Template:Hebrew (abbr. Template:Hebrew) = "fourth day" = Wednesday
5. Yom chamishi - Template:Hebrew (abbr. Template:Hebrew) = "fifth day" = Thursday
6. Yom shishi - Template:Hebrew (abbr. Template:Hebrew) = "sixth day" = Friday
7. Yom Shabbat - Template:Hebrew (abbr. Template:Hebrew) or more usually שבת - Shabbat = "Sabbath day (Rest day)" = Saturday

The names of the days of the week are modeled on the seven days mentioned in the Creation story. For example, Genesis 1:5 "... And there was evening and there was morning, one day". "One day" also translates to "first day" or "day one". Similarly, see Genesis 1:8, 1:13, 1:19, 1:23, 1:31 and 2.2.

The Jewish Shabbat has a special place in the Jewish weekly cycle. There are many special rules which relate to the Shabbat, discussed more fully in the Talmudic tractate "Shabbat".

In Hebrew, the word "Shabbat" (Template:Hebrew) can also mean "(Talmudic) week", so that in ritual liturgy a phrase like "Yom Reviʻi bəShabbat" means "the fourth day in the week".

Importance of lunar months

From very early times, the Mesopotamian lunisolar calendar was in wide use by the countries of the western Asia region. The structure, which was also used by the Israelites, was based on lunar months with the intercalation of an additional month to bring the cycle closer to the solar cycle.

Num 10:10 stresses the importance in Israelite religious observance of the new month (Hebrew: Template:Hebrew, Rosh Chodesh, "beginning of the month"): "... in your new moons, ye shall blow with the trumpets over your burnt-offerings..." Similarly in Num 28:11. "The beginning of the month" meant the appearance of a new moon.

In his work Mishneh Torah (1178), Maimonides included a chapter "Sanctification of the New Moon", in which he discusses the calendrical rules and their scriptural basis. He notes,

"By how much does the solar year exceed the lunar year? By approximately 11 days. Therefore, whenever this excess accumulates to about 30 days, or a little more or less, one month is added and the particular year is made to consist of 13 months, and this is the so-called embolismic (intercalated) year. For the year could not consist of twelve months plus so-and-so many days, since it is said: throughout the months of the year (Num 28:14), which implies that we should count the year by months and not by days."

Names of Months

Mosaic pavement of a zodiac in the 6th century synagogue at Beit Alpha, Israel.

Biblical references to the pre-Jewish calendar include ten months identified by number rather than by name. In parts of the Torah portion Noach (Noah) (specifically, Gen 7:11, Gen 8:4–5, Gen 8:13–14) it is implied that the months are thirty days long. There is no indication as to the total number of months in the annual cycle.

Many countries in the western Asian region used the Mesopotamian calendar from very early times, though the names of months varied. Prior to the Babylonian exile, the names of only four months are referred to in the Tanakh:

• Aviv - first month - literally "spring", which originally probably meant "the ripening of barley" (Exodus 12:2, 13:4, 23:15, 34:18, Deut. 16:1);
• Ziv - second month - literally "light" (1 Kings 6:1, 6:37);
• Ethanim - seventh month - literally "strong" in plural, perhaps referring to strong rains (1 Kings 8:2); and
• Bul - eighth month (1 Kings 6:38).

All of these are believed to be Canaanite names, and at least two are Phoenician (Northern Canaanite).

During the Babylonian exile, which started in 586 BCE, Babylonian names for the months were adopted, which are still in use. The Babylonian calendar also used a lunisolar calendar, derived from the Sumerian calendar, which was similar in structure to the Hebrew one. The Syrian calendar used in the Levant region shares many of the names for months as the Hebrew calendar, such as Nisan, Iyyar, Tammuz, Ab, Elul, Tishri, and Adar, indicating a common source.

Hebrew names and romanized transliteration may somewhat differ, as they do for חשוון / Marheshvan or כסלו / Kislev: the Hebrew words shown here are those commonly indicated e.g. in newspapers.

Hebrew names of the months with their Babylonian analogs

#	Hebrew	Tiberian	Academy	Common/ Other	Length	Babylonian analog	Holidays/ Notable days	Notes
1	נִיסָן‎	Nīsān	Nisan	Nissan	30 days	Nisanu	Passover	Called Abib and Nisan in the Tanakh.
2	אִיָּר / אִייָר‎	ʼIyyār	Iyyar	Iyar	29 days	Ayaru	Pesach Sheni Lag B'Omer	Called Ziv
3	סִיוָן / סיוון‎	Sīwān	Sivan	Siwan	30 days	Simanu	Shavuot
4	תַּמּוּז ‎	Tammūz	Tammuz	Tamuz	29 days	Dumuzu	Seventeenth of Tammuz	Named for the Babylonian god Dumuzi
5	אָב ‎	ʼĀḇ	Av	Ab	30 days	Abu	Tisha B'Av Tu B'Av
6	אֱלוּל ‎	ʼĔlūl	Elul		29 days	Ululu
7	תִּשְׁרֵי / תִּשְׁרִי‎	Tišrī	Tishri	Tishrei	30 days	Tashritu	Rosh Hashanah Yom Kippur Sukkot Shemini Atzeret Simchat Torah	Called Ethanim in Kings 8:2. First month of civil year.
8	מַרְחֶשְׁוָן / מרחשוון ‎	Marḥešwān	Marẖeshvan	Marcheshvan Cheshvan Marẖeshwan	29 or 30 days	Arakhsamna		Called Bul in Kings 6:38.
9	כִּסְלֵו / כסליו‎	Kislēw	Kislev	Kislev Chisleu Chislev	29 or 30 days	Kislimu	Hanukkah
10	טֵבֵת ‎	Ṭēḇēṯ	Tevet	Tebeth	29 days	Tebetu	Tenth of Tevet
11	שְׁבָט ‎	Šəḇāṭ	Shvat	Shevat Shebat Sebat	30 days	Shabatu	Tu Bishvat
12L*	אֲדָר א׳ ‎		Adar I*		30 days			*Only in Leap years.
12	אֲדָר / אֲדָר ב׳* ‎	ʼĂḏār	Adar / Adar II*		29 days	Adaru	Purim

In a short (chaser) year, both Cheshvan and Kislev have 29 days. In a regular (kesidran) year, Cheshvan has 29 days and Kislev has 30 days. In a full (maleh) year, both Cheshvan and Kislev have 30 days.

