Hebrew calendar

The Hebrew calendar (הלוח העברי) or Jewish calendar is the used by  for religious purposes. It is a used to reckon the Jewish New Year and to determine the dates for, the appropriate s for , s (dates to commemorate the death of a relative), and which daily  is to be read, among many ceremonial uses. Originally the Hebrew calendar was used by Jews for all quotidian purposes, but by the era of the (1st Century BCE), Jews were compelled to follow the  for all civic matters such as the payment of taxes and dealings with government officials.

The Hebrew calendar's (reference date), 1 Tishrei 1, is equivalent to Monday, ,  in the , the equivalent tabular date (same daylight period) and is about one year before the traditional Jewish  on 25 Elul AM 1, based upon the  of Rabbi , a second century CE sage. Thus, adding 3760 or 3761 to any Julian/Gregorian year number after 1 CE will yield the Hebrew year. For earlier years there may be a discrepancy (see: ).

Two major forms of the calendar have been used. Before the of the  in 70, the calendar was observational, with the beginning of each month determined by the testimony of witnesses who had observed a new. Between 70 and 1178 CE a rule-based fixed-arithmetic system was adopted to achieve the same effect.

The origins of the Hebrew calendar are found in the, which refers to the existence of several numbered but un-named months in the ide (pre-Jewish) period, and which recounts several calendar-based , including God's commandment during the from Egypt to fix the month of  as the first month of the year. The development of the calendar was likely influenced by the in the 6th Century BCE, during which ian names for the months were adapted; the  also employed a lunisolar calendar derived from the. Following the of Roman times (c. 1st Century CE), calculations were increasingly used to fix dates, with the principles fully described by  in 1178 CE in the .

Because of the roughly eleven-day difference between twelve s and one, the year lengths of the Hebrew calendar vary in a repeating 19-year of 235 lunar months, with an  lunar month added 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 and the times and climate of the. With respect to the present-day mean solar year, the Hebrew calendar's year is longer by about 6 minutes and 25+25/57 seconds, meaning 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. This is due to the 0.6 second discrepancy between the Calendric "" (lunar conjunction interval), which is fixed by, and the actual mean lunar conjunction interval, which itself is slowly changing over time.

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

Concurrently there is a weekly cycle of seven days, mirroring the seven day period of the 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 being the seventh day. The Jewish day runs from sunset to the next sunset, and accordingly, s and s have no place in the Jewish calendar.

The twelve regular months include:  (30 days),  (29 days), (30 days),  (29 days),  (30 days),  (29 days),   (30 days),  (29 or 30 days),  (29 or 30 days),  (29 days),  (30 days), and  (30 days). In the leap years an additional month, Adar II (29 days) is added.

The first month of the year is Nisan, as ordained in the. The 14th of Nisan is the start of the festival of, a date also prescribed in the Bible, corresponding to the of Nisan. Though it is not expressly prescribed in these terms, Pesach is a spring festival, so the 14th of Nisan is the first full moon after the. Therefore, from the standpoint of determining the annual calendar cycle, the principal problem is that the lunar month/new moon of Nisan must occur before the spring equinox. Since at least the 12th Century, the Hebrew calendar has determined this time mathematically, but prior to this tradition held that the 1st of Nisan does not start (and an would be added) "until the barley is ripe."

Biblical period
Biblical references to the pre-Jewish calendar include ten months identified by number rather than by name. In parts of the  (Noah) (specifically,, , ) 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.

In the parts of the (the ) prior to the Babylonian exile, only four months are named: ' (first; literally "Spring", originally this probably meant "the ripening of barley"), ' (second; literally "Light"), ' (literally "Strong" in plural, perhaps referring to strong rains) : seventh month; and ' : eighth month. All of these are ite names, and at least two are n (Northern Canaanite).

The Torah contains several related to the keeping of the calendar and the lunar cycle. The first commandment the Jewish people received as a nation was to determine the : states, "This month [Nissan] is for you the first of months." refers to a specific month: "Observe the month of Abib, and keep the passover unto the LORD thy God; for in the month of Abib the LORD thy God brought thee forth out of Egypt by night."

stresses the importance of the new moon and consequently lunar months, "... in your new moons, ye shall blow with the trumpets over your burnt-offerings,". Similarly in.

