The proleptic Julian calendar is produced by extending the Julian calendar backwards to dates preceding AD 8 when the quadrennial leap year stabilized. The leap years that were actually observed between the implementation of the Julian calendar in 45 BC and AD 8 were erratic (see the Julian calendar article for details).

A calendar obtained by extension earlier in time than its invention or implementation is called the "proleptic" version of the calendar. Likewise, the proleptic Gregorian calendar is occasionally used to specify dates before the introduction of the Gregorian calendar in 1582. Because the Julian calendar was used before that time, one must explicitly state that a given quoted date is based on the proleptic Gregorian calendar if that is the case.

The Julian calendar itself was introduced by Julius Caesar, and as such is older than the introduction of the Anno Domini era (or the "Common Era"), counting years since the birth of Christ as calculated by Dionysus Exiguus in the 6th century, and widely used in medieval European annals since about the 8th century, notably by Bede. The proleptic Julian calendar uses Anno Domini throughout, including for dates of Late Antiquity when the Julian calendar was in use but Anno Domini wasn't, and for times predating the introduction of the Julian calendar.

Years are given cardinal numbers, using inclusive counting (AD 1 is the first year of the Anno Domini era, immediately preceded by 1 BC, the first year preceding the Anno Domini era, there is no "zeroth" year).

Thus, the year 1 BC of the proleptic Julian calendar is a leap year.

This is to be distinguished from the astronomical year numbering, introduced in 1740 by French astronomer Jacques Cassini, which considers each New Year an integer on a time axis, with year 0 corresponding to 1 BC, and "year 1" corresponding to 2 BC, so that in this system, Julian leap years have a number divisible by four.

The determination of leap years in the proleptic Julian calendar (in either numbering) is distinct from the question of which years were historically considered leap years during the Roman era, due to the leap year error: Between 45 BC and AD 8, the leap day was somewhat unsystematic. Thus there is no simple way to find an equivalent in the proleptic Julian calendar of a date quoted using either the Roman pre-Julian calendar or the Julian calendar before AD 8. The year 46 BC itself is a special case: because of the historical introduction of the Julian calendar in that year, it was allotted 445 days. Before then, the Roman Republican calendar used a system of intercalary months rather than leap days.

The Hebrew calendar (Hebrew: הַלּוּחַ הָעִבְרִי, romanized: HaLuah HaIvri), also called Jewish calendar, is a lunisolar calendar used today for Jewish religious observance, and as an official calendar of the state of Israel. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, 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 holidays, alongside the Gregorian calendar.

The present Hebrew calendar is the result of a process of development, 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 the lunar year of twelve lunar months and the solar year. The year in which it was added was based on observation of natural agriculture-related events in ancient Israel. Through the Amoraic period (200–500 CE) and into the Geonic period, this system was gradually displaced by the mathematical rules of the Metonic cycle 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 11 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.The era used for the calendar since the Middle Ages is Anno Mundi (Latin: "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. The epoch of this era is the moment when, according to the Genesis creation narrative, the world was created.

AM 5782 began at sunset on 6 September 2021 and will end at sunset on 25 September 2022.