The calendar rules have been designed to ensure that Rosh Hashanah does not fall on a Sunday, Wednesday or Friday. This is to ensure that Yom Kippur does not directly precede or follow Shabbat, which would create practical difficulties, and that Hoshana Rabbah is not on a Shabbat, in which case certain ceremonies would be lost for a year.

Leap months

The solar year is about eleven days longer than twelve lunar months. The Bible does not directly mention the addition of "embolismic" or intercalary months. However, without the insertion of embolismic months, Jewish festivals would gradually shift outside of the seasons required by the Torah. This has been ruled as implying a requirement for the insertion of embolismic months to reconcile the lunar cycles to the seasons, which are integral to solar yearly cycles.

When the observational form of the calendar was in use, whether or not an embolismic month was announced after the "last month" (Adar) depended on whether "the barley was ripe". It may be noted that in the Bible the name of the first month, Aviv, literally means "spring" but originally it probably meant "the ripening of barley". Thus, if Adar was over and the barley was not yet ripe, an additional month was observed. However, according to some traditions, the announcement of the month of Aviv could also be postponed depending on the condition of roads used by families to come to Jerusalem for Passover, adequate numbers of lambs to be sacrificed at the Temple, and on the ripeness of the barley that was needed for the first fruits ceremony.

Under the codified rules, the Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). The leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. Year 19 (there is no year 0) of the Metonic cycle is a year exactly divisible by 19 (when the Jewish year number, when divided by 19, has no remainder). In the same manner, the remainder of the division indicates the year in the Metonic cycle (years 1 to 18) the year is in.

During leap years Adar I (or Adar Aleph — "first Adar") is added before the regular Adar. Adar I is actually considered to be the extra month, and has 30 days. Adar II (or Adar Bet — "second Adar") is the "real" Adar, and has the usual 29 days. For this reason, holidays such as Purim are observed in Adar II, not Adar I.

New year

A shofar made from a ram's horn is traditionally blown in observance of Rosh Hashanah, the beginning of the Jewish civic year.

According to Exodus 12:2 and Deut 16:1, the new year begins with Aviv (now Nisan) as "the first of months" and the month in which Passover is to be celebrated.

However, in fact the Jewish calendar has four distinct starting points, according to the Mishnah, Rosh Hashanah 1:1.

The day most commonly referred to as the "New Year" is 1 Tishrei, when the formal New Year festival, Rosh Hashanah ("head of the year") is observed. (see Ezekiel 40:1, which uses the phrase "beginning of the year".) This is the civil new year, and the point at which the year number advances. Certain agricultural practices are also marked from this date.

However, the first month of the year referred to in Exodus 12:2 is Aviv (now called Nisan): "This month shall be to you the beginning of months". This is referred to as the ecclesiastical new year, which means that the civil new year, Rosh Hashanah, actually begins in the seventh month of the ecclesiastical year.

Josephus, in the first century CE, states that while -

Moses...appointed Nisan...as the first month for the festivals...the commencement of the year for everything relating to divine worship, but for selling and buying and other ordinary affairs he preserved the ancient order [i. e. the year beginning with Tishrei]."

In ancient Israel, the start of the ecclesiastical new year (i.e. Nisan) was determined by reference to Passover. Passover begins on the 14th day of the month of Nisan, (Leviticus 23:4–6) which corresponds to the full moon of Nisan. As Passover is a spring festival, the 14th of Nisan begins on the night of a full moon after the vernal equinox. To ensure that Passover did not start before spring, the tradition in ancient Israel held that the 1st of Nisan would not start until the barley is ripe, being the test for the onset of spring. If the barley was not ripe an intercalary month would be added before Nisan.

Edwin Thiele has concluded that the ancient northern Kingdom of Israel counted years using the ecclesiastical new year starting on 1 Aviv (Nisan), while the southern Kingdom of Judah counted years using the civil new year starting on 1 Tishrei. The practice of the Kingdom of Israel was also that of Babylon, as well as other countries of the region. The practice of Judah has been followed to this day.

The month of Elul is the new year for counting animal tithes (ma'aser). Tu Bishvat ("the 15th of Shevat") marks the new year for trees (and agricultural tithes).

There may be an echo here of a controversy in the Talmud about whether the world was created in Tishrei or Nisan; it was determined that the answer is Tishrei, and this is now reflected in the prayers on Rosh Hashanah.

The use of multiple starting dates for a year is comparable to different starting dates for civil "calendar years", "tax or fiscal years", "academic years", "religious cycles", etc.

The multiplicity of new years for different purposes has long been in use. By the time of the redaction of the Mishnah, Rosh Hashanah 1:1 (ca. 200 CE), jurists had identified four new-year dates:

The 1st of Nisan is the new year for kings and feasts; the 1st of Elul is the new year for the tithe of cattle... the 1st of Tishri is the new year for years, of the years of release and jubilee years, for the planting and for vegetables; and the 1st of Shevat is the new year for trees-so the school of Shammai; and the school of Hillel say: On the 15th thereof.

Epoch

The Jewish calendar's reference point is traditionally held to be about one year before the Creation of the world.

Since about the third century CE, the Jewish calendar has used the Anno Mundi epoch (Latin for "in the year of the world", Hebrew: Template:Hebrew), abbreviated AM or A.M. According to Rabbinic reckoning, the beginning of "year 1" is not Creation, but about one year before Creation, with the new moon of its first month (Tishrei) to be called molad tohu (the mean new moon of chaos or nothing).

The Jewish calendar's epoch (reference date), 1 Tishrei 1 AM, is equivalent to Monday, 7 October 3761 BCE in the proleptic Julian calendar, the equivalent tabular date (same daylight period) and is about one year before the traditional Jewish date of Creation on 25 Elul AM 1, based upon the Seder Olam Rabbah of Rabbi Yossi ben Halafta, a second century CE sage. Thus, adding 3760 before Rosh Hashanah or 3761 after to a Julian or Gregorian year number after 1 CE will yield the Hebrew year. For earlier years there may be a discrepancy (see: "Missing Years" in the Hebrew Calendar).