Leap months


Due to the difference in length between twelve lunar months and a solar year, a purely lunar calendar cycle would have resulted in a drift of the Hebrew calendar from the seasons. However, the Torah requires that certain festivals take place during certain s. This implies that a system of reconciling lunar months in the context of solar years and consequently seasons was in use. The Bible does not directly mention the addition of an "embolismic" or that would prevent the drifting of the calendar year, however, it is hinted that the first month was started only following the ripening of, and according to some traditions, if the barley had not yet ripened, another monthly cycle would be interjected after the "last month" , before the first month of the year was announced.

Thus, if Adar was over and the barley was not yet ripe, an additional month, "" was observed before Nisan. During such s Adar I (or Adar &mdash; "first Adar") is actually considered to be the extra month, and has 30 days. Adar II (or Adar &mdash; "second Adar") is the "real" Adar, and has the usual 29 days. For this reason, during a leap year, holidays such as are observed in Adar II, not Adar I.  Later, a mathematical system was developed to replace the observational method.

Babylonian exile and nomenclature
During the, which started in 586 BCE, Jews adopted ian names for the months, which are still in use. The also used a lunisolar calendar, derived from the.

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

Weeks and days
The Hebrew calendar follows the common 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 of the Hebrew letters, for example יום א׳ (Day 1, or Yom Rishon (: יום ראשון):

Yom Rishon (: יום ראשון), abbreviated יום א׳ = "first day" = Sunday Yom Sheni (יום שני), abbr. יום ב׳ = "second day" = Monday Yom Shlishi (יום שלישי), abbr. יום ג׳ = "third day" = Tuesday Yom Reviʻi (יום רבעי), abbr. יום ד׳ = "fourth day" = Wednesday Yom Ḥamishi (יום חמישי), abbr. יום ה׳ = "fifth day" = Thursday Yom Shishi (יום ששי), abbr. יום ו׳ = "sixth day" = Friday Yom Shabbat (יום שבת or more usually שבת - Shabbat), abbr. יום ש׳ = "Sabbath day (Rest day)" = Saturday

The names of the days of the week are modeled on the seven days mentioned in the story. For example, "... And there was evening and there was morning, one day". "One day" also translates to "first day" or "day one". Similarly,, , , , and.

Modeled on the same verses and the reference to "...there was evening and there was morning...", the Jewish day runs from sunset (start of "the evening") to the next sunset. Accordingly, s and s have no place in the Jewish calendar. However, the stready progression of sunset around the world has its own built in time zone. These are gradual and based on observable atronomical phenomona (the sunset) and not on man-made laws and conventions.

The Jewish Shabbat has a special place in the Jewish weekly cycle. There are many special rules which relate to the, discussed more fully in. In Hebrew, the word "Shabbat" (שַׁבָּת) can also mean "(Talmudic) week", so that in ritual liturgy a phrase like "Yom Reviʻi bəShabbat" means "the fourth day in the week".

Second Temple era, c. 518 BCE - 70 CE
In times (c. 518 BCE - 70 CE), the beginning of each lunar month was decided on the basis of two eyewitnesses testifying to having seen the new lunar crescent at sunset. Patriarch (c. 100) asked the 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. According to tradition, these observations were compared against calculations made by the supreme Jewish court, the. Whether or not an embolismic month was to be inserted depended on the calculated estimate of the spring equinox moment, the condition of roads used by families to come to Jerusalem for, 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.

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

If one back-calculates the moments of the traditional moladot using modern astronomical calculations then the closest that their reference of  ever got to Israel was midway between the  and the end of the  (about 4° east of Jerusalem), and that was in the era of the Second Temple.

