The Hebrew or Jewish calendar (הַלּוּחַ הָעִבְרִי,
Ha-Luah ha-Ivri) is a lunisolar calendar used today predominantly for
Jewish religious observances. It determines the dates for Jewish
holidays and the appropriate public reading of
yahrzeits (dates to commemorate the death of a relative), and daily
Psalm readings, among many ceremonial uses. In Israel, it is used for
religious purposes, provides a time frame for agriculture and is an
official calendar for civil purposes, although the latter usage has
been steadily declining in favor of the Gregorian calendar.
Hebrew calendar is the product of evolution, including a
Babylonian influence. Until the
Tannaitic period (approximately
10–220 CE), the calendar employed a new crescent moon, with an
additional month normally added every two or three years to correct
for the difference between twelve lunar months and the solar year. The
year in which it was added was based on observation of natural
agriculture-related events in Israel. Through the
(200–500 CE) and into the
Geonic period, this system was gradually
displaced by the mathematical rules used today. The principles and
rules were fully codified by
Maimonides in the
Mishneh Torah in the
12th century. Maimonides' work also replaced counting "years since the
destruction of the Temple" with the modern creation-era Anno Mundi.
The Hebrew lunar year is about eleven days shorter than the solar year
and uses the 19-year
Metonic cycle to bring it into line with the
solar year, with the addition of an intercalary month every two or
three years, for a total of seven times per 19 years. Even with this
intercalation, the average
Hebrew calendar year is longer by about 6
minutes and 40 seconds than the current mean tropical year, so that
every 216 years the
Hebrew calendar will fall a day behind the current
mean tropical year; and about every 231 years it will fall a day
behind the mean
Gregorian calendar year.
The era used since the
Middle Ages is the
Anno Mundi epoch (
"in the year of the world"; Hebrew: לבריאת העולם,
"from the creation of the world"). As with
Anno Domini (A.D. or AD),
the words or abbreviation for
Anno Mundi (A.M. or AM) for the era
should properly precede the date rather than follow it.
AM 5778 began at sunset on 20 September 2017 and will end at sunset on
9 September 2018.
1.1 Day and hours
1.2.1 Names of weekdays
1.2.2 Days of week of holidays
1.3.1 Importance of lunar months
1.3.2 Names of months
1.3.3 Leap months
1.4.1 Anno Mundi
1.4.2 Previous systems
1.4.3 New year
1.4.4 Leap years
Rosh Hashanah postponement rules
1.4.6 Deficient, regular, and complete years
1.4.7 Four gates
2.1 Mishnaic period
2.2 Modern calendar
2.3 Usage in contemporary Israel
3 Other practices
3.1 Karaite calendar
3.3 The Qumran calendar
3.4 Persian civil calendar
4 Astronomical calculations
Synodic month – the molad interval
4.2 Seasonal drift
4.3 Implications for Jewish ritual
4.4 Worked example
5 Rectifying the Hebrew calendar
6 Conversion between Jewish and civil calendars
7 See also
10 External links
10.1 Date converters
Day and hours
Further information: Zmanim
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 account in the first chapter of Genesis. Based on the classic
rabbinic interpretation of this text, a day in the rabbinic Hebrew
calendar runs from sunset (start of "the evening") to the next
sunset. Halachically, a day ends and a new one starts when three
stars are visible in the sky. The time between true sunset and the
time when the three stars are visible (known as 'tzait ha'kochavim')
is known as 'bein hashmashot', and there are differences of opinion as
to which day it falls into for some uses. This may be relevant, for
example, in determining the date of birth of a child born during that
There is no clock in the Jewish scheme, so that the local civil clock
is used. Though the civil clock, including the one in use in Israel,
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.
In Judaism, an hour is defined as 1/12 of the time from sunrise to
sunset, so, during the winter, an hour can be much less than 60
minutes, and during the summer, it can be much more than 60 minutes.
This proportional hour is known as a sha'ah z'manit (lit. a timely
hour). A Jewish hour is divided into 1080 halakim (singular: helek) 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). These measures are not generally used for everyday
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. (See
International date line
International date line in Judaism.)
The weekdays start with Sunday (day 1, or
Yom Rishon) and proceed to
Saturday (day 7), Shabbat. 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 17th 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
6:00 pm, sunrise at 6:00 am and each hour were equal to a
fixed hour. For example, halachic noon may be after 1:00 pm 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.
Shavua [שבוע] is a weekly cycle of seven days, mirroring the
seven-day period of the
Book of Genesis
Book of Genesis in which the world is created.
The names for the days of the week, like those in the creation
account, are simply the day number within the week, with
the seventh day. Each day of the week runs from sunset to the
following sunset and is figured locally.
Names of weekdays
Shabbat candlestick holder made in British Mandate Palestine
in the 1940s.
Hebrew calendar follows a seven-day weekly cycle, which runs
concurrently with 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 יום א׳ (Day
Yom Rishon (יום ראשון)):
Yom Rishon – יום ראשון (abbreviated יום א׳),
meaning "first day" [corresponds to Sunday] (starting at preceding
sunset of Saturday)
Yom Sheni – יום שני (abbr. יום ב׳) meaning "second
day" [corresponds to Monday]
Yom Shlishi – יום שלישי (abbr. יום ג׳) meaning
"third day" [corresponds to Tuesday]
Yom Reviʻi – יום רביעי (abbr. יום ד׳) meaning
"fourth day" [corresponds to Wednesday]
Yom Chamishi – יום חמישי (abbr. יום ה׳) = "fifth
day" [corresponds to Thursday]
Yom Shishi – יום ששי (abbr. יום ו׳) meaning "sixth
day" [corresponds to Friday]
Shabbat – יום שבת (abbr. יום ש׳), or more
Shabbat – שבת meaning "rest day" [corresponds
Shabbat (יום שבת) is also known as
Shabbat Kodesh –
יום שבת קודש meaning "holy rest day."
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 (יוֹם
אֶחָד) in Genesis 1:15 is translated in JPS as first day, and
in some other contexts (including KJV) as day one. In subsequent
verses, the Hebrew refers to the days using ordinal numbers, e.g.,
'second day', 'third day', and so forth, but with the sixth and
seventh days the Hebrew includes the definite article ("the").
The rest day, Shabbat, has a special role in the Jewish weekly cycle
as being a special and set apart day, where no work is done. There are
many special rules that relate to Shabbat, discussed more fully in the
Talmudic tractate Shabbat.
In (Talmudic) Hebrew, the word
Shabbat (שַׁבָּת) can also
mean "week", so that in ritual liturgy a phrase like "
bəShabbat" means "the fourth day in the week".
Days of week of holidays
Main article: Days of week on Hebrew calendar
The period from 1
Adar II, in leap years) to 29 Marcheshvan
contains all of the festivals specified in the Bible –
Pesach (15 Nisan),
Shavuot (6 Sivan),
Rosh Hashanah (1
Yom Kippur (10 Tishrei),
Sukkot (15 Tishrei), and Shemini
Atzeret (22 Tishrei). This period is fixed, during which no
adjustments are made.
Sun or Mon
Sun or Tue
Sat or Mon
Wed or Thu
Wed, Thu, or Fri
Tue, Wed, or Thu
Fri or Sat
Fri or Sun
Thu or Sat
*Postponed from Shabbat
There are additional rules in the
Hebrew calendar to prevent certain
holidays from falling on certain days of the week. (See Rosh Hashanah
postponement rules, below.) These rules are implemented by adding an
extra day to
Marcheshvan (making it 30 days long) or by removing one
Kislev (making it 29 days long). Accordingly, a common Hebrew
calendar year can have a length of 353, 354 or 355 days, while a leap
Hebrew calendar year can have a length of 383, 384 or 385 days.
Hebrew calendar is a lunisolar calendar, meaning that months are
based on lunar months, but years are based on solar years. The
calendar year features twelve lunar months of twenty-nine or thirty
days, with an intercalary lunar month added periodically to
synchronize the twelve lunar cycles with the longer solar year. (These
extra months are added seven times every nineteen years. See Leap
months, below.) The beginning of each Jewish lunar month is based on
the appearance of the new moon. Although originally the new lunar
crescent had to be observed and certified by witnesses, the moment
of the true new moon is now approximated arithmetically as the molad,
which is the mean new moon to a precision of one part.
The mean period of the lunar month (precisely, the synodic month) is
very close to 29.5 days. Accordingly, the basic
Hebrew calendar year
is one of twelve lunar months alternating between 29 and 30 days:
Marcheshvan (or Cheshvan)
353, 354 or 355
In leap years (such as 5779) an additional month,
Adar I (30 days) is
added after Shevat, while the regular
Adar is referred to as "Adar
The insertion of the leap month mentioned above is based on the
requirement that Passover—the festival celebrating the Exodus from
Egypt, which took place in the spring—always occurs in the [northern
hemisphere's] spring season. Since the adoption of a fixed calendar,
intercalations in the
Hebrew calendar have been assigned to fixed
points in a 19-year cycle. Prior to this, the intercalation was
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.