The Jewish year 5771 AM starting on Rosh Hashanah, 1 Tishrei, will fall on 8 September 2010.

Before the adoption of the current year numbering system, other systems were in use. For example, during the Greek period, Seleucid era counting was used. (e.g. 1 Maccabees 1:54) During the Baylonian captivity, Ezekiel counted the years from the first deportation, that of Jehoiachin, (e.g. Ezekiel 1:1–2). The era year was then called "year of the captivity of Jehoiachin". (e.g. 2 Kings 25:27) During the period of the divided kingdoms, the years were counted in relation to the accession year of the monarch of the other kingdom. (e.g. 2 Kings 8:16)

Karaite calendar

For several centuries, many Karaite Jews, especially those outside Israel, followed the calculated Rabbinic calendar, because it was not possible during the exile to retrieve accurate new moon sightings, and aviv barley data from the land of Israel, which had to be relayed to the entire Karaite Jewish community. However, since the establishment of the State of Israel, and especially since the Six Day War, most Karaite Jews have made Aliyah, and can now again use the observational calendar.

Karaites use the lunar month and the solar year, but the Karaite calendar differs from the Rabbinic calendar in a number of ways.

For Karaites, the beginning of each month, the Rosh Chodesh, can be calculated, but is confirmed by the observation in Israel of the first sightings of the new moon. This may result in an occasional variation of a maximum of one day, depending on the inability to observe the new moon. The day is usually "picked up" in the next month.

The addition of the leap month (Adar II) is determined by observing in Israel the ripening of barley (called aviv), rather than using the calculated and fixed calendar of Rabbinic Judaism. Occasionally this results in Karaites being one month ahead of other Jews using the calculated Rabbinic calendar. The "lost" month would be "picked up" in the next cycle when Karaites would observe a leap month while other Jews would not.

Furthermore, the seasonal drift of the Rabbinic calendar is avoided, resulting in the years affected by the drift starting one month earlier in the Karaite calendar.

Also, the four rules of postponement of the Rabbinic calendar are not applied, as they are not found in the Tanakh. This affects the dates observed for all the Jewish holidays by one day.

Change to a calculated calendar

Observational principles

A stone (2.43x1 m) with Hebrew inscription "To the Trumpeting Place" is believed to be a part of the Second Temple.

Later postexilic period: evidence of the Mishnah

According to the Mishnah and Tosefta, in the Maccabean, Herodian, and Mishnaic periods, new months were determined by the sighting of a new crescent, with two eye witnesses required to testify to the Sanhedrin to having seen the new lunar crescent at sunset. The practice in the time of Gamaliel II (c. 100 CE) was for witnesses to select the appearance of the moon from a collection of drawings that depicted the crescent in a variety of orientations, only a few of which could be valid in any given month. These observations were compared against calculations. When thirty days elapsed since the last new moon, the witnesses were readily believed.

At first the beginning of each Jewish month was signaled to the communities of Israel and beyond by fires lit on mountaintops, but after the Samaritans began to light false fires, messengers were sent. The inability of the messengers to reach communities outside Israel before mid-month High Holy Days (Succot and Passover) led outlying communities to celebrate scriptural festivals for two days rather than one, observing the second feast-day of the Jewish diaspora because of uncertainty of whether the previous month ended after 29 or 30 days.

Evaluation of the Mishnaic evidence

It has been noted that the procedures described in the Mishnah and Tosefta are all plausible procedures for regulating an empirical lunar calendar. Fire-signals, for example, or smoke-signals, are known from the pre-exilic Lachish ostraca. Furthermore, the Mishnah contains laws that reflect the uncertainties of an empirical calendar. Mishnah Sanhedrin, for example, holds that when one witness holds that an event took place on a certain day of the month, and another that the same event took place on the following day, their testimony can be held to agree, since the length of the preceding month was uncertain. Another Mishnah takes it for granted that it cannot be known in advance whether a year's lease is for twelve or thirteen months. Hence it is a reasonable conclusion that the Mishnaic calendar was actually used in the Mishnaic period.

The accuracy of the Mishnah's claim that the Mishnaic calendar was also used in the late 2nd temple period is less certain. One scholar has noted that there are no laws from Second Temple period sources that indicate any doubts about the length of a month or of a year. This led him to propose that the priests must have had some form of computed calendar or calendrical rules that allowed them to know in advance whether a month would have 30 or 29 days, and whether a year would have 12 or 13 months.

Modern calendar

The Arch of Titus depicting the objects from the Temple being carried through Rome.

Between 70 CE and 1178 CE, the observation based calendar was gradually replaced by a mathematically calculated one. Except for the epoch year number, the calendar rules reached their current form by the beginning of the 9th century, as described by al-Khwarizmi in 823.

One notable difference between the calendar of that era and the modern form was the date of the epoch (the fixed reference point at the beginning of year 1), which at that time was one year later than the epoch of the modern calendar.

Most of the present rules of the calendar were in place by 823, according to a treatise by the Muslim astronomer al-Khwarizmi (c. 780–850 CE). Al-Khwarizmi's study of the Jewish calendar,

Risāla fi istikhrāj taʾrīkh al-yahūd "Extraction of the Jewish Era" describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall, the interval between the Jewish era (creation of Adam) and the Seleucid era, and the rules for determining the mean longitude of the sun and the moon using the Jewish calendar.

In 921, Aaron ben Meir proposed changes to the calendar. Though the proposals were rejected, it indicates that all of the rules of the modern calendar (except for the epoch) were in place before that date. In 1000, the Muslim chronologist al-Biruni described all of the modern rules of the Hebrew calendar, except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch.

There is a tradition, first mentioned by Hai Gaon (d.1038 CE), that Hillel b. R. Yehuda "in the year 670 of the Seleucid era" (i.e. 358–359 CE) was responsible for the new calculated calendar with a fixed intercalation cycle. Later writers, such as Nachmanides, explained Hai Gaon's words to mean that the entire computed calendar was due to Hillel b. Yehuda. Maimonides, in the 12th century, stated that the Mishnaic calendar was used "until the days of Abaye and Rava", who flourished ca. 320–350 CE, and that the change came when "the land of Israel was destroyed, and no permanent court was left." Taken together, these two traditions suggest that Hillel b. Yehuda (whom they identify with the mid-4th century Jewish patriarch Ioulos, attested in a letter of the Emperor Julian, and the Jewish patriarch Ellel, mentioned by Epiphanius) instituted the computed Hebrew Calendar because of persecution. H. Graetz attempted to link the introduction of the computed calendar to a sharp repression following a failed Jewish insurrection that occurred during the rule of Constantius and Gallus. A later writer, S. Lieberman, argued instead that the introduction of the fixed calendar was due to measures taken by Roman authorities to prevent the Jewish patriarch from sending calendrical messengers.