From the times of the im (third to fifth centuries), calculations were increasingly used, for example by, who stated during the first half of the third century that the year contained 365 ¼ days, and by "calculators of the calendar" circa 300. Jose, an Amora who lived during the second half of the fourth century, stated that the feast of, 14 Adar, could not fall on a Sabbath nor a Monday, lest 10 Tishrei fall on a Friday or a Sunday. This indicates 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.

1st-3rd Centuries CE
By the Roman era, some sects, such as the, used a solar calendar during the last two centuries.

The of 66–73, 115–117, and 132–135 caused major disruptions in Jewish life, also disrupting the calendar. During the third and fourth centuries, sources describe the use of eight, nineteen, and 84 year lunisolar cycles by Jews, all linked to the civil calendars used by various communities of Diaspora Jews, which were effectively isolated from  Jews and their calendar. Some assigned major Jewish festivals to fixed solar calendar dates, whereas others used s to specify how many days before major civil solar dates Jewish lunar months were to begin.

The Talmud notes the irregular intercalation (adding of extra months) performed in three successive years in the early second century.

The Christian  (used to calculate ) describes in detail a Jewish calendar which must have been used by n Jews near the end of the third century. These Jews formed a relatively new community in the aftermath of the annihilation (by murder or enslavement) of all Alexandrian Jews by Emperor at the end of the 115–117. Their calendar used the same epacts in nineteen year cycles that were to become canonical in the Easter computus used by almost all medieval Christians, both those in the West and the  East. Only those churches beyond the eastern border of the differed, changing one epact every nineteen years, causing four Easters every 532 years to differ.

Transition period
The period between 70 and 1178 was a transition period between the two forms, with the gradual adoption of more and more of the rules characteristic of the modern form. Except for the modern year number, the modern rules reached their final form before 820 or 921, with some uncertainty regarding when.

Under the ate of Rabbi (300-330) the testimony of the witnesses with regard to the appearance of the new moon was received as a mere formality, the settlement of the day depending entirely on calculation. This innovation seems to have been viewed with disfavor by some members of the, particularly , who wrote to both the Babylonian and the Alexandrian communities, advising them to follow the customs of their fathers and continue to celebrate two days, an advice which was followed, and is still followed, by the majority of Jews living outside of Palestine.

The, which did not reach its final form until c. 500, does not mention the continuous calendar or even anything as mundane as either the nineteen-year cycle or the length of any month, despite discussing the characteristics of earlier calendars, suggesting the final form of the modern calendar was fixed subsequent to the 6th Century. This is despite a popular tradition, first mentioned by (d.1038), which holds that the modern continuous calendar was once a secret known only to a council of sages or "calendar committee," and that Patriarch  revealed it in 359 due to Christian persecution.

Furthermore, Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible using modern rules, and all evidence points to the development of the arithmetic rules of the modern calendar in Babylonia during the times of the (seventh to eighth centuries), under the  ate. The Babylonian rules required the delay of the first day of Tishrei when the occurred after.

Most of the modern rules appear to have been in place by about 820, according to a treatise by the astronomer  (c. 780-850 CE) a   noted for his contributions to, ,  and. Al-Khwārizmī's study of the Hebrew calendar,  "Extraction of the Jewish Era" describes the, the rules for determining on what day of the week the first day of the month shall fall, the interval between the  (creation of Adam) and the , and the rules for determining the mean longitude of the sun and the moon using the Jewish calendar.

One notable difference between the calendar of that era and the modern form was the date of the (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.

In 921,, a leader of the Jewish community in otherwise unknown to history, sought to return the authority for the calendar to the  by asserting that the first day of Tishrei should be the day of the new moon unless the new moon occurred more than 642 parts (35⅔ minutes, where a "part" is 1/1080 of an hour or 1/18 of a minute or 3⅓ seconds) after noon, when it should be delayed by one or two days. He may have been asserting that the calendar should be run according to Jerusalem time, not Babylonian. Local time on the Babylonian was indeed about 642 parts (35 minutes and 40 seconds) later than (ahead of) the meridian of, corresponding to a longitude difference of 8° 55'.