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, although there is no evidence of a thirteenth month
mentioned anywhere in the Hebrew Bible.
Num 10:10 stresses the importance in Israelite religious observance of
the new month (Hebrew: ראש חודש, 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, and in Exod 12:2.
"This month is to you".
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 eyewitnesses 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
At first the beginning of each Jewish month was signaled to the
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
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
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
Both the Syrian calendar, currently used in the Arabic-speaking
countries of the Fertile crescent, and the modern Assyrian calendar
share many of the names for months with the Hebrew calendar, such as
Nisan, Iyyar, Tammuz, Ab, Elul, Tishri and Adar, indicating a common
origin. The origin is thought to be the Babylonian calendar.
The modern Turkish calendar includes the names Şubat (February),
Nisan (April), Temmuz (July) and Eylul (September). The former name
for October was Tesrin.
Biblical references to the pre-exilic calendar include ten months
identified by number rather than by name. In parts of the Torah
portion Noach ("Noah") (specifically, Gen 7:11, 8:3–4, 8:13–14) it
is implied that the months are thirty days long. There is also an
indication that there were twelve months in the annual cycle (1 Kings
4:7, 1 Chronicles 27:1–15). Prior to the Babylonian exile, the names
of only four months are referred to in the Tanakh:
Aviv – first month – literally "spring" (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. These names are
only mentioned in connection with the building of the First Temple.
Håkan Ulfgard suggests that the use of what are rarely used Canaanite
(or in the case of
Ethanim perhaps Northwest-semitic) names indicates
that "the author is consciously utilizing an archaizing terminology,
thus giving the impression of an ancient story...".
In a regular (kesidran) year,
Marcheshvan has 29 days and
30 days. However, because of the
Rosh Hashanah postponement rules (see
Kislev may lose a day to have 29 days, and the year is called a
short (chaser) year, or
Marcheshvan may acquire an additional day to
have 30 days, and the year is called a full (maleh) year. 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.
Hebrew names of the months with their Babylonian analogs
Called Abib (Exodus 13:4, 23:15, 34:18, Deut. 16:1)
Nisan (Esther 3:7) in the Tanakh.
אִיָּר / אייר
Called Ziv in 1 Kings 6:1, 6:37.
סִיוָן / סיוון
Seventeenth of Tammuz
Named for the Babylonian god Dumuzi
Ethanim in 1 Kings 8:2.
First month of civil year.
מַרְחֶשְׁוָן / מרחשוון
Called Bul in 1 Kings 6:38.
כִּסְלֵו / כסליו
Tenth of Tevet
*Only in Leap years.
אֲדָר / אֲדָר ב׳*
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 '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. It may be noted that in the Bible the
name of the first month, Aviv, literally means "spring". Thus, if Adar
was over and spring had not yet arrived, an additional month was
Traditionally, for the Babylonian and Hebrew lunisolar calendars, the
years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the
Metonic cycle. This cycle forms the basis of the Christian
ecclesiastical calendar and the
Hebrew calendar and is used for the
computation of the date of Easter each year
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
Purim are observed in
Adar II, not
Hebrew astronomy and Jewish views on astrology
Chronology was a chief consideration in the study of astronomy among
the Jews; sacred time was based upon the cycles of the Sun and the
Talmud identified the twelve constellations of the zodiac
with the twelve months of the Hebrew calendar. The
correspondence of the constellations with their names in Hebrew and
the months is as follows:
Aries – Taleh – Nisan
Taurus – Shor – Iyar
Gemini – Teomim – Sivan
Cancer – Sartan – Tammuz
Leo – Arye – Av
Virgo – Betulah – Elul
Libra – Moznayim – Tishrei
Scorpio – 'Akrab – Marcheshvan
Sagittarius – Keshet – Kislev
Capricorn – Gdi – Tevet
Aquarius – Dli – Shevat
Pisces – Dagim – Adar
Some scholars identified the 12 signs of the zodiac with the 12 sons
of Jacob/twelve tribes of Israel. It should be noted that the 12
lunar months of the
Hebrew calendar are the normal months from new
moon to new moon: the year normally contains twelve months averaging
29.52 days each. The discrepancy compared to the mean synodic month of
29.53 days is due to
Adar I in a leap year always having thirty days.
This means that the calendar year normally contains 354 days.
Year 5778 since the creation of the world,
according to the traditional count.
This year has 354 days,
making it a regular (כסדרה) year.
Rosh Hashanah is on Thursday,
Passover is on Saturday.
According to the Machzor Katan, the 19-year (Metonic) cycle used to
Hebrew calendar aligned with the solar year:
This year is the 2nd year of the 305th cycle.
It is not a leap year.
According to the Machzor Gadol, a 28-year solar cycle used to
calculate the date to recite Birkat Hachama, a blessing on the sun:
This year is the 10th year of the 207th cycle.
According to the current reckoning of sabbatical (shmita) years:
This year is the 3rd year of the cycle.
It is a maaser ani year.
Hebrew calendar year conventionally begins on Rosh Hashanah.
However, other dates serve as the beginning of the year for different
There are three qualities that distinguish one year from another:
whether it is a leap year or a common year, on which of four
permissible days of the week the year begins, and whether it is a
deficient, regular, or complete year. Mathematically, there are 24
(2×4×3) possible combinations, but only 14 of them are valid. Each
of these patterns is called a keviyah (Hebrew קביעה for "a
setting" or "an established thing"), and is encoded as a series of two
or three Hebrew letters. See Four gates.
In Hebrew there are two common ways of writing the year number: with
the thousands, called לפרט גדול ("major era"), and without
the thousands, called לפרט קטן ("minor era"). Thus, the
current year is written as ה'תשע"ח (5778) using the "major
era" and תשע"ח (778) using the "minor era".
Further information: Anno Mundi
The Jewish calendar's reference point is traditionally held to be
about one year before the Creation of the world.
In 1178 CE,
Maimonides wrote in the Mishneh Torah, Sanctification of
the Moon (11.16), that he had chosen the epoch from which calculations
of all dates should be as "the third day of
Nisan in this present year
... which is the year 4938 of the creation of the world" (March 22,
1178). He included all the rules for the calculated calendar and
their scriptural basis, including the modern epochal year in his work,
and beginning formal usage of the anno mundi era. From the eleventh
century, anno mundi dating became dominant throughout most of the
world's Jewish communities.[page needed] Today, the rules
detailed in Maimonides' calendrical code are those generally used by
Jewish communities throughout the world.
Since the codification by
Maimonides in 1178, the Jewish calendar has
Anno Mundi epoch (
Latin for "in the year of the world,"
abbreviated AM or A.M., Hebrew לבריאת העולם), sometimes
referred to as the "Hebrew era", to distinguish it from other systems
based on some computation of creation, such as the Byzantine calendar.
There is also reference in the
Talmud to years since the creation
based on the calculation in the
Seder Olam Rabbah
Seder Olam Rabbah of
Rabbi Jose ben
Halafta in about 160 CE. By his calculation, based on the
Adam was created in 3760 BCE, later confirmed by the
Muslim chronologist al-Biruni as 3448 years before the Seleucid
era. An example is the c. 8th century
Baraita of Samuel.
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 AM 1, is equivalent to Monday, 7 October 3761 BC/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. Thus,
adding 3760 before
Rosh Hashanah or 3761 after to a Julian year number
starting from 1 CE (AD 1) will yield the Hebrew year. For earlier
years there may be a discrepancy [see: Missing years (Jewish
Seder Olam Rabbah
Seder Olam Rabbah also recognized the importance of the Jubilee
and Sabbatical cycles as a long-term calendrical system, and attempted
at various places to fit the Sabbatical and Jubilee years into its
Anno Mundi is styled as Anno Hebraico (AH), though
this is subject to confusion with notation for the Islamic Hijri year.
Before the adoption of the current AM year numbering system, other
systems were in use. In early times, the years were counted from some
significant historic event. (e.g., 1 Kings 6:1) During the period of
the monarchy, it was the widespread practice in western Asia to use
era year numbers according to the accession year of the monarch of the
country involved. This practice was also followed by the united
Israel (e.g., 1 Kings 14:25), kingdom of Judah (e.g., 2
Kings 18:13), kingdom of
Israel (e.g., 2 Kings 17:6),
Nehemiah 2:1) and others. Besides, the author of Kings coordinated
dates in the two kingdoms by giving the accession year of a monarch in
terms of the year of the monarch of the other kingdom, (e.g., 2 Kings
8:16) though some commentators note that these dates do not always
synchronise. Other era dating systems have been used at other
times. For example, Jewish communities in the Babylonian diaspora
counted the years from the first deportation from Israel, that of
Jehoiachin in 597 BCE, (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 Hellenistic Maccabean period,
Seleucid era counting was
used, at least in the Greek-influenced area of Israel. The Books of
the Maccabees used
Seleucid era dating exclusively (e.g., 1 Maccabees
1:54, 6:20, 7:1, 9:3, 10:1).