Both the tradition that Hillel b. Yehuda instituted the complete computed calendar, and the theory that the computed calendar was introduced due to repression or persecution, have been questioned. Furthermore, two Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible under the rules of the modern calendar, indicating that its arithmetic rules were developed in Babylonia during the times of the Geonim (seventh to eighth centuries). The Babylonian rules required the delay of the first day of Tishrei when the new moon occurred after noon.

The Talmuds do, however, indicate at least the beginnings of a transition from a purely empirical to a computed calendar. According to a statement attributed to Yose, an Amora who lived during the second half of the third century, the feast of Purim, 14 Adar, could not fall on a Sabbath nor a Monday, lest 10 Tishrei (Yom Kippur) fall on a Friday or a Sunday. This indicates that, by the time of the redaction of the Jerusalem Talmud (ca. 400 CE), there were a fixed number of days in all months from Adar to Elul, also implying that the extra month was already a second Adar added before the regular Adar. In another passage, a sage is reported to have counseled "those who make the computations" not to set the first day of Tishrei or the Day of the Willow on the sabbath. This indicates that there was a group which "made computations" and was in a position to control, to some extent, the weekday on which Rosh Hashanah would fall.

Practice

Outside of Rabbinic circles, evidence shows a diversity of Jewish practice.

Calendrical evidence for the postexilic Persian period is found in papyri from the Jewish colony at Elephantine, in Egypt. These documents show that the Jewish community of Elephantine used the Egyptian and Babylonian calendars.

The Sardica paschal table shows that the Jewish community of some eastern city, possibly Antioch, used a calendrical scheme that kept Nisan 14 within the limits of the Julian month of March. Some of the dates in the document are clearly corrupt, but they can be emended to make the sixteen years in the table consistent with a regular intercalation scheme. Peter, the bishop of Alexandria (early 4th century CE), mentions that the Jews of his city "hold their Passover according to the course of the moon in the month of Phamenoth, or according to the intercalary month every third year in the month of Pharmuthi", suggesting a fairly consistent intercalation scheme that kept Nisan 14 approximately between the Phamenoth 10 (March 6 in the 4th century CE) and Pharmuthi 10 (April 5). Jewish funerary inscriptions from Zoar, south of the Dead Sea, dated from the 3rd to the 5th century CE, indicate that when years were intercalated, the intercalary month was at least sometimes a repeated month of Adar. But the inscriptions reveal no clear pattern of regular intercalations, nor do they indicate any consistent rule for determining the start of the lunar month.

In 1178, Maimonides included all the rules for the calculated calendar and their scriptural basis, including the modern epochal year in his work, Mishneh Torah. Today, the rules detailed in Maimonides' code are those generally used by Jewish communities throughout the world.

Principles

Measurement of month

Traditional new moon

Originally the "new moon" was the day on which the first visible crescent of the moon is observed. It occurs 29 or 30 days after the preceding visible crescent and traditionally signaled the start of a Jewish lunar month. However, it is no longer used in determining the calendar.

Synodic month

A synodic month is the period between two lunar conjunctions, such as between two new moons. Since the actual length of a synodic month varies by several hours from month to month, the calendar is based on a long-term average length called the mean synodic month. The virtual lunar conjunctions at the start of each mean synodic month are called molads. The mean synodic month used in the Hebrew calendar is exactly ${\tfrac {765433}{25920}}$ days, or 29 days, 12 hours, and 793 parts (44+¹/₁₈ minutes) (i.e. 29.5306 days). This interval exactly matches the mean synodic month determined by the Babylonians before 250 BCE and as adopted by the Greek astronomer Hipparchus and the Alexandrian astronomer Ptolemy. Its remarkable accuracy (less than one second from the true value) is thought to have been achieved using records of lunar eclipses from the eighth to fifth centuries BCE.

Pattern of calendar years

The Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). A Metonic cycle equates to 235 lunar months in each 19-year cycle. This gives an average of 6939 days, 16 hours and 595 parts for each cycle.

But due to the Rosh Hashanah postponement rules (see below), a cycle of 19 Jewish years can be either 6939, 6940, 6941, or 6942 days in duration. Since none of these values is evenly divisible by seven, the Jewish calendar repeats exactly only following 36,288 Metonic cycles, or 689,472 Jewish years. There is a near-repetition every 247 years, except for an excess of 50 minutes (905 parts).

There are 14 different patterns that Jewish years may take. Each of these patterns is called a "keviyah" / "קביעה" (Hebrew for "a setting" or "an established thing"), and is distinguished by the day of the week for Rosh Hashanah of that particular year and by that particular year's length.

A Jewish non-leap year can only have 353, 354, or 355 days. A leap year can have 383, 384, or 385 days (always 30 days longer than the non-leap length).

• A chaserah year (Hebrew for "deficient" or "incomplete") is 353 or 383 days long. Both Kislev and Cheshvan have 29 days. The Hebrew letter ח "het", and the letter for the weekday denotes this pattern.
• A kesidrah year ("regular" or "in-order") is 354 or 384 days long. Kislev has 30 days and Cheshvan has 29 days. The Hebrew letter כ "kaf", and the letter for the week-day denotes this pattern.
• A shlemah year ("abundant" or "complete") is 355 or 385 days long. Both Kislev and Cheshvan have 30 days. The Hebrew letter ש "shin", and the letter for the week-day denotes this pattern.

Determining leap years

The Jewish leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. To determine whether a year is a leap year, find the remainder when dividing the Jewish year number by 19. If the remainder is 3, 6, 8, 11, 14 or 17, the year is a leap year and an extra month, Adar I, is added, preceding Adar II (sometimes called "the real Adar"). If the remainder is zero, the year is also a leap year since year 19 of the Metonic cycle is a year exactly divisible by 19. Another way to check a specific year is to find the remainder in the following calculation: ( 7 x the Jewish year number + 1 ) / 19. If the remainder is less than 7, the year is a leap year.