An alternative explanation for the 642 parts is that Ben Meir may have believed, along with many earlier Jewish scholars, in a placing  in the Spring season, and that the calendar rules had been adjusted by 642 parts to fit in with an Autumn date. If Creation occurred in the, to coincide with the observance of , the calculated time of New Moon during the six days of creation was on Friday at 14 hours exactly (counting from the day starting at 6pm the previous evening). However, if Creation actually occurred six months earlier, in the, the new moon would have occurred at 9 hours and 642 parts on Wednesday.

In any event he was opposed by of the Talmudic academy of. Only a few Jewish communities accepted ben Meir's opinion, and even these soon rejected it. Accounts of the controversy show that all of the rules of the modern calendar (except for the epoch) were in place before 921.

Middle Ages, codification of rules
In 1000, the Muslim chronologist also described all of the modern rules except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch. Finally, in 1178 described all of the modern rules, including the modern epochal year.

In his work , 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."

Maimonides continues, showing analytically how the scriptural procedure for determining the calendar must be flawed, something he could explain through his faith. He noted that non-Jewish savants had presented mathematically correct methods of calculating the potential visibility of the new crescent, and reasoned that since these methods exist, they must have been used by the Court and the record of their use lost.

Karaite interpretation
use the lunar month and the solar year, but the Karaite calendar differs from the Rabbinical calendar in a few ways: Determination of the first month of the year - (called ), which is the month Passover falls out and determination of the first day of each month.

The 4 rules of postponement are not applied, as they are not found in the. It is determined when to add a 13th month by observing the ripening of (called ) in, rather than the calculated and fixed calendar of. This puts Karaites in sync with the Written, while other Jews are often a month later.

The beginning of each month is determined by the - which can be calculated, but is confirmed by observation of the first sightings of the new moon in.

For several centuries, many Karaites, especially those outside Israel, have just followed the calculated dates of the (the  and the ) with other Jews for the sake of simplicity. However, in recent years most Karaites have chosen to again follow the Written practice.

Initial month
The Jewish or Hebrew year has four distinct starting points, according to the, "Rosh Hashanah 1:1":

The day most commonly referred to as the start of the New Year is the first of Tishrei, when the formal New Year festival, ("Head of the Year") is observed. This is the beginning of the civil year, and the point at which the year number advances by one. Certain agricultural practices are also marked from this date.

However, the first month of the year is, reflecting the injunction in 12:2, "This month shall be to you the beginning of months," meaning the civil New Year actually begins in the seventh month of the year. The month of is the new year for counting animal tithes.  ("the 15th of ") marks the new year for trees (and agricultural tithes).

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

Epoch
The Hebrew calendar uses a  ("in the year of the world"), abbreviated AM. Interestingly, the beginning of "year 1" is not, but about one year before Creation. This caused the new moon of its first month (Tishrei) to be called molad tohu (the mean new moon of chaos or nothing). Its (reference date), 1 Tishrei 1 AM, is equivalent to Monday,,  in the , the equivalent tabular date (same daylight period). This date is about one year before the traditional Jewish on 25 Elul AM 1, based upon the  of Rabbi, a second century CE sage. (A minority opinion places Creation on 25 Adar AM 1, six months earlier, or six months after the modern epoch.) Thus, adding 3760 (from September-October through December, 3761) to any Julian/Gregorian year number after 1 CE will yield the Hebrew year, ending in September-October, which roughly coincides with that Julian/Gregorian year. Owing to the slow drift of the modern Jewish calendar relative to the Gregorian calendar, this will be true for about another 20,000 years.

The traditional Hebrew date for the destruction of the (3338 AM = 423 BCE) differs from the modern scientific date, which is usually expressed using the Gregorian calendar (586 BCE). The scientific date takes into account evidence from the ancient Babylonian calendar and its astronomical observations. In this and related cases, a difference between the traditional Hebrew year and a scientific date in a Gregorian year results from a disagreement about when the event happened — and not simply a difference between the Hebrew and Gregorian calendars. See.