Josephus writing in the Roman period also
Seleucid era dating exclusively. During the Talmudic era, from
the 1st to the 10th century, the center of world
Judaism was in the
Middle East, primarily in the Talmudic Academies of Iraq and
Jews in these regions used
Seleucid era dating (also known
as the "
Era of Contracts"). The
Avodah Zarah states:
Rav Aha b.
Jacob then put this question: How do we know that our Era
[of Documents] is connected with the Kingdom of Greece at all? Why not
say that it is reckoned from the Exodus from Egypt, omitting the first
thousand years and giving the years of the next thousand? In that
case, the document is really post-dated!
Rav Nahman: In the Diaspora the Greek
Era alone is used. He [the
questioner] thought that
Rav Nahman wanted to dispose of him anyhow,
but when he went and studied it thoroughly he found that it is indeed
taught [in a Baraita]: In the Diaspora the Greek
Era alone is
The use of the era of documents (i.e., Seleucid era) continued till
the 16th century in the East, and was employed even in the 19th
century among the
Jews of Yemen.
Occasionally in Talmudic writings, reference was made to other
starting points for eras, such as destruction era dating, being
the number of years since the 70 CE destruction of the Second Temple.
In the 8th and 9th centuries, as the center of Jewish life moved from
Babylonia to Europe, counting using the
Seleucid era "became
meaningless". There is indication that
Jews of the Rhineland in
Middle Ages used the "years after the destruction of the
Temple" (e.g., Mainz Anonymous).
A shofar made from a ram's horn is traditionally blown in observance
of Rosh Hashanah, the beginning of the Jewish civic year.
Exodus 12:2 and Deut 16:1 set
Aviv (now Nisan) as "the first of
this month shall be unto you the beginning of months; it shall be the
first month of the year to you.
Nisan 1 is referred to as the ecclesiastical new year.
In ancient Israel, the start of the ecclesiastical new year for the
counting of months and festivals (i.e., Nisan) was determined by
reference to Passover.
Passover is on 15 Nisan, (Leviticus 23:4–6)
which corresponds to the full moon of Nisan. As
Passover is a spring
festival, it should fall on a full moon day around, and normally just
after, the vernal (northward) equinox. If the twelfth full moon after
Passover is too early compared to the equinox, a leap
month is inserted near the end of the previous year before the new
year is set to begin. According to normative Judaism, the verses in
Exodus 12:1–2 require that the months be determined by a proper
court with the necessary authority to sanctify the months. Hence the
court, not the astronomy, has the final decision.
According to some Christian and Karaite sources, the tradition in
Israel was that 1
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.
The day most commonly referred to as the "New Year" is 1 Tishrei,
which actually begins in the seventh month of the ecclesiastical year.
On that day the formal New Year for the counting of years (such as
Shmita and Yovel),
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 date on which the year number
advances. Certain agricultural practices are also marked from this
In the 1st century,
Josephus stated 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]."
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
Kingdom of Judah counted years using the
civil new year starting on 1 Tishrei. The practice of the Kingdom
Israel was also that of Babylon, as well as other countries of
the region. The practice of Judah is still followed.
In fact the Jewish calendar has a multiplicity of new years for
different purposes. The use of these dates has been in use for a long
time. 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. By the time of the
redaction of the Mishnah,
Rosh Hashanah 1:1 (c. 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
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).
For the dates of the Jewish New Year see Jewish and Israeli holidays
2000–2050 or calculate using the section "Conversion between Jewish
and civil calendars".
The Jewish calendar is based on the
Metonic cycle of 19 years, of
which 12 are common (non-leap) years of 12 months and 7 are leap years
of 13 months. To determine whether a Jewish year is a leap year, one
must find its position in the 19-year Metonic cycle. This position is
calculated by dividing the Jewish year number by 19 and finding the
remainder. For example, the Jewish year 5778 divided by 19 results in
a remainder of 2, indicating that it is year 2 of the Metonic cycle.
Since there is no year 0, a remainder of 0 indicates that the year is
year 19 of the cycle.
Years 3, 6, 8, 11, 14, 17, and 19 of the
Metonic cycle are leap years.
To assist in remembering this sequence, some people use the mnemonic
Hebrew word GUCHADZaT "גוחאדז"ט", where the Hebrew letters
gimel-vav-het aleph-dalet-zayin-tet are used as Hebrew numerals
equivalent to 3, 6, 8, 1, 4, 7, 9. The keviyah records whether the
year is leap or common: פ for peshuta (פשוטה), meaning simple
and indicating a common year, and מ indicating a leap 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
plain in the context of 19 equal temperament: counting the tonic as 0,
the notes of the major scale in
19 equal temperament
19 equal temperament are numbers 0 (or
19), 3, 6, 8, 11, 14, 17, the same numbers as the leap years in the
A simple rule for determining whether a year is a leap year has been
given above. However, there is another rule which not only tells
whether the year is leap but also gives the fraction of a month by
which the calendar is behind the seasons, useful for agricultural
purposes. To determine whether year n of the calendar is a leap year,
find the remainder on dividing [(7 × n) + 1] by
19. If the remainder is 6 or less it is a leap year; if it is 7 or
more it is not. For example, the remainder on dividing
[(7 × 5778) + 1] by 19 is 15, so the year 5778 is
not a leap year. The remainder on dividing
[(7 × 5779) + 1] by 19 is 3, so the year 5779 is
a leap year. This works because as there are seven leap years in
nineteen years the difference between the solar and lunar years
increases by 7/19-month per year. When the difference goes above
18/19-month this signifies a leap year, and the difference is reduced
by one month.
Rosh Hashanah postponement rules
Day of week
Number of days
To calculate the day on which
Rosh Hashanah of a given year will fall,
it is necessary first to calculate the expected molad (moment of lunar
conjunction or new moon) of
Tishrei in that year, and then to apply a
set of rules to determine whether the first day of the year must be
postponed. The molad can be calculated by multiplying the number of
months that will have elapsed since some (preceding) molad whose
weekday is known by the mean length of a (synodic) lunar month, which
is 29 days, 12 hours, and 793 parts (there are 1080 "parts" in an
hour, so that one part is equal to 31⁄3 seconds). The very first
molad, the molad tohu, fell on Sunday evening at 11.111⁄3, or in
Jewish terms Day 2, 5 hours, and 204 parts.
In calculating the number of months that will have passed since the
known molad that one uses as the starting point, one must remember to
include any leap month(s) that falls within the elapsed interval,
according to the cycle of leap years. A 19-year cycle of 235 synodic
months has 991 weeks 2 days 16 hours 595 parts, a common year of 12
synodic months has 50 weeks 4 days 8 hours 876 parts, while a leap
year of 13 synodic months has 54 weeks 5 days 21 hours 589 parts.
The two months whose numbers of days may be adjusted,
Kislev, are the eighth and ninth months of the Hebrew year, whereas
Tishrei is the seventh month (in the traditional counting of the
months, even though it is the first month of a new calendar year). Any
adjustments needed to postpone
Rosh Hashanah must be made to the
adjustable months in the year that precedes the year of which the Rosh
Hashanah will be the first day.
Just four potential conditions are considered to determine whether the
Rosh Hashanah must be postponed. These are called the Rosh
Hashanah postponement rules, or deḥiyyot:
If the molad occurs at or later than noon,
Rosh Hashanah is postponed
a day. This is called deḥiyyah molad zaken (literally, "old birth",
i.e., late new moon).
If the molad occurs on a Sunday, Wednesday, or Friday, Rosh Hashanah
is postponed a day. If the application of deḥiyyah molad zaken would
Rosh Hashanah on one of these days, then it must be postponed a
second day. This is called deḥiyyah lo ADU, an acronym that means
"not [weekday] one, four, or six."
The first of these rules (deḥiyyah molad zaken) is referred to in
the Talmud. Nowadays, molad zaken is used as a device to prevent
the molad falling on the second day of the month. The second rule,
(deḥiyyah lo ADU), is applied for religious reasons.
Another two rules are applied much less frequently and serve to
prevent impermissible year lengths. Their names are Hebrew acronyms
that refer to the ways they are calculated:
If the molad in a common year falls on a Tuesday after 9 hours and 204
Rosh Hashanah is postponed to Thursday. This is deḥiyyah
GaTaRaD, where the acronym stands for "3 [Tuesday], 9, 204."
If the molad following a leap year falls on a Monday, more than 15
hours and 589 parts after the Hebrew day began (for calculation
purposes, this is taken to be 6 pm Sunday),
Rosh Hashanah is
postponed to Tuesday. This is deḥiyyah BeTUTeKaPoT, where the
acronym stands for "2 [Monday], 15, 589."