A mnemonic word in Hebrew is GUCHADZaT "גוחאדז"ט" (the Hebrew letters gimel-vav-het aleph-dalet-zayin-tet, i.e. 3, 6, 8, 1, 4, 7, 9. See Hebrew numerals). A variant of this pattern of naming includes another letter which specifies the day of the week for the first day of Pesach (Passover) in the year.

Another memory aid notes that intervals of the major scale follow the same pattern as do Jewish leap years, with do corresponding to year 19 (or 0): a whole step in the scale corresponds to two common years between consecutive leap years, and a half step to one common year between two leap years. This connection with the major scale is more remarkable in the context of 19 equal temperament.

Special holiday rules

Adjustments are made to ensure certain holy days and festivals do or do not fall on certain days of the week.

Rosh Hashanah postponement

Day of week	Number of days
Monday	353	355	383	385
Tuesday	354			384
Thursday	354	355	383	385
Saturday	353	355	383	385

Adjustments are made to ensure that Yom Kippur, on which no work can be done, does not fall on Friday (the day prior to the Sabbath) to avoid having Yom Kippur's restrictions still going on at the start of Sabbath, or on Sunday (the day after Shabbat) to avoid having the Shabbat restrictions still going on at the start of Yom Kippur. As Yom Kippur falls on Tishrei 10, and Rosh Hashanah falls on the 1st, an adjustment is made so that Rosh Hashanah does not fall on a Wednesday or Friday. Furthermore to ensure that Hoshana Rabbah (Tishrei 21) is not on a Shabbat, in which case certain ceremonies (carrying willows, which is work) would be lost for a year, Rosh Hashanah may not be on Sunday. Thus,the first day of Rosh Hashanah may only occur on Mondays, Tuesdays, Thursdays, and Saturdays (the "four gates"). Adjustments are made to ensure that Rosh Hashanah does not fall on the other three days. To achieve that result the year may be made into a short (chaser) year (both Kislev and Cheshvan have 29 days) or full (maleh) year (both Kislev and Cheshvan have 30 days) (see table).

The day of the week on which Rosh Hashanah falls in any given year will also be the day on which Sukkot and Shmini Atzeret will occur.

The period from 1 Adar (or Adar II, in leap years) to 29 Heshvan contains all of the festivals specified in the Bible - Purim (14 Adar), Pesach (15 Nisan), Shavuot (6 Sivan), Rosh Hashanah (1 Tishrei), Yom Kippur (10 Tishrei), Sukkot (15 Tishrei), and Shemini Atzeret (22 Tishrei). This period is fixed, during which no adjustments are made.

Days of week of holidays

Main article: Days of week on Hebrew calendar

Purim	Passover (first day)	Shavuot (first day)	17 Tammuz/ Tisha B'Av	Rosh Hashanah/ Sukkot/ Shmini Atzeret/ (first day)	Yom Kippur	Chanukah (first day)	10 Tevet	Tu Bishvat
Sun	Tue	Wed	Tue	Thu	Sat	Wed or Thu	Wed, Thu, or Fri	Tue, Wed, or Thu
Tue	Thu	Fri	Thu	Sat	Mon	Fri or Sat	Fri or Sun	Thu or Sat
Thu	Sat	Sun	Sun*	Mon	Wed	Sun or Mon	Sun or Tue	Sat or Mon
Fri	Sun	Mon	Sun	Tue	Thu	Mon	Tue	Mon
			*Postponed from Shabbat

Calculating the calendar--the four hindrances (deḥiyyot)

Given the above, concretely how is the calendar determined? If the length of the year is set, the lengths of all the months are fixed, so if we know the year length and the day of the week of Rosh Ha-Shanah, the beginning of each month is fixed.

Number of days between Rosh Ha-Shanah molads

The day of Rosh Ha-Shanah and the length of the year are determined by the time and the day of the week of the Tishri molad, that is, the moment of the average conjunction. Given the Tishri molad of a certain year, we find the length of the year thus: First, whether the year is ordinary or leap is determined by its position in the 19-year Metonic cycle. As mentioned above, years 3, 6, 8, 11, 14, 17, and 19 are leap years. Given this, one must find the number of days between the starting Tishri molad (TM1) and the Tishri molad of the next year (TM2). For calendar descriptions in general the day begins at 6 pm, but for the purpose of determining Rosh Ha-Shanah, a molad occuring on or after noon is treated as belonging to the next day (the second deḥiyyah). All months are calculated as 29d, 12h, 44m, 3 1/3s long (MonLen). Therefore, in an ordinary year TM2 occurs 12 x MonLen days after TM1. This is usually 354 calendar days after TM1, but if TM1 is on or after 3:11:20 a.m. and before noon, it will be 355 days. Similarly, in a leap year, TM2 occurs 13 x MonLen days after TM1. This is usually 384 days after TM1, but if TM1 is on or after noon and before 2:27:16 2/3 pm., TM2 will be only 383 days after TM1. In the same way, from TM2 we calculate TM3. Thus the four natural year lengths are 354, 355, 383, and 384 days.

Adjusting for day of the week

However, Rosh Ha-Shanah (RH) is not necessarily the Tishri molad. As mentioned above, Sun., Wed. or Fri. cannot be RH , so if TM2 is one of those days, RH2 is postponed one day (the first deḥiyyah). This means that the length of year 1 is one day longer that calculated from the molad, while the length of year 2 is one day shorter. This postponement is why 353-day (short ordinary) and 385-day (long leap) years exist.

But how can we lengthen year 1 in the case that it already a long ordinary year of 355 days or shorten year 2 if it is a short leap year of 383 days?

In the first case (the third deḥiyyah ) the length of the first year (355 days) will be a problem if TM1 is on a Tuesday as that means TM2 is a Sunday. So in this case, as well as postponing RH2 from Sunday to Monday, the RH1 is also postponed. As it cannot be postponed to Wednesday, it is postponed to Thursday and year 1 ends up being 354 days.

