Intercalation (timekeeping)

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

Solar calendars

The solar or tropical year does not have a whole number of days (it is about 365.24 days), but a calendar year must have a whole number of days. The most common way to reconcile the two is to vary the number of days in the calendar year.

In solar calendars, this is done by adding to a common year of 365 days, an extra day ("leap day" or "intercalary day") about every four years, causing a leap year to have 366 days (Julian, Gregorian and Indian national calendars).

The Decree of Canopus, which was issued by the pharaoh Ptolemy III Euergetes of Ancient Egypt in 239 BCE, decreed a solar leap day system; an Egyptian leap year was not adopted until 25 BC, when the Roman Emperor Augustus successfully instituted a reformed Alexandrian calendar.

In the Julian calendar, as well as in the Gregorian calendar, which improved upon it, intercalation is done by adding an extra day to February in each leap year. In the Julian calendar this was done every four years. In the Gregorian, years divisible by 100 but not 400 were exempted in order to improve accuracy. Thus, 2000 was a leap year; 1700, 1800, and 1900 were not.

Epagomenal[1] days are days within a solar calendar that are outside any regular month. Usually five epagomenal days are included within every year (Egyptian, Coptic, Ethiopian, Mayan Haab' and French Republican Calendars), but a sixth epagomenal day is intercalated every four years in some (Coptic, Ethiopian and French Republican calendars).

The Bahá'í calendar includes enough epagomenal days (usually 4 or 5) before the last month (علاء, ʿalāʾ) to ensure that the following year starts on the March equinox. These are known as the Ayyám-i-Há.

Lunisolar calendars

The solar year does not have a whole number of lunar months (it is about 12.37 lunations), so a lunisolar calendar must have a variable number of months in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" or "embolismic" month every second or third year (see blue moon). Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year Metonic cycle (Hebrew calendar and in the determination of Easter) or using calculations of lunar phases (Hindu lunisolar and Chinese calendars). The Buddhist calendar adds both an intercalary day and month on a usually regular cycle. The Jewish year is arranged according to a luni-solar system.

Islamic calendars

The tabular Islamic calendar usually has 12 lunar months that alternate between 30 and 29 days every year, but an intercalary day is added to the last month of the year 11 times within a 30-year cycle. Some historians also linked the pre-Islamic practice of Nasi' to intercalation.

The Solar Hijri calendar is based on solar calculations and is similar to the Gregorian calendar in its structure, and hence the intercalation, with the exception that the year date starts with the Hegira.[2]

Leap seconds

The International Earth Rotation and Reference Systems Service can insert or remove leap seconds from the last day of any month (June and December are preferred). These are sometimes described as intercalary.[3]

Other uses

ISO 8601 includes a specification for a 52/53-week year. Any year that has 53 Thursdays has 53 weeks; this extra week may be regarded as intercalary.

See also


  1. ^ From ἐπαγόμενος, epagomenos (present participle passive of ἐπάγειν, epagein "to bring in") + -al
  2. ^ "Hijri-Shamsi Calendar". Al Islam. Retrieved June 14, 2014.
  3. ^ leap second by Merriam-Webster OnLine
Bahá'í calendar

The Bahá'í Calendar, also called the Badíʿ Calendar (Badíʿ means wondrous or unique), is a solar calendar with years composed of 19 months of 19 days each (361 days) plus an extra period of "Intercalary Days". Years begin at Naw-Rúz, on the day of the vernal equinox in Tehran, Iran, coinciding with March 20 or 21.

The first year is dated from 21 March 1844 CE, the year during which the Báb proclaimed his religion. Years are annotated with the date notation of BE (Bahá'í Era),

The year 176 BE started on the day of the vernal equinox (in Tehran) in 2019, that is on 21 March 2019.

Embolism (disambiguation)

Embolism may refer to:

Embolism, when an object (the embolus) migrates from one part of the body (through circulation) and causes a blockage (occlusion) of a blood vessel in another part of the body.

Embolization is the passage of an embolus within the bloodstream, either pathologically or therapeutically.

Embolism in calendars: Intercalation (timekeeping)

Embolism (liturgy), a liturgical prayer


Intercalation may refer to:

Intercalation (chemistry), insertion of a molecule (or ion) into layered solids such as graphite

Intercalation (timekeeping), insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons

Intercalation (university administration), period when a student is officially suspended from studying for an academic degree

Intercalation (geology), a special form of interbedding, where two distinct depositional environments in close spatial proximity migrate back and forth across the border zone

In biology:

Intercalary segment, an appendage-less segment in the segmental composition of the heads of insects and Myriapoda

Intercalation (biochemistry), process discovered by Leonard Lerman by which certain drugs and mutagens insert themselves between base pairs of DNA

Intercalated cells of the amygdala

Intercalated cells of the collecting duct

Intercalated disc of cardiac muscle

Intercalated duct of exocrine glands

Key concepts
Measurement and
  • Religion
  • Mythology
Philosophy of time
Human experience
and use of time
Time in
Related topics
International standards
Obsolete standards
Time in physics
Archaeology and geology
Astronomical chronology
Other units of time
Related topics

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.