At the innovation of the sages, the calendar was arranged to ensure
Yom Kippur would not fall on a
Friday or Sunday, and Hoshana
Rabbah would not fall on Shabbat. These rules have been instituted
Shabbat restrictions also apply to
Yom Kippur, so that if Yom
Kippur were to fall on Friday, it would not be possible to make
necessary preparations for
Shabbat (such as candle lighting).
Yom Kippur fell on a Sunday, it would not be possible to
make preparations for
Yom Kippur because the preceding day is
Shabbat. Additionally, the laws of
Shabbat override those of
Hoshana Rabbah, so that if
Hoshana Rabbah were to fall on Shabbat
certain rituals that are a part of the
Hoshana Rabbah service (such as
carrying willows, which is a form of work) could not be performed.
Yom Kippur (10 Tishrei) from falling on a
Friday or Sunday,
Rosh Hashanah (1 Tishrei) cannot fall on Wednesday or Friday.
Likewise, to prevent
Hoshana Rabbah (21 Tishrei) from falling on a
Rosh Hashanah cannot fall on a Sunday. This leaves only four
days on which
Rosh Hashanah can fall: Monday, Tuesday, Thursday, and
Saturday, which are referred to as the "four gates". Each day is
associated with a number (its order in the week, beginning with Sunday
as day 1). Numbers in Hebrew have been traditionally denominated by
Hebrew letters. Thus the keviyah uses the letters ה ,ג ,ב and ז
(representing 2, 3, 5, and 7, for Monday, Tuesday, Thursday, and
Saturday) to denote the starting day of the year.
Deficient, regular, and complete years
The postponement of the year is compensated for by adding a day to the
second month or removing one from the third month. A Jewish common
year can only have 353, 354, or 355 days. A leap year is always 30
days longer, and so can have 383, 384, or 385 days.
A chaserah year (Hebrew for "deficient" or "incomplete") is 353 or 383
days long. Both
Kislev have 29 days. The Hebrew letter ח
"het" is used in the keviyah.
A kesidrah year ("regular" or "in-order") is 354 or 384 days long.
Cheshvan has 29 days while
Kislev has 30 days. The Hebrew letter כ
"kaf" is used in the keviyah.
A shlemah year ("complete" or "perfect", also "abundant") is 355 or
385 days long. Both
Kislev have 30 days. The Hebrew
letter ש "shin" is used in the keviyah.
Whether a year is deficient, regular, or complete is determined by the
time between two adjacent
Rosh Hashanah observances and the leap year.
While the keviyah is sufficient to describe a year, a variant
specifies the day of the week for the first day of
in lieu of the year length.
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 (preceding
section) 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 about 50 minutes (905 parts).
The annual calendar of a numbered Hebrew year, displayed as 12 or 13
months partitioned into weeks, can be determined by consulting the
table of Four gates, whose inputs are the year's position in the
19-year cycle and its molad Tishrei. The resulting type (keviyah) of
the desired year in the body of the table is a triple consisting of
two numbers and a letter (written left-to-right in English). The left
number of each triple is the day of the week of 1 Tishrei, Rosh
Hashanah (2 3 5 7); the letter indicates whether that year is
deficient (D), regular (R), or complete (C), the number of days in
Chesvan and Kislev; while the right number of each triple is the day
of the week of 15 Nisan, the first day of
Pesach (1 3 5
7), within the same Hebrew year (next Julian/Gregorian year). The
keviyah in Hebrew letters are written right-to-left, so their days of
the week are reversed, the right number for 1
Tishrei and the left for
15 Nisan. The year within the 19-year cycle alone determines whether
that year has one or two Adars.
This table numbers the days of the week and hours for the limits of
Tishrei in the Hebrew manner for calendrical calculations, that
is, both begin at 6 pm, thus 7d 18h 0p is noon Saturday. The years of
a 19-year cycle are organized into four groups: common years after a
leap year but before a common year (1 4 9 12 15); common years between
two leap years (7 18); common years after a common year but before a
leap year (2 5 10 13 16); and leap years (3 6 8 11 14 17 19), all
between common years. The oldest surviving table of Four gates was
Saadia Gaon (892–942). It is so named because it
identifies the four allowable days of the week on which 1
Comparing the days of the week of molad
Tishrei with those in the
keviyah shows that during 39% of years 1
Tishrei is not postponed
beyond the day of the week of its molad Tishrei, 47% are postponed one
day, and 14% are postponed two days. This table also identifies the
seven types of common years and seven types of leap years. Most are
represented in any 19-year cycle, except one or two may be in
neighboring cycles. The most likely type of year is 5R7 in 18.1% of
years, whereas the least likely is 5C1 in 3.3% of years. The day of
the week of 15
Nisan is later than that of 1
Tishrei by one, two or
three days for common years and three, four or five days for leap
years in deficient, regular or complete years, respectively.
Year of 19-year cycle
1 4 9 12 15
2 5 10 13 16
3 6 8 11 14 17 19
7d 18h 0p
1d 9h 204p
1d 20h 491p
2d 15h 589p
2d 18h 0p
3d 9h 204p
3d 18h 0p
4d 11h 695p
5d 9h 204p
5d 18h 0p
6d 0h 408p
6d 9h 204p
6d 20h 491p
See Jewish and Israeli holidays 2000–2050
Part of a series on the
History of Israel
Israel and Judah
Kingdom of Judah
Second Temple period
Second Temple period (530 BC–AD 70)
Middle Ages (70–1517)
Revolt against Constantius Gallus
Revolt against Heraclius
Modern history (1517–1948)
History of the Land of
Israel by topic
The Trumpeting Place inscription, a stone (2.43×1 m) with Hebrew
inscription "To the Trumpeting Place" is believed to be a part of 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.
It has been noted that the procedures described in the
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
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
Second Temple period
Second 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.
Arch of Titus
Arch of Titus depicting the objects from the Temple being carried
Between 70 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 the Persian Muslim
astronomer al-Khwarizmi (c. 780–850 CE) 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 al-Khwarizmi. 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. Not all the rules were in place by 835.
Aaron ben Meïr proposed changes to the calendar. Though the
proposals were rejected, they indicate 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 (died 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 in response to persecution of Jews.
Maimonides, in the 12th century, stated that the Mishnaic calendar was
used "until the days of Abaye and Rava", who flourished c. 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 linked the introduction of the computed
calendar to a sharp repression following a failed Jewish insurrection
that occurred during the rule of the Christian emperor Constantius and
Gallus. A later writer, S. Lieberman, argued instead that the
introduction of the fixed calendar was due to measures taken by
Christian 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 (7th to 8th
centuries). The Babylonian rules required the delay of the first
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 3rd century, the feast of Purim, 14 Adar, could not
fall on a Sabbath nor a Monday, lest 10
Yom Kippur) fall on a
Friday or a Sunday. This indicates that, by the time of the
redaction of the
Talmud (c. 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 who "made computations" and were in a position to control, to
some extent, the day of the week on which
Rosh Hashanah would fall.
Usage in contemporary Israel
Zionist pioneers were impressed by the fact that the calendar
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 transition from the
dry season to the rainy one, and major
Jewish holidays such as Sukkot,
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.
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
Nevertheless, since the 1950s usage of the
Hebrew calendar has
steadily declined, in favor of the Gregorian calendar. At present,
Israelis—except for the religiously observant—conduct their
private and public life according to the Gregorian calendar, although
Hebrew calendar is still widely acknowledged, appearing in public
venues such as banks (where it is legal for use on cheques 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
Wall calendars commonly used in
Israel are hybrids. Most are organised
according to Gregorian rather than Jewish months, but begin in
September, when the Jewish New Year usually falls, and provide the
Jewish date in small characters.
Outside of Rabbinic Judaism, evidence shows a diversity of practice.
Karaites use the lunar month and the solar year, but the Karaite
calendar differs from the current Rabbinic calendar in a number of
ways. The Karaite calendar is identical to the Rabbinic calendar used
Sanhedrin changed the Rabbinic calendar from the lunar,
observation based, calendar to the current, mathematically based,
calendar used in
Rabbinic Judaism today.
In the lunar Karaite calendar, 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 at a specific stage (defined by Karaite
tradition) (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
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, since they are not mentioned in the Tanakh. This can affect
the dates observed for all the
Jewish holidays in a particular year by
one or two days.
Middle Ages many
Karaite Jews outside
Israel followed the
calculated rabbinic calendar, because it was not possible to retrieve
accurate aviv barley data from the land of Israel. However, since the
establishment of the State of Israel, and especially since the Six Day
Karaite Jews that have made aliyah can now again use the
Samaritan community's calendar also relies on lunar months and
solar years. Calculation of the
Samaritan calendar has historically
been a secret reserved to the priestly family alone, and was based
on observations of the new crescent moon. More recently, a
Samaritan High Priest transferred the calculation to a
computer algorithm. The current High Priest confirms the results twice
a year, and then distributes calendars to the community.