On the other hand, how can we shorten year 2 if it is already the minimum 383 days (the fourth deḥiyyah )? This will be a problem if TM2 is on a calendrical Wednesday. In this case, besides postponing RH2 from Wednesday to Thursday, the RH3 is also postponed from Monday to Tuesday, and year 2 ends up being 383 days.

Measurement of hours

Every hour is divided into 1080 halakim or parts. A part is 3⅓ seconds or ¹/₁₈ minute. The ultimate ancestor of the helek was a small Babylonian time period called a barleycorn, itself equal to ¹/₇₂ of a Babylonian time degree (1° of celestial rotation). Actually, the barleycorn or she was the name applied to the smallest units of all Babylonian measurements, whether of length, area, volume, weight, angle, or time.

But by the twelfth century that source had been forgotten, causing Maimonides to speculate that there were 1080 parts in an hour because that number was evenly divisible by all numbers from 1 to 10 except 7. But the same statement can be made regarding 360. The weekdays start with Sunday (day 1) and proceed to Saturday (day 7). Since some calculations use division, a remainder of 0 signifies Saturday.

While calculations of days, months and years are based on fixed hours equal to ¹/₂₄ of a day, the beginning of each halachic day is based on the local time of sunset. The end of the Shabbat and other Jewish holidays is based on nightfall (Tzeth haKochabim) which occurs some amount of time, typically 42 to 72 minutes, after sunset. According to Maimonides, nightfall occurs when three medium-sized stars become visible after sunset. By the seventeenth century this had become three second-magnitude stars. The modern definition is when the center of the sun is 7° below the geometric (airless) horizon, somewhat later than civil twilight at 6°. The beginning of the daytime portion of each day is determined both by dawn and sunrise. Most halachic times are based on some combination of these four times and vary from day to day throughout the year and also vary significantly depending on location. The daytime hours are often divided into Sha`oth Zemaniyoth or "Halachic hours" by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The nighttime hours are similarly divided into 12 equal portions, albeit a different amount of time than the "hours" of the daytime. The earliest and latest times for Jewish services, the latest time to eat Chametz on the day before Passover and many other rules are based on Sha`oth Zemaniyoth. For convenience, the modern day using Sha`oth Zemaniyoth is often discussed as if sunset were at 6:00pm, sunrise at 6:00am and each hour were equal to a fixed hour. For example, halachic noon may be after 1:00pm in some areas during daylight saving time. Within the Mishnah, however, the numbering of the hours starts with the "first" hour after the start of the day.

Accuracy

Seasonal drift

The Hebrew calendar's mean year is 365.2468 days long (exactly 365 days 5 hours 55 minutes and 25+²⁵/₅₇ seconds - i.e. the molad/monthly interval × 235 months per 19-year cycle ÷ 19 years per cycle). As the present-era mean northward equinoctal year is about 365.2424 days long, the Hebrew calendar mean year is slightly longer than this tropical year. This results in a "drift" of the Hebrew calendar of about a day every 224 years.

Also, the mean Gregorian calendar year is 365.2425 days long (365 days 5 hours 49 minutes and 12 seconds), resulting in a drift of the Hebrew calendar in relation to the Gregorian calendar of about a day every 231 years.

The impact of the drift is reflected in the drift of the date of Passover from the vernal full moon:

Comparison of vernal full moon to
actual dates of Passover: 2001–2020
In Gregorian dates

Year	Astronomical vernal full moon	Passover*
2001	8 April	8 April
2002	28 March	28 March
2003	16 April	17 April
2004	5 April	6 April
2005	25 March	24 April
2006	13 April	13 April
2007	2 April	3 April
2008	21 March	20 April
2009	9 April	9 April
2010	30 March	30 March
2011	18 April	19 April
2012	6 April	7 April
2013	27 March	26 March
2014	15 April	15 April
2015	4 April	4 April
2016	23 March	23 April
2017	11 April	11 April
2018	31 March	31 March
2019	21 March	20 April
2020	8 April	9 April
*Passover commences at sunset preceding the date indicated.

Molad intervals

The value 29^d12^h793^p for the molad interval is identical to the value in the Babylonian System B (about 300 BCE), and in Ptolemy's Almagest (2nd century CE), and is approximately equal to 29.530594 days. This is as close to the correct value of 29.530589 days as it is possible for a value to come that is rounded off to whole parts (¹/₁₈ minute). So the molad interval is about 0.6 seconds too long. Put another way, if the molad is taken as the time of mean conjunction at some reference meridian, then this reference meridian is drifting slowly eastward. If this drift of the reference meridian is traced back to the mid-4th century CE, the traditional date of the introduction of the fixed calendar, then it is found to correspond to a longitude midway between the Nile River and the end of the Euphrates River. The modern molad moments match the mean solar times of the lunar conjunction moments near the meridian of Kandahar, Afghanistan, more than 30° east of Jerusalem.

In the present era actual lunar conjunction intervals can be as short as 29 days 6 hours and 30 minutes to as long as 29 days and 20 hours, a variation range of about 13 hours and 30 minutes. Furthermore, due to the eccentricity of Earth's orbit, series of shorter lunations alternate with series of longer lunations. Consequently the actual lunar conjunction moments can range from 12 hours earlier than to 16 hours later than the molad moment, in terms of Jerusalem mean solar time.

Furthermore, the discrepancy between the molad interval and the mean synodic month is accumulating at an accelerating rate, since the mean synodic month is progressively shortening due to gravitational tidal effects. Measured on a strictly uniform time scale, such as that provided by an atomic clock, the mean synodic month is becoming gradually longer, but since the tides slow Earth's rotation rate even more, the mean synodic month is becoming gradually shorter in terms of mean solar time.

Implications for Jewish ritual

This figure, in a detail of a medieval Hebrew calendar, reminded Jews of the palm branch (Lulav), the myrtle twigs, the willow branches, and the citron (Etrog) to be held in the hand and to be brought to the synagogue during the holiday of sukkot, near the end of the autumn holiday season.

Although the molad of Tishrei is the only molad moment that is not ritually announced, it is actually the only one that is relevant to the Hebrew calendar, for it determines the provisional date of Rosh Hashanah, subject to the Rosh Hashanah postponement rules. The other monthly molad moments are announced for mystical reasons. With the moladot on average almost 100 minutes late, this means that the molad of Tishrei lands one day later than it ought to in (100 minutes) ÷ (1440 minutes per day) = 5 of 72 years or nearly 7% of years!