Measurement of the month
Traditionally "" refers to the first visible crescent of the moon, an event that usually can be observed 29 or 30 days after the preceding visible crescent, producing a lunar month length of 29 or 30 days. However, an actual, as scientifically defined based on the position of the moon in the , is a , known in as a "".

The calendar is based on estimated mean lunar conjunctions called ot spaced at intervals of exactly 29 days, 12 hours, and 793 parts (44+1/18 minutes). The traditional molad interval matches the mean synodic month as determined by the Babylonians before 300 BCE and as adopted by the Greek astronomer and the Alexandrian astronomer. Its remarkable accuracy is thought to have been achieved using records of lunar eclipses from the eighth to fifth centuries BCE, with a reference meridian midway between the Nile River and the end of the Euphrates River, about 4° east of Jerusalem.

The mean interval between molads, or the adopted mean lunar month length based on calculations, is exactly 765433/25920 days, or 29 days 12 hours and 44+1/18 minutes (or 29.5306 days).

Combining the observation method with the scientific lunar month length works as follows: assuming we start at a particular new month (which we'll call "the base date"), that month will be 29 days long, with 12 hours, 44+1/18 minutes left over ("the carry forward amount"). Adding that carry forward amount to the next month will make it equal 30 days, 1 hour and 24+2/18 minutes (30.0612 days). So the second month would be 30 days long, and 1 hour 24+2/18 minutes (2 x carry forward amount) would be carried forward to be added to the next cycle, and so on. Then every 17 lunar cycles the carry forward amounts are over 24 hours, which would require an additional day to be added to whatever length that month would have been. In summary, the progression becomes: year 1 | 29 - 30 - 29 -30 - 29 - 30 - 29 - 30 - 29 - 30 - 29 - 30 | year 2 | 29 - 30 - 29 - 30 - 30 - 29 - etc.

The other issue is the number of months in a year. Twelve lunar months are about 354 or 355 days (see above) while the is about 365 days so an extra lunar month is added every two or three years in accordance with a  (12 regular months every year plus 7 extra or embolismic months every 19 years).

Pattern of calendar years
The 19 year cycle has 12 common and 7 leap years. There are 235 lunar months in each. This gives a total of 6939 days, 16 hours and 595 parts for each cycle. Due to the Rosh HaShanah postponement rules of the Hebrew calendar, a cycle of 19 Hebrew years can be either 6939, 6940, 6941, or 6942 days in duration. Since none of these values is evenly divisible by seven, the Hebrew calendar repeats exactly only following 36,288 cycles, or 689,472 Hebrew years. There is a near-repetition every 247 years, except for an excess of 50 minutes (905 parts).

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

A Hebrew 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 because a day is taken away from the month of Kislev. 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. 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 because a day is added to the month of Heshvan. The Hebrew letter ש "shin", and the letter for the week-day denotes this pattern.

A Hebrew leap year is one that has 13 months, a common year has 12 months. Leap years of 13 months are the 3rd, 6th, 8th, 11th, 14th, 17th, and the 19th years beginning at the epoch of the modern calendar. Dividing the Hebrew year number by 19, and looking at the remainder will tell you if the year is a leap year (for the 19th year, the remainder is zero). Alternatively, the following expression yields the leap status of the year:

hYear is a leap year if the remainder of ( 7 x hYear + 1 ) / 19 is less than 7, where hYear is the Hebrew year number.

With 7 leap years per 19-year cycle, the average interval between leap years = 19/7 = 2+5/7 years, which means that 3-year intervals are more common that 2-year intervals.

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 ). Another mnemonic is that the intervals of the follow the same pattern as do Hebrew leap years: a  in the scale corresponds to two common years between consecutive leap years, and a  to one common between two leap years.

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.

Special holiday rules
Although simple math would calculate 21 patterns for calendar years, there are other limitations which mean that may only occur on Mondays, Tuesdays, Thursdays, and Saturdays (the "four gates"), according to the following table:

The lengths are described in the section.