The epoch of the
Samaritan calendar is year of the entry of the
Israel into the Land of
Israel with Joshua. The month of
Passover is the first month in the
Samaritan calendar, but the year
number increments in the sixth month. Like in the Rabbinic calendar,
there are seven leap years within each 19-year cycle. However, the
Samaritan calendars' cycles are not synchronized, so
Samaritan festivals—notionally the same as the Rabbinic festivals of
Torah origin—are frequently one month off from the date according to
the Rabbinic calendar. Additionally, as in the Karaite calendar, the
Samaritan calendar does not apply the four rules of postponement,
since they are not mentioned in the Tanakh. This can affect the dates
observed for all the
Jewish holidays in a particular year by one or
The Qumran calendar
Enoch calendar and Qumran calendrical texts
Many of the Dead Sea (Qumran) Scrolls have references to a unique
calendar, used by the people there, who are often assumed to be
The year of this calendar used the ideal Mesopotamian calendar of
twelve 30-day months, to which were added 4 days at the equinoxes and
solstices (cardinal points), making a total of 364 days.
There was some ambiguity as to whether the cardinal days were at the
beginning of the months or at the end, but the clearest calendar
attestations give a year of four seasons, each having three months of
30, 30, and 31 days with the cardinal day the extra day at the end,
for a total of 91 days, or exactly 13 weeks. Each season started on
the 4th day of the week (Wednesday), every year. (Ben-Dov, Head of All
Years, pp. 16–17)
With only 364 days, it is clear that the calendar would after a few
years be very noticeably different from the actual seasons, but there
is nothing to indicate what was done about this problem. Various
suggestions have been made by scholars. One is that nothing was done
and the calendar was allowed to change with respect to the seasons.
Another suggestion is that changes were made irregularly, only when
the seasonal anomaly was too great to be ignored any longer. (Ben-Dov,
Head of All Years, pp. 19–20)
The writings often discuss the moon, but the calendar was not based on
the movement of the moon any more than indications of the phases of
the moon on a modern western calendar indicate that that is a lunar
calendar. Recent analysis of one of the last scrolls remaining to be
deciphered has revealed it relates to this calendar and that the sect
used the word tekufah to identify each of the four special days
marking the transitions between the seasons.
Persian civil calendar
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.
Sardica paschal table
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
Nisan 14 approximately between 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, indicate that when years were intercalated, the
intercalary month was at least sometimes a repeated month of Adar. The
inscriptions, however, reveal no clear pattern of regular
intercalations, nor do they indicate any consistent rule for
determining the start of the lunar month.
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.
Synodic month – the molad interval
A "new moon" (astronomically called a lunar conjunction and, in
Hebrew, a molad) is the moment at which the sun and moon are aligned
horizontally with respect to a north-south line (technically, they
have the same ecliptical longitude). The period between two new moons
is a synodic month. The actual length of a synodic month varies from
about 29 days 6 hours and 30 minutes (29.27 days) to about 29 days and
20 hours (29.83 days), a variation range of about 13 hours and 30
minutes. Accordingly, for convenience, a long-term average length,
identical to the mean synodic month of ancient times (also called the
molad interval) is used. The molad interval is
displaystyle tfrac 765433 25920
days, or 29 days, 12 hours, and 793 "parts" (1 "part" = 1/18 minute;
3 "parts" = 10 seconds) (i.e., 29.530594 days), and is the same value
determined by the Babylonians in their System B about 300 BCE and
was adopted by the Greek astronomer
Hipparchus in the 2nd century BCE
and by the Alexandrian astronomer
Ptolemy in the
centuries later (who cited
Hipparchus as his source). Its remarkable
accuracy (less than one second from the true value) is thought to have
been achieved using records of lunar eclipses from the 8th to 5th
This value 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". The
discrepancy makes the molad interval 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, the traditional date of the introduction
of the fixed calendar, then it is found to correspond to a longitude
midway between the
Nile and the end of the Euphrates. 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
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.
The mean year of the current mathematically based
Hebrew calendar is
365 days 5 hours 55 minutes and 25+25/57 seconds (365.2468 days) –
computed as the molad/monthly interval of 29.530594 days × 235 months
in a 19-year metonic cycle ÷ 19 years per cycle. In relation to the
Gregorian calendar, the mean
Gregorian calendar year is 365 days 5
hours 49 minutes and 12 seconds (365.2425 days), and the drift of the
Hebrew calendar in relation to it is about a day every 231 years.
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
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
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
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
When the 19-year intercalary cycle was finalised in the 4th century,
Passover (in year 16 of the cycle) coincided with the
northward equinox, which means that
Passover fell near the first full
moon after the northward equinox, or that the northward equinox landed
within one lunation before 16 days after the molad of Nisan. 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 AM 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
AM 5817 (2057 CE), year 3 of each 19-year cycle will also be a month
late. If the calendar is not amended, then
Passover will start to land
on or after the summer solstice around AM 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. The
Hebrew calendar also
drifts 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 AM
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
Israel will start before the end of Sukkot.
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 031⁄3s 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 currently falls on
26 March (as in AM 5773 / 2013 CE).
Given the length of the year, the length of each month is fixed as
described above, so the real problem in determining the calendar for a
year is determining the number of days in the year. In the modern
calendar, this is determined in the following manner.
The day of
Rosh Hashanah and the length of the year are determined by
the time and the day of the week of the
Tishrei molad, that is, the
moment of the average conjunction. Given the
Tishrei molad of a
certain year, the length of the year is determined as follows:
First, one must determine whether each year is an ordinary or leap
year by its position in the 19-year Metonic cycle. Years 3, 6, 8, 11,
14, 17, and 19 are leap years.
Secondly, one must determine the number of days between the starting
Tishrei molad (TM1) and the
Tishrei molad of the next year (TM2). For
calendar descriptions in general the day begins at 6 p.m., but for the
purpose of determining Rosh Hashanah, a molad occurring on or after
noon is treated as belonging to the next day (the first
deḥiyyah). All months are calculated as 29d, 12h, 44m,
31⁄3s long (MonLen). Therefore, in an ordinary year TM2 occurs 12
× 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 × MonLen days
after TM1. This is usually 384 days after TM1, but if TM1 is on or
after noon and before 2:27:162⁄3 p.m., TM2 will be only 383 days
after TM1. In the same way, from TM2 one calculates TM3. Thus the four
natural year lengths are 354, 355, 383, and 384 days.
However, because of the holiday rules,
Rosh Hashanah cannot fall on a
Sunday, Wednesday, or Friday, so if TM2 is one of those days, Rosh
Hashanah in year 2 is postponed by adding one day to year 1 (the
second deḥiyyah). To compensate, one day is subtracted from year 2.
It is to allow for these adjustments that the system allows 385-day
years (long leap) and 353-day years (short ordinary) besides the four
natural year lengths.
But how can year 1 be lengthened if it is already a long ordinary year
of 355 days or year 2 be shortened if it is a short leap year of 383
days? That is why the third and fourth deḥiyyahs are needed.
If year 1 is already a long ordinary year of 355 days, there will be a
problem if TM1 is on a Tuesday, as that means TM2 falls on a
Sunday and will have to be postponed, creating a 356-day year. In this
Rosh Hashanah in year 1 is postponed from Tuesday (the third
deḥiyyah). As it cannot be postponed to Wednesday, it is postponed
to Thursday, and year 1 ends up with 354 days.
On the other hand, if year 2 is already a short year of 383 days,
there will be a problem if TM2 is on a Wednesday. because Rosh
Hashanah in year 2 will have to be postponed from Wednesday to
Thursday and this will cause year 2 to be only 382 days long. In this
case, year 2 is extended by one day by postponing
Rosh Hashanah in
year 3 from Monday to Tuesday (the fourth deḥiyyah), and year 2 will
have 383 days.
Rectifying the Hebrew calendar
The attribution of the fixed arithmetic
Hebrew calendar solely to
Hillel II has, however, been questioned by a few authors, such as
Sasha Stern, who claim that the calendar rules developed gradually
over several centuries.
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. The mean year of the current
Hebrew calendar has "drifted" an average of 7–8
days late relative to the equinox relationship that it originally had.
It is not possible, however, for any individual Hebrew date to be a
week or more "late", because Hebrew months always begin within a day
or two of the molad moment. What happens instead is that the
Hebrew calendar "prematurely" inserts a leap month one
year before it "should have been" inserted, where "prematurely" means
that the insertion causes the spring equinox to land more than 30 days
before the latest acceptable moment, thus causing the calendar to run
"one month late" until the time when the leap month "should have been"
inserted prior to the following spring. This presently happens in 4
years out of every 19-year cycle (years 3, 8, 11, and 19), implying
Hebrew calendar currently runs "one month late" more than 21%
of the time.