Therefore the seemingly small drift of the moladot is already significant enough to affect the date of Rosh Hashanah, which then cascades to many other dates in the calendar year and sometimes, due to the Rosh Hashanah postponement rules, also interacts with the dates of the prior or next year. The molad drift could be corrected by using a progressively shorter molad interval that corresponds to the actual mean lunar conjunction interval at the original molad reference meridian. Furthermore, the molad interval determines the calendar mean year, so using a progressively shorter molad interval would help correct the excessive length of the Hebrew calendar mean year, as well as helping it to "hold onto" the northward equinox for the maximum duration.

If the intention of the calendar is that Passover should fall near the first full moon after the northward equinox, or that the northward equinox should land within one lunation before 16 days after the molad of Nisan, then this is still the case in about 80% of years, but in about 20% of years Passover is a month late by these criteria (as it was in Hebrew years 5765 and 5768, the 8th and 11th years of the 19-year cycle = Gregorian 2005 and 2008 CE). Presently this occurs after the "premature" insertion of a leap month in years 8, 11, and 19 of each 19-year cycle, which causes the northward equinox to land on exceptionally early Hebrew dates in such years. This problem will get worse over time, and so beginning in Hebrew year 5817 (2057 CE), year 3 of each 19-year cycle will also be a month late. Furthermore, the drift will accelerate in the future as perihelion approaches and then passes the northward equinox, and if the calendar is not amended then Passover will start to land on or after the summer solstice around Hebrew year 16652 (12892 CE). (The exact year when this will begin to occur depends on uncertainties in the future tidal slowing of the Earth rotation rate, and on the accuracy of predictions of precession and Earth axial tilt.)

The seriousness of the spring equinox drift is widely discounted on the grounds that Passover will remain in the spring season for many millennia, and the text of the Torah is generally not interpreted as having specified tight calendrical limits. On the other hand, the mean southward equinoctial year length is considerably shorter, so the Hebrew calendar has been drifting faster with respect to the autumn equinox, and at least part of the harvest festival of Sukkot is already more than a month after the equinox in years 1, 9, and 12 of each 19-year cycle; beginning in Hebrew year 5818 (2057 CE), this will also be the case in year 4. (These are the same year numbers as were mentioned for the spring season in the previous paragraph, except that they get incremented at Rosh Hashanah.) This progressively increases the probability that Sukkot will be cold and wet, making it uncomfortable or impractical to dwell in the traditional succah during Sukkot. The first winter seasonal prayer for rain is not recited until Shemini Atzeret, after the end of Sukkot, yet it is becoming increasingly likely that the rainy season in Israel will start before the end of Sukkot.

It should be explained, for the benefit of those who may puzzle over these matters, that everything evens itself out in the end. No equinox or solstice will ever be more than a day or so away from its mean date according to the solar calendar, while nineteen Jewish years average 6939d 16h 33m 03 1/3s compared to the 6939d 14h 26m 15s of nineteen mean tropical years. This discrepancy has mounted up to six days, which is why the earliest Passover (in year 16 of the cycle) currently falls around 27 March.

"Rectifying" the Hebrew calendar

Given the importance in Jewish ritual of establishing the accurate timing of monthly and annual times, some futurist writers and researchers have considered whether a "corrected" system of establishing the Hebrew date is required, due to the small but accelerating changes in the actual lunar cycle interval. Further religious questions include how such a system might be implemented and administered throughout the diverse aspects of the world Jewish community.

It has been argued by some that, as the fixed arithmetic Hebrew calendar was established on the authority of Hillel ben Yehudah, President of the Sanhedrin in Hebrew year 4119, only an equal authority (a modern Sanhedrin) can either amend it or reinstate the observational Hebrew calendar.

A 353-year leap cycle of 4366 months, including 130 leap months, along with use of a progressively shorter molad interval, could keep an amended fixed arithmetic Hebrew calendar from drifting for more than 7 millennia.

Irregularities and "missing years"

Main article: Missing years (Hebrew calendar)

The traditional dates of events in Jewish history are often used interchangeably with the modern secular dates according to the Gregorian calendar. For example, the traditional Jewish date for the destruction of the First Temple (3338 AM = 423 BCE) differs from the modern scientific date, which is usually expressed using the Gregorian calendar (586 BCE). Implicit in this practice is the view that if all the differences in structure between the Hebrew and Gregorian calendars are taken into consideration, the two dates can be derived from each other. This is not the case. If the traditional dates of events before the Second Temple era are assumed to be using the standard Hebrew calendar, they refer to different objective years than those of the secular dates. The discrepancy is some 165 years.

The conflict does not necessarily imply that either the traditional dates or the secular dates must be objectively wrong. It is possible that the traditional dates did not use a consistent calendar matching the year count of the standard Hebrew calendar. It could be that one or more substantial calendar shifts have occurred, or the years counted might in certain periods have differed from astronomical years. Taking into account the possibility of a changing structure of the Hebrew calendar, theoretically, both the traditional dates and those of secular scholars could be correct. Even so, the account of history in the traditional sourcebook Seder Olam Rabba, and in particular its description of the period of Persian domination, seems to be irrevocably at odds with modern scientific understanding.

Furthermore, the modern Hebrew calendar cannot be used to calculate Biblical dates because new moon dates may be in error by ±2 days and months may be in error by ±2 months. The latter accounts for the irregular intercalation (adding of extra months) that was performed in three successive years in the early second century, according to the Talmud.

Usage in contemporary Israel

Early Zionist pioneers were impressed by the fact that the calendar preserved by Jews over many centuries in far-flung diasporas, as a matter of religious ritual, was geared to the climate of their original country: the Jewish New Year marks the moment of transition from the dry season to the rainy one, and major Jewish holidays such as Sukkot, Passover or Shavuot correspond to major points of the country's agricultural year such as planting and harvest.

Accordingly, in the early 20th century the Hebrew calendar was re-interpreted as an agricultural rather than religious calendar. The Kibbutz movement was especially inventive in creating new rituals fitting this interpretation.