In leap years, a 30 day month called Adar I is inserted immediately after the month of Shevat, and the regular 29 day month of Adar is called Adar II. This is done to ensure that the months of the Jewish calendar always fall in roughly the same seasons of the solar year, and in particular that Nisan is always in spring. Whether either Chesvan or Kislev both have 29 days, or both have 30 days, or one has 29 days and the other 30 days depends upon the number of days needed in each year. Thus a leap year of 13 months has an average length of 383½ days, so for this reason alone sometimes a leap year needs 383 and sometimes 384 days. Additionally, adjustments are needed to ensure certain holy days and festivals do or do not fall on certain days of the week in the coming year. For example, Yom Kippur, on which no work can be done, can never fall on Friday (the day prior to the ), to avoid having the previous day's fast day still going on at the start of Sabbath. Thus some flexibility has been built in.

The 265 days from the first day of the 29 day month of Adar (i.e. the twelfth month, but the thirteenth month, Adar II, in leap years) and ending with the 29th day of Heshvan forms a fixed length period that has all of the festivals specified in the Bible, such as (Nisan 15),  (Sivan 6),  (Tishrei 1),  (Tishrei 10),  (Tishrei 15), and  (Tishrei 22).

The festival period from Pesach up to and including Shemini Atzeret is exactly 185 days long. The time from the traditional day of the vernal  up to and including the traditional day of the autumnal equinox is also exactly 185 days long. This has caused some unfounded speculation that Pesach should be, and Shemini Atzeret should be , which are the traditional days for the equinoxes. Just as the Hebrew day starts at sunset, the Hebrew year starts in the Autumn (Rosh Hashanah), although the mismatch of solar and lunar years will eventually move it to another season if the modern fixed calendar isn't moved back to its original form of being judged by the Sanhedrin (which requires the )

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 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. The end of the and other s is based on nightfall (Tzeis Hacochavim) 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 and. 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 Shaos Zemaniyos or Halachic hours by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The earliest and latest times for, the latest time to eat on the day before  and many other rules are based on Shaos Zemaniyos. For convenience, the day using Shaos Zemaniyos is often discussed as if sunset were at 6:00pm, sunrise at 6:00am and each hour were equal to a fixed hour. However, for example, halachic may be after 1:00pm in some areas during.

Irregularities and "Missing Years"
The traditional dates of events in Jewish history are often used interchangeably with the modern secular dates according to the. For example, year 3338 AM on the Hebrew calendar is typically equated to 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 tradional 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. For instance, 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, 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 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.

Mean year length
The mean Hebrew calendar year length is 365.2468 days, or 365 days, 5 hours 55 minutes, and 25+25/57 seconds (the molad/monthly interval × 235 months per 19-year cycle ÷ 19 years per cycle). The present-era mean northward equinoctial year is about 365 days 5 hours 49 minutes and zero seconds, so the Hebrew calendar mean year is too long by about 6 minutes and 25+25/57 seconds per year. Approximately every 224 years, those minutes add up so that the Hebrew calendar will fall a full day behind the modern fixed solar year.

In addition, since the mean Gregorian calendar year is 365.2425 days (exactly 365 days 5 hours 49 minutes and 12 seconds) and the mean Hebrew calendar year is 365.2468 days, the Hebrew calendar falls further behind the Gregorian calendar by about a day about every 231 years.

Molad intervals
The source of the discrepancy is the difference between the molad interval and the actual lunar conjunction cycle. The molad interval is currently about 0.6 seconds too long, and the discrepancy is accumulating at an accelerating rate, since the mean lunation interval is progressively shortening due to gravitational effects. The accumulated "error" since the era of Hillel II is such that the molad moments are now almost 1 hour and 40 minutes late relative to the mean lunar conjunctions at the original reference, which was midway between the and the end of the. The modern molad moments match the mean solar times of the lunar conjunction moments near the meridian of, , more than 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, an astonishing 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 (make the conjunction moments 16 minutes earlier if referred to the original molad reference meridian midway between the Nile River and the end of the Euphrates River, about 4° east of Jerusalem). Today, in terms of the mean solar time at the meridian of Qandahar, Afghanistan the actual lunar conjunctions vary ±14 hours relative to the traditional moladot.