Dr. Irv Bromberg has proposed a 353-year cycle of 4366 months, which
would include 130 leap months, along with use of a progressively
shorter molad interval, which would keep an amended fixed arithmetic
Hebrew calendar from drifting for more than seven millennia. It
takes about 31⁄2 centuries for the spring equinox to drift an
average of 1⁄19th of a molad interval earlier in the Hebrew
calendar. That is a very important time unit, because it can be
cancelled by simply truncating a 19-year cycle to 11 years, omitting 8
years including three leap years from the sequence. That is the
essential feature of the 353-year leap cycle ((9 × 19) + 11 + (9 ×
19) = 353 years).
Religious questions abound about how such a system might be
implemented and administered throughout the diverse aspects of the
world Jewish community.
Conversion between Jewish and civil calendars
The list below gives a time which can be used to determine the day the
Jewish ecclesiastical (spring) year starts over a period of nineteen
displaystyle tfrac 15 18
Monday, 31 March 2014
displaystyle tfrac 9 18
Saturday, 21 March 2015
displaystyle tfrac 4 18
Friday, 8 April 2016
displaystyle tfrac 16 18
Tuesday, 28 March 2017
displaystyle tfrac 10 18
Saturday, 17 March 2018
displaystyle tfrac 5 18
Friday, 5 April 2019
displaystyle tfrac 17 18
Wednesday, 25 March 2020
displaystyle tfrac 11 18
Sunday, 14 March 2021
displaystyle tfrac 6 18
Saturday, 2 April 2022
17:49 Wednesday, 22 March 2023
displaystyle tfrac 13 18
Tuesday, 9 April 2024
displaystyle tfrac 7 18
Sunday, 30 March 2025
displaystyle tfrac 1 18
Thursday, 19 March 2026
displaystyle tfrac 14 18
Wednesday, 7 April 2027
displaystyle tfrac 8 18
Sunday, 26 March 2028
displaystyle tfrac 2 18
Friday, 16 March 2029
displaystyle tfrac 15 18
Wednesday, 3 April 2030
displaystyle tfrac 9 18
Monday, 24 March 2031
displaystyle tfrac 3 18
Friday, 12 March 2032
Every nineteen years this time is 2 days, 16 hours, 33 1/18 minutes
later in the week. That is either the same or the previous day in the
civil calendar, depending on whether the difference in the day of the
week is three or two days. If 29 February is included fewer than five
times in the nineteen – year period the date will be later by the
number of days which corresponds to the difference between the actual
number of insertions and five. If the year is due to start on Sunday,
it actually begins on the following Tuesday if the following year is
due to start on
Friday morning. If due to start on Monday, Wednesday
Friday it actually begins on the following day. If due to start on
Saturday, it actually begins on the following day if the previous year
was due to begin on Monday morning.
The table below lists, for a Jewish year commencing on 23 March, the
civil date of the first day of each month. If the year does not begin
on 23 March, each month's first day will differ from the date shown by
the number of days that the start of the year differs from 23 March.
The correct column is the one which shows the correct starting date
for the following year in the last row. If 29 February falls within a
Jewish month the first day of later months will be a day earlier than
Civil date of first day of Jewish months
Length of year:
For long period calculations, dates should be reduced to the Julian
calendar and converted back to the civil calendar at the end of the
calculation. The civil calendar used here (Exigian) is correct to one
day in 44,000 years and omits the leap day in centennial years which
do not give remainder 200 or 700 when divided by 900. It is
identical to the
Gregorian calendar between 15 October 1582 CE and 28
February 2400 CE (both dates inclusive).
To find how many days the civil calendar is ahead of the Julian in any
year from 301 BCE (the calendar is proleptic [assumed] up to 1582 CE)
add 300 to the year, multiply the hundreds by 7, divide by 9 and
subtract 4. Ignore any fraction of a day. When the difference between
the calendars changes the calculated value applies on and from March 1
(civil date) for conversions to Julian. For earlier dates reduce the
calculated value by one. For conversions to the civil date the
calculated value applies on and from February 29 (Julian date). Again,
for earlier dates reduce the calculated value by one. The difference
is applied to the calendar one is converting into. A negative value
indicates that the Julian date is ahead of the civil date. In this
case it is important to remember that when calculating the civil
equivalent of February 29 (Julian), February 29 is discounted. Thus if
the calculated value is −4 the civil equivalent of this date is
February 24. Before 1 CE use astronomical years rather than years BCE.
The astronomical year is (year BCE) – 1.
Up to the 4th century CE, these tables give the day of the Jewish
month to within a day or so and the number of the month to within a
month or so. From the 4th century, the number of the month is given
exactly and from the 9th century the day of the month is given exactly
In the Julian calendar, every 76 years the Jewish year is due to start
5h 47 14/18m earlier, and 3d 18h 12 4/18m later in the week.
On what civil date does the eighth month begin in CE 20874-5?
20874=2026+(248x76). In (248x76) Julian years the Jewish year is due
to start (248x3d 18h 12 4/18m) later in the week, which is 932d 2h 31
2/18m or 1d 2h 31 2/18m later after removing complete weeks. Allowing
for the current difference of thirteen days between the civil and
Julian calendars, the Julian date is 13+(248x0d 5h 47 4/18m) earlier,
which is 72d 21h 28 16/18m earlier. Convert back to the civil calendar
by applying the formula.
1477/9=164 remainder 1
160d-72d 21h 28 16/18m=87d 2h 31 2/18m.
So, in 20874 CE, the Jewish year is due to begin 87d 2h 31 2/18m later
than in 2026 CE and 1d 2h 31 2/18m later in the week. In 20874 CE,
therefore, the Jewish year is due to begin at 11.30 3/18 A.M. on
Friday, 14 June. Because of the displacements, it actually begins on
Saturday, 15 June. Odd months have 30 days and even months 29, so the
starting dates are 2, 15 July; 3, 13 August; 4, 12 September; 5, 11
October; 6, 10 November; 7, 9 December, and 8, 8 January.
The rules are based on the theory that
Maimonides explains in his book
"Rabbinical Astronomy" – no allowance is made for the secular
(centennial) decrease of ½ second in the length of the mean tropical
year and the increase of about four yards in the distance between the
earth and the moon resulting from tidal friction because astronomy was
not sufficiently developed in the 12th century (when
his book) to detect this.
Biblical and Talmudic units of measurement
Chol HaMoed, the intermediate days during
Passover and Sukkot.
Chronology of the Bible
Counting of the Omer
Jewish and Israeli holidays 2000–2050
Lag BaOmer, 33rd day of counting the Omer.
^ Specifically, the ripening of the barley crop; the age of the kids,
lambs, and doves; the ripeness of the fruit trees; and the relation of
the date to the tekufah (seasons). See the Talmud,
^ "Tishrei, 5777". Chabad.org. Retrieved September 13, 2015.
^ Gen 1:5, Gen 1:8, Gen 1:13, Gen 1:19, Gen 1:23, Gen 1:31 and Gen
^ Kurzweil, Arthur (9 February 2011). "The
Torah For Dummies". John
Wiley & Sons – via Google Books.
^ Otto Neugebauer, "The astronomy of
Maimonides and its sources",
Hebrew Union College Annual 23 (1949) 322–363.
^ See Willie Roth's essay The International Date Line and Halacha.
^ "Appendix II: Baal HaMaor's Interpretation of 20b and its Relevance
to the Dateline" in
Talmud Bavli, Schottenstein Edition, Tractate Rosh
HaShanah, Mesorah Publications Ltd. ("ArtScroll") 1999, where "20b"
refers to the 20th page 2nd folio of the tractate.
^ See, for example, Berachot chapter 1,
^ See Genesis 1:8, 1:13, 1:19, 1:23, 1:31 and 2.2.
^ For example, according to Morfix מילון מורפיקס, Morfix
Dictionary, which is based upon Prof. Yaakov Choeka's
dictionary. But the word meaning a non-Talmudic week is שָׁבוּע
(shavuʻa), according to the same "מילון מורפיקס".
^ For example, when referring to the daily psalm recited in the
morning prayer (Shacharit).
^ In contrast, the
Gregorian calendar is a pure solar calendar, while
Islamic calendar is a pure lunar calendar.
^ Under the fixed, calculated calendar, this is only loosely true.
Because the calculations are based on mean lunar months, not observed
ones–and because of the
Rosh Hashanah postponement rules—a given
month may not begin on the same day as its astronomical conjunction.
See Bromberg, Dr. Irv (August 5, 2010). "Moon and the
Molad of the
Hebrew Calendar". utoronto.ca. Retrieved December 16, 2012.
^ This practice continues to be used in
Karaite Judaism as well as in
the Islamic calendar.
^ a b
Sanhedrin 2.2, Herbert Danby, Trans., Tractate Sanhedrin
Mishnah and Tosefta, Society for Promoting Christian Knowledge, London
and New York, 1919, p. 31. Also quoted in Sacha Stern,
History of the Jewish
Calendar Second Century BCE –
Tenth Century CE, Oxford University Press, 2001, p. 70.