After the creation of the State of Israel, the Hebrew calendar became one of the official calendars of Israel, along with the Gregorian calendar. Holidays and commemorations not derived from previous Jewish tradition were to be fixed according to the Hebrew calendar date. For example, the Israeli Independence Day falls on 5 Iyar, Jerusalem Reunification Day on 28 Iyar, and the Holocaust Commemoration Day on 27 Nisan.

Nevertheless, since the 1950s usage of the Hebrew calendar has steadily declined, in favor of the Gregorian calendar. At present, Israelis — except for the minority of religiously observant — conduct their private and public life according to the Gregorian calendar, although the Hebrew calendar is still widely acknowledged, appearing in public venues such as banks (where it is legal for use on checks and other documents, though only rarely do people make use of this option) and on the mastheads of newspapers.

The Jewish New Year (Rosh Hashanah) is a two-day public holiday in Israel. However, since the 1980s an increasing number of secular Israelis celebrate the Gregorian New Year (usually known as "Silvester Night" — "ליל סילבסטר") on the night between 31 December and 1 January. Prominent Rabbis have on several occasions sharply denounced this practice, but with no noticeable effect on the secularist celebrants.

The disparity between the two calendars is especially noticeable with regard to commemoration of the assassinated Prime Minister Yitzchak Rabin. The official Day of Commemoration, instituted by a special Knesset law, is marked according to the Hebrew calendar - on 12 Heshvan. However, left-leaning Israelis, who revere Rabin as a martyr for the cause of peace and who are predominantly secular, hold their commemoration on 4 November. In some years the two competing Rabin Memorial Days are separated by as much as two weeks.

Wall calendars commonly used in Israel are hybrids. Most are organised according to Gregorian rather than Jewish months, but begin in September, where the Jewish New Year usually falls, and providing the Jewish date in small characters.

Notes

 This article incorporates text from a publication now in the public domain: Singer, Isidore; et al., eds. (1901–1906). The Jewish Encyclopedia. New York: Funk & Wagnalls. {{cite encyclopedia}}: Missing or empty |title= (help)

References

Wikibooks

Wikibooks Programming:Hebrew calendar has a page on the topic of

Computer programming for the Hebrew calendar

• al-Biruni. The Chronology of Ancient Nations, Chapter VII. tr. C. Edward Sachau. London, 1879.
• Ari Belenkiy. "A Unique Feature of the Jewish Calendar — Dehiyot". Culture and Cosmos 6 (2002) 3-22.
• Bonnie Blackburn and Leofranc Holford-Strevens. The Oxford Companion to the Year: An Exploration of Calendar Customs and Time-reckoning. Oxford University Press; USA, 2000. pp * Sherrard Beaumont Burnaby. Elements of the Jewish and Muhammadan Calendars. George Bell and Sons, London, 1901.
• Nathan Bushwick. Understanding the Jewish Calendar. Moznaim, 1989. ISBN 0-940118-17-3
• W.H. Feldman. Rabbinical Mathematics and Astronomy,3rd edition, Sepher-Hermon Press, 1978.
• M. Kühntopf, Jüdische Chronik, 1st edition, Norderstedt 2008, vol. 1, ISBN 978-3-8334-8628-9, pp. 113–138
• Otto Neugebauer. Ethiopic astronomy and computus. Österreichische Akademie der Wissenschaften, philosophisch-historische Klasse, Sitzungsberichte 347. Vienna, 1979.
• The Code of Maimonides (Mishneh Torah), Book Three, Treatise Eight: Sanctification of the New Moon. Translated by Solomon Gandz. Yale Judaica Series Volume XI, Yale University Press, New Haven, Conn., 1956.
• Samuel Poznanski. "Calendar (Jewish)". Encyclopædia of Religion and Ethics, 1911.
• Edward M. Reingold and Nachum Dershowitz. Calendrical Calculations: The Millennium Edition. Cambridge University Press; 2 edition (2001). ISBN 0-521-77752-6

723-730.

• L.A. Resnikoff. "Jewish calendar calculations", Scripta Mathematica 9 (1943) 191-195, 274-277.
• Eduard Schwartz, Christliche und jüdische Ostertafeln (Abhandlungen der königlichen Gesellschaft der Wissenschaften zu Göttingen. Philologisch-Historische Klasse. Neue Folge, Band viii), Berlin, 1905.
• Arthur Spier. The Comprehensive Hebrew Calendar. Feldheim, 1986.
• Sacha Stern, Calendar and Community: A History of the Jewish Calendar Second Century BCE-Tenth Century CE, Oxford University Press, 2001.
• Ernest Wiesenberg. "Appendix: Addenda and Corrigenda to Treatise VIII". The Code of Maimonides (Mishneh Torah), Book Three: The Book of Seasons. Yale Judaica Series Volume XIV, Yale University Press, New Haven, Conn., 1961. pp. 557–602.
• F.H. Woods. "Calendar (Hebrew)", Encyclopædia of Religion and Ethics, 1911.

See also

• Babylonian calendar
• Jewish holidays 2000-2050
• molad
• Biblical and Talmudic units of measurement

External links

• Perpetual Hebrew / Civil Calendar
• The Jewish Controversy about Calendar Postponements
• Jewish Calendar with Zmanim - Halachic times and date converter chabad.org
• Jewish calendar scientific explanation at the NASA web site
• Jewish Encyclopedia: Calendar
• Karaite Holidays Karaite website
• Hebrew Calendar Dates and Holydays (Diaspora or Israel) for both the Traditional and the Rectified calendars
• Hebrew - Gregorian Calendar with options (Multilingual)
• Bet Ha Bracha Hebrew Calendar

Date converters

• Molad - Jewish Calendar with Zmanim and holidays for Mobiles.
• Jewish Calendar for many platforms
• Kaluach - Hebrew/civil calendars
• Hebcal Hebrew Date Converter
• Jewish/Gregorian/Julian Perpetual Calendar Converter - Also contains a full year view for the Hebrew Calendar.
• Template:Wayback
• Jewish / Civil Date Converter
• Software program that converts Hebrew dates to the civil calendar and vice versa
• Gregorian-Mayan-Julian-Islamic-Persian-Hebrew Calendar Converter
• Kalendis Calendar Calculator
• Gregorian to Hebrew date with weekly Parshat HaShavua.
• Firefox Add-ons. Hebrew Calendar