Measured on a strictly uniform time scale, such as that provided by an, the mean synodic month is becoming gradually longer, but since due to the tides the Earth rotation rate slowing even more the mean synodic month is becoming gradually shorter in terms of mean solar time. The value 29-12-793 was almost exactly correct at the time of and is now about 0.6 seconds per month too long. However, it is still the most correct value possible as long as only whole parts (1/18 minute) are used.

Implications for Jewish ritual
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 year 5765, an 8th year of the 19-year cycle = Gregorian 2005 AD). Presently this occurs after the "premature" insertion of a leap month in years 8, 19, and 11 of each 19-year cycle, which causes the northward equinox to land at exceptionally early moments in such years. This problem will get worse over time, and so beginning in Hebrew year 5817 the 3rd year 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, or about 10885 years from the present. (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 9, 1, 12 and 4 of each 19-year cycle (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.

"Rectifying" the Hebrew calendar
Given the importance, in Jewish ritual, of establishing the accurate timing of monthly and annual times, some 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.

Professor Irv Bromberg notes that the 19-year cycle (and indeed all aspects of the calendar) are part of codified Jewish law, and thus it would only be possible to amend it if a could be convened. It is traditionally assumed that this will take place upon the coming of the, which will mark the beginning of the according to Jewish belief.

"A 353-year cycle of 4366 lunations, including 130 leap months...[along with] use of a progressively shorter molad interval, will keep the amended calendar from drifting for more than 7 millennia." Adopting an astronomical calendar would require more explicit definition of the calendar rules. Other questions include whether or not a progressive molad should be used, or the actual lunar conjunction, or a prediction of new lunar crescent visibility, and which meridian of longitude should the moment be referred to.

Usage in contemporary Israel
Early 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, , or  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 movement was especially inventive in creating new rituals fitting this interpretation.

With the creation of the State of the Hebrew Calendar was made its official calendar. New holidays and commemorations not derived from previous Jewish tradition invariably were to be defined according to their Hebrew dates - notably the Israeli Independence Day on Iyar 5, Jerusalem Reunification Day on 28 Iyar, and the Holocaust Commemoration Day on Nisan 27 (close to the Hebrew date of the start of the ).

Nevertheless, since the 1950s the Hebrew calendar steadily declined in importance in Israeli daily life, in favor of the worldwide. At present, Israelis - except for the minority of religiously observant - conduct their private and public life according to the Gregorian Calendar, and an average Israeli would not know what the Hebrew date is without specifically looking it up&#91;citation needed&#93;, and questions such as "On what date does Hanukkah start this year?" are not uncommon.

The Jewish New Year is a two-day public holiday in Israel. However, since the 1980s an increasing number of secularist Israelis had taken up the habit of celebrating the Gregorian New Year (usually known as " Night" - "ליל סילבסטר") by holding all-night parties on the night between December 31 and January 1. Prominent Rabbis have on several occasions sharply denounced this practice, but with no noticeable effect on the secularist celebrants. &#91;citation needed&#93;

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

The wall Calendars commonly used in Israel are hybrids - organised according to Gregorian rather than Jewish months, but beginning in September, where the Jewish New Year usually falls, and providing the Jewish date in small characters.

Date converters

 * Jewish Calendar for Outlook - Incorporate Jewish dates and holidays into.
 * Molad - Jewish Calendar with Zmanim and holidays for.
 * Kaluach - Hebrew/civil calendars
 * Hebcal Hebrew Date Converter
 * Jewish/Gregorian/Julian Perpetual Calendar Converter - Also contains a full year view for the Hebrew Calendar.
 * Sample VB.Net and Javascript code to convert the Hebrew Date to the Gregorian Date
 * Jewish / Civil Date Converter
 * Gregorian-Mayan-Julian-Islamic-Persian-Hebrew Calendar Converter
 * Kalendis Calendar Calculator
 * Gregorian to Hebrew date with weekly Parshat HaShavua.
 * Full Jewish Year in Hebrew Characters
 * Full Jewish Year in Western Characters