^ a b c d Ancient Israel: Its Life and Institutions (1961) by Roland
De Vaux, John McHugh, Publisher: McGraw–Hill,
ISBN 978-0-8028-4278-7, p.179
Rosh Hashanah 1.7
Rosh Hashanah 2.6–8
^ a b b.
Rosh Hashanah 20b: "This is what Abba the father of R. Simlai
meant: 'We calculate the new moon's birth. If it is born before
midday, then certainly it will have been seen shortly before sunset.
If it was not born before midday, certainly it will not have been seen
shortly before sunset.' What is the practical value of this remark? R.
Ashi said: Confuting the witnesses." I. Epstein, Ed., The Babylonian
Talmud Seder Mo'ed, Soncino Press, London, 1938, p. 85.
Rosh Hashanah 2.2
^ b. Betzah 4b
^ Sanctification of the New Moon. Archived 2010-06-21 at the Wayback
Machine. Translated from the Hebrew by Solomon Gandz; supplemented,
introduced, and edited by Julian Obermann; with an astronomical
commentary by Otto Neugebauer. Yale Judaica Series, Volume 11, New
Haven: Yale University Press, 1956
^ Gen 7:11 says "... on the seventeenth day of the second month—on
that day all the springs of the great deep burst forth..." and 8:3–4
says "...At the end of the hundred and fifty days the water had gone
down, (4) and on the seventeenth day of the seventh month the ark came
to rest on the mountains of Ararat..." There is an interval of 5
months and 150 days, making each month 30 days long.
^ Hachlili, Rachel (2013). Ancient Synagogues –
Archaeology and Art:
New Discoveries and Current Research. Brill. p. 342.
^ Ulfgard, Håkan (1998). The Story of Sukkot : the Setting,
Shaping and Sequel of the Biblical Feast of Tabernacles. Mohr Siebeck.
p. 99. ISBN 3-16-147017-6.
^ (12 Signs, 12 Sons: Astrology in the Bible, David Womack, Harper
& Row, San Francisco 1978, pg 43)
^ Solomon, Gandz (1947–1948). "Date of the Composition of
Maimonides' Code". Proceedings of the American Academy for Jewish
Research, Vol. 17, pp. 1–7. doi:10.2307/3622160.
JSTOR 3622160. Retrieved March 14, 2013.
^ a b c
Chronology of the Old Testament, Dr. Floyd Nolen Jones "When
the center of Jewish life moved from Babylonia to Europe during the
8th and 9th centuries CE, calculations from the
Seleucid era became
meaningless. Over those centuries, it was replaced by that of the anno
mundi era of the Seder Olam. From the 11th century, anno mundi dating
became dominant throughout most of the world's Jewish communities."
^ Alden A. Mosshammer. The Easter
Computus and the Origins of the
^ p.107, Kantor
^ a b See The Remaining Signs of Past Centuries.
^ A minority opinion places Creation on 25
Adar AM 1, six months
earlier, or six months after the modern epoch.
^ Fisher Saller, Carol; Harper, Russell David, eds. (2010). "9.34:
Eras". The Chicago Manual of Style (16th ed.). Chicago: Univiversity
of Chicago Press. ISBN 978-0-226-10420-1.
^ a b Edwin Thiele, The Mysterious Numbers of the Hebrew Kings, (1st
ed.; New York: Macmillan, 1951; 2d ed.; Grand Rapids: Eerdmans, 1965;
3rd ed.; Grand Rapids: Zondervan/Kregel, 1983).
ISBN 0-8254-3825-X, 9780825438257
^ Adsole, Atenebris. "Babylonian Talmud: 'Abodah Zarah 10".
^ a b Avodah Zarah, tractate 9 Footnote: "The Eras in use among Jews
in Talmudic Times are: (a) ERA OF CONTRACTS [H] dating from the year
380 before the Destruction of the Second Temple (312–1 BCE) when, at
the Battle of Gaza, Seleucus Nicator, one of the followers of
Alexander the Great, gained dominion over Palestine. It is also termed
Seleucid or Greek
Era [H]. Its designation as Alexandrian Era
connecting it with Alexander the Great (Maim. Yad, Gerushin 1, 27) is
an anachronism, since Alexander died in 323 BCE—eleven years before
Era began (v. E. Mahler, Handbuch der judischen Chronologie, p.
145). This Era, which is first mentioned in Mac. I, 10, and was used
by notaries or scribes for dating all civil contracts, was generally
in vogue in eastern countries till the 16th cent, and was employed
even in the 19th cent, among the
Jews of Yemen, in South Arabia (Eben
Saphir, Lyck, 1866, p. 62b). (b) THE ERA OF THE DESTRUCTION (of the
Second Temple) [H] the year 1 of which corresponds to 381 of the
Seleucid Era, and 69–70 of the Christian Era. This
Era was mainly
employed by the Rabbis and was in use in Palestine for several
centuries, and even in the later
Middle Ages documents were dated by
it. One of the recently discovered Genizah documents bears the date 13
Tammuz 987 after the Destruction of the Temple—i.e., 917 C.E. (Op.
cit. p. 152, also Marmorstein ZDMG, Vol. VI, p. 640). The difference
between the two Eras as far as the tens and units are concerned is
thus 20. If therefore a Tanna, say in the year 156
Era of Dest. (225
CE), while remembering, naturally, the century, is uncertain about the
tens and units, he should ask the notary what year it is according to
his—Seleucid—era. He will get the answer 536 (156 + 380), on
adding 20 to which he would get 556, the last two figures giving him
the year  56 of the
Era of Destruction."
^ Scherman, Nosson (2005). Artscroll Chumash.
^ The barley had to be "eared out" (ripe) in order to have a
wave-sheaf offering of the first fruits according to the Law. Jones,
Stephen (1996). Secrets of Time.
^ See Maaser Rishon, Maaser Sheni, Maaser Ani.
^ Josephus, Antiquities 1.81, Loeb Classical Library, 1930.
Chronology of the Old Testament, 16th ed., Floyd Nolan Jones,
ISBN 978-0-89051-416-0, pp. 118–123
Rosh Hashanah 1, in Herbert Danby, trans., The Mishnah, Oxford
University Press, 1933, p. 188.
^ See also Golden number.
^ "The Jewish Calendar: A Closer Look".
Judaism 101. Retrieved 25
^ Dershowitz, Nachum; Reingold, Edward M. (December 2007). Calendrical
Calculations (Third ed.). Cambridge University Press.
^ R. Avraham bar Chiya ha-nasi. Sefer ha-Ibbur (part 2, chapters
^ Tur, O.C. (section 428).
^ Rambam. Hilchos Kiddush ha-Chodesh (chapters 6,7,8).
^ W. M. Feldman (1965). "Chapter 17: The Fixed Calendar". Rabbinical
Astronomy (2nd ed.). Hermon Press.
^ Hugo Mandelbaum (1986). "Introduction: Elements of the Calendar
Calculations". In Arthur Spier. The Comprehensive Hebrew
^ Landau, Remy. "Hebrew
Calendar Science and Myth: 'The Debatable
Molad Zaquen'". Retrieved 7 February 2015.
^ This is the reason given by most halachic authorities, based on the
Rosh Hashanah 20b and Sukkah 43b.
Maimonides (Mishneh Torah,
Kiddush Hachodesh 7:7), however, writes that the arrangement was made
(possible days alternating with impossible ones) in order to average
out the difference between the mean and true lunar conjunctions.
Rosh Hashanah 20b) puts it differently: over two
consecutive days of full
Shabbat restrictions, vegetables would wilt
(since they can't be cooked), and unburied corpses would putrefy.
^ Yerushalmi, Sukkah 54b.
^ Bushwick, Nathan (1989). Understanding the Jewish Calendar. New
York/Jerusalem: Moznaim. pp. 95–97.
^ Poznanski, Samuel (1910). "
Calendar (Jewish)". In Hastings, James.
Encyclopædia of Religion and Ethics. 3. Edinburgh: T. & T. Clark.
^ Resnikoff, Louis A. (1943). "Jewish
Calendar Calculations". Scripta
Mathematica. 9: 276.
^ In the Four gates sources (keviyot cited here are in Hebrew in
sources): Bushwick forgot to include 5D for leap years. Poznanski
forgot to include 5D for a limit in his table although he did include
it in his text as 5D1; for leap years he incorrectly listed 5C7
instead of the correct 5C3. Resnikoff's table is correct.
^ Robert Schram, Kalendariographische und Chronologische Tafeln, 1908,
pp. XXIII–XXVI, 190–238. Schram gives the type of Hebrew year for
all years 1–6149 AM (−3760 – 2388 Julian/Gregorian) in a main
table (3946+) and its adjunct (1+, 1742+) on pages 191–234 in the
form 2d, 2a, 3r, 5r, 5a, 7d, 7a for common years and 2D, 2A, 3R, 5D,
5A, 7D, 7A for leap years. The type of year 1 AM, 2a, is on page
200 at the far right.
^ a b Sacha Stern,
Calendar and Community, Oxford University Press,
2001, pp. 162ff.
^ James B. Pritchard, ed., The Ancient Near East: An Anthology of
Texts and Pictures, Vol. 1, Princeton University Press, p. 213.
Sanhedrin 5.3: "If one testifies, 'on the second of the month,
and the other, 'on the third of the month:' their evidence is valid,
for one may have been aware of the intercalation of the month and the
other may not have been aware of it. But if one says, 'on the third',
and the other 'on the fifth', their evidence is invalid."
^ M. Baba Metzia 8.8.
^ Gandz, Solomon. "Studies in the Hebrew Calendar: II. The origin of
the Two New Moon Days", Jewish Quarterly Review (New Series), 40(2),
1949–50. JSTOR 1452961. doi:10.2307/1452961. Reprinted in
Shlomo Sternberg, ed., Studies in Hebrew
Astronomy and Mathematics by
Solomon Gandz, KTAV, New York, 1970, pp. 72–73.
^ Sacha Stern,
Calendar and Community.
^ a b E.S. Kennedy, "
Al-Khwarizmi on the Jewish calendar", Scripta
Mathematica 27 (1964) 55–59.
^ a b "al-Khwarizmi", Dictionary of Scientific Biography, VII: 362,
^ Stern, Sacha (2001).
Calendar and Community: A
History of the Jewish
Calendar Second Century BCE – Tenth Century CE. Oxford.
^ Julian, Letter 25, in John Duncombe, Select Works of the Emperor
Julian and some Pieces of the Sophist Libanius, Vol. 2, Cadell,
London, 1784, pp. 57–62.
^ Epiphanius, Adversus Haereses 30.4.1, in Frank Williams, trans., The
Panarion of Epiphanius of Salamis
Book I (Sections 1–46), Leiden, E.
J.Brill, 1987, p. 122.
^ H. Graetz, Popular
History of the Jews, (A. B. Rhine, trans.,)
Hebrew Publishing Company, New York, 1919, Vol. II, pp. 410–411.
Quoted in Sacha Stern,
Calendar and Community, p. 216.
^ Lieberman, S. "Palestine in the Third and Fourth Centuries", Jewish
Quarterly Review, New Series 36, pp. 329–370(1946).
JSTOR 1452134. doi:10.2307/1452134. Quoted in Sacha Stern,
Calendar and Community, pp. 216–217.
^ Sacha Stern,
Calendar and Community: A
History of the Jewish
Calendar Second Century BCE – Tenth Century CE, Oxford University
Press, 2001. In particular section 5.1.1, discussion of the
^ Poznanski, Samuel, "Ben Meir and the Origin of the Jewish Calendar",
Jewish Quarterly Review, Original Series, Vol. 10, pp.
152–161(1898). JSTOR 1450611. doi:10.2307/1450611.
^ "While it is not unreasonable to attribute to
Hillel II the fixing
of the regular order of intercalations, his full share in the present
fixed calendar is doubtful." Entry "Calendar", Encyclopedia Judaica,
Keter, Jerusalem, 1971.
^ Samuel Poznanski, "
Calendar (Jewish)", Encyclopaedia of Religion and
Ethics, vol. 3.
^ Yerushalmi Megillah 70b.
^ Yerushalmi Sukkah 54b.
^ David Lev (23 December 2012). "Rabbinate: New Year's Eve Parties
'Not Kosher'". Arutz Sheva. Retrieved 30 November 2013.
^ "Karaite Korner – New Moon and the Hebrew Month".
Barley in the Biblical
Calendar – Nehemia's Wall". 24
^ a b "The
Samaritan Calendar" (PDF). www.thesamaritanupdate.com.
2008. Retrieved 28 December 2017.
^ a b Benyamim, Tzedaka. "Calendar". www.israelite-samaritans.com.
Retrieved 28 December 2017.
^ Glowatz, Elana (23 January 2018). "One Of The Last Dead Sea Scroll
Mysteries Has Been Deciphered". International Business Times.
Retrieved 23 January 2018.
^ Sacha Stern, "The Babylonian
Calendar at Elephantine", Zeitschrift
für Papyrologie und Epigraphik 130, 159–171(2000).
^ Lester L. Grabbe, A
History of the
Judaism in the Second
Temple Period, Volume 1: Yehud: A
History of the Persian Province of
Judah, T&T Clark, London, 2004, p. 186.
^ Eduard Schwartz, Christliche und jüdische Ostertafeln,
(Abhandlungen der königlichen Gesellschaft der Wissenschaften zu
Göttingen. Philologisch-Historische Klasse. Neue Folge, Band viii,
^ Peter of Alexandria, quoted in the Chronicon Paschale. Corpus
Scriptorum Historiae Byzantinae, Chronicon Paschale Vol. 1, Weber,
Bonn, 1832, p. 7
^ Sacha Stern,
Calendar and Community, pp. 87–97, 146–153.
^ Neugebauer, Astronomical cuneiform texts, Vol 1, pp 271–273
^ G. J. Toomer, Hipparchus' Empirical Basis for his Lunar Mean
Motions, Centaurus, Vol 24, 1980, pp. 97–109
^ Weinberg, I., Astronomical Aspects of the Jewish Calendar, Monthly
Notes of the Astronomical Society of South Africa, Vol. 15, p. 86;
available at 
^ The following description is based on the article "Calendar" in
Encyclopaedia Judaica (Jerusalem: Ketter, 1972). It is an explanatory
description, not a procedural one, in particular explaining what is
going on with the third and fourth deḥiyyot
^ So for example if the
Tishrei molad is calculated as occurring from
noon on Wednesday (the 18th hour of the fourth day) up until noon on
Rosh Hashanah falls on a Thursday, which starts Wednesday at
sunset wherever one happens to be.
^ This will happen if TM1 is on or after 3:11:20 a.m. and before noon
on a Tuesday. If TM1 is Monday, Thursday or Saturday,
Rosh Hashanah in
year 2 does not need to be postponed. If TM1 is Sunday, Wednesday or
Rosh Hashanah in year 1 is postponed, so year 1 is not the
^ TM2 will be between noon and 2:27:162⁄3 p.m. on Tuesday, and
TM3 will be between 9:32:431⁄3 and noon on Monday.
^ Bromberg, Irv. "The Rectified Hebrew Calendar". Retrieved
^ "Committee concerning the fixing of the
Calendar – The Sanhedrin
^ Cassidy, Simon. "Re: How long is a year..EXACTLY? East Carolina
Calendar discussion List CALNDR-L". 25 October 1996.
Retrieved 7 February 2015.
^ Feldman, W M. Rabbinical Mathematics and Astronomy:Judaic Studies
Library; no. SHP 4. New York, 1978. ISBN 978-0872030268.
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.
Jonathan Ben-Dov. Head of All Years:
Astronomy and Calendars at Qumran
in their Ancient Context. Leiden: Brill, 2008.
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.
Sherrard Beaumont Burnaby. Elements of the Jewish and Muhammadan
Calendars. George Bell and Sons, London, 1901.
Nathan Bushwick. Understanding the Jewish Calendar. Moznaim, New
York/Jerusalem, 1989. ISBN 0-940118-17-3
William Moses Feldman. Rabbinical Mathematics and Astronomy, 3rd
edition, Sepher-Hermon Press, New York, 1978.
Eduard Mahler, Handbuch der jüdischen Chronologie. Buchhandlung
Gustav Fock, Leipzig, 1916.
Helen R. Jacobus.
Zodiac Calendars in the Dead Sea Scrolls and Their
Astronomy and Astrology in Early Judaism. Leiden:
Brill, 2014. ISBN 9789004284050
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.,
Samuel Poznanski. "
Calendar (Jewish)". Encyclopædia of Religion and
Ethics. T. & T. Clark, Edinburgh, 1910, vol. 3,
Edward M. Reingold and Nachum Dershowitz. Calendrical Calculations:
The Millennium Edition. Cambridge University Press; 2 edition (2001).
Louis 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: Twentieth to the
Twenty-Second Century 5660–5860/1900–2100. Feldheim Publishers,
Jerusalem/New York, 1986.
Calendar and Community: A
History of the Jewish Calendar
2nd Century BCE to 10th Century CE. Oxford University Press, 2001.
Ernest Wiesenberg. "Appendix: Addenda and Corrigenda to Treatise
VIII". The Code of
Maimonides (Mishneh Torah),
Book Three: The
Seasons. Yale Judaica Series Volume XIV, Yale University Press, New
Haven, Conn., 1961. pp. 557–602.
Francis Henry Woods. "
Calendar (Hebrew)", Encyclopædia of Religion
and Ethics. T. & T. Clark, Edinburgh, 1910, vol. 3,
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