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Civil year {{ safesubst:#invoke:Unsubst||$N=Refimprove section |date=__DATE__ |$B= {{ safesubst:#invoke:Unsubst||$N=Refimprove |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} }} A calendar year is the time between two dates with the same name in a calendar.

No astronomical year has an integer number of days or lunar months, so any calendar that follows an astronomical year must have a system of intercalation such as leap years. Financial and scientific calculations often use a 365-day calendar to simplify daily rates.

In international calendars

In the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a leap year there are 366 days. A leap year occurs every four years.

The Gregorian calendar tracks the mean tropical year.<ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> In particular, it seeks to ensure that the astronomical vernal equinox falls no later than 21 March. Since this oscillates within a 53-hour range it is, therefore, most likely to fall on 20 March.<ref>Ziggelaar, A. (1983). "The Papal Bull of 1582 Promulgating a Reform of the Calendar". In Coyne, Hoskin, Pedersen (eds), Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican City: Pontifical Academy of Sciences, Specolo Vaticano, p. 223</ref> The mean length of the calendar year is 365.2425 days (as 97 out of 400 years are leap years); this is within one ppm of the current length of the mean tropical year ({{safesubst:#invoke:val|main}} days).

Since AD 800 the vernal equinox year has been longer than the mean tropical year. The astronomical equinox is moving towards its mean date (in 1983 the mean equinox fell at 1.48 AM GMT on 23 March.<ref>Astronomical Almanac 1983, Her Majesty's Stationery Office, London, 1982.</ref> though the actual equinox that year was on 21 March.) The mean calendar year is longer than both the mean tropical year and the vernal equinox year, the reason being that the tables used by the Papal astronomers were based on historical observations, and over centuries tidal drag slows the earth's diurnal rotation. Clavius noted that the tables did not agree on when the sun passed through the vernal equinox. As a result of this slowing down the equinox will never reach 22 March.

The Revised Julian calendar, as used in some Eastern Orthodox Churches, currently does a better job of synchronizing with the mean tropical year. The average length of this calendar's year is {{safesubst:#invoke:val|main}} days (as 218 out of 900 years are leap years). Gregorian and Revised Julian calendars will start to differ in 2800.<ref>Shields, Miriam Nancy. (1924). "The New Calendar of the Eastern Churches, Popular Astronomy, Vol. 32, p.407. Courtesy NASA Astrophysics Data System.</ref>

A calendar era is used to assign a number to individual years, using a reference point in the past as the beginning of the era. In many countries, the most common era is from the traditional (though now believed incorrect) year of the birth of Jesus. Dates in this era are designated Anno Domini (Latin for in the year of the Lord), abbreviated AD, or CE (for common era). The year before 1 AD or CE is designated 1 Before Christ (BC) or Before the Common Era (BCE), the year before that 2 BC/BCE, etc. Hence there was no year 0 AD/CE.

When computations involving years are done involving both years AD and years BC, it is common to use Astronomical year numbering, in which 1 BC is designated 0, 2 BC is designated −1, and so on.

Other eras are also used to enumerate the years in different cultural, religious or scientific contexts.

In the Persian calendar

The Persian calendar, in use in Afghanistan and Iran, has its year begin at the midnight closest to the instant of the northward equinox as determined by astronomical computation (for the time zone of Tehran), as opposed to using an algorithmic system of leap years.

Fiscal year

A fiscal year or financial year is a 12-month period used for calculating annual financial statements in businesses and other organizations. In many jurisdictions, regulations regarding accounting require such reports once per twelve months, but do not require that the twelve months constitute a calendar year.

For example, in Canada and India the fiscal year runs from April 1; in the United Kingdom it runs from April 1 for purposes of corporation tax and government financial statements, but from April 6 for purposes of personal taxation and payment of state benefits; in Australia it runs from July 1; while in the United States the fiscal year of the federal government runs from October 1.

Academic year

An academic year is the annual period during which a student attends an educational institution. The academic year may be divided into academic terms, such as semesters or quarters. The school year in many countries starts in August or September and ends in May, June or July. In Israel the academic year begins around October or November, aligned with the second month of the Hebrew Calendar.

Some schools in the UK and USA divide the academic year into three roughly equal-length terms (called trimesters or quarters in the USA), roughly coinciding with autumn, winter, and spring. At some, a shortened summer session, sometimes considered part of the regular academic year, is attended by students on a voluntary or elective basis. Other schools break the year into two main semesters, a first (typically August through December) and a second semester (January through May). Each of these main semesters may be split in half by mid-term exams, and each of the halves is referred to as a quarter (or term in some countries). There may also be a voluntary summer session and/or a short January session.

Some other schools, including some in the United States, have four marking periods. Some schools in the United States, notably Boston Latin School, may divide the year into five or more marking periods. Some state in defense of this that there is perhaps a positive correlation between report frequency and academic achievement.

There are typically 180 days of teaching each year in schools in the USA, excluding weekends and breaks, while there are 190 days for pupils in state schools in Canada, New Zealand and the United Kingdom, and 200 for pupils in Australia.

In India the academic year normally starts from June 1 and ends on May 31. Though schools start closing from mid-March, the actual academic closure is on May 31 and in Nepal it starts from July 15.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

Schools and universities in Australia typically have academic years that roughly align with the calendar year (i.e., starting in February or March and ending in October to December), as the southern hemisphere experiences summer from December to February.

In the International System of Quantities

{{#invoke:main|main}} In the International System of Quantities, the year (symbol, a) is defined as either 365 days or 366 days.

Astronomical years

Julian year

{{#invoke:main|main}} The Julian year, as used in astronomy and other sciences, is a time unit defined as exactly 365.25 days. This is the normal meaning of the unit "year" (symbol "a" from the Latin annus) used in various scientific contexts. The Julian century of {{safesubst:#invoke:val|main}} days and the Julian millennium of {{safesubst:#invoke:val|main}} days are used in astronomical calculations. Fundamentally, expressing a time interval in Julian years is a way to precisely specify how many days (not how many "real" years), for long time intervals where stating the number of days would be unwieldy and unintuitive. By convention, the Julian year is used in the computation of the distance covered by a light-year.

In the Unified Code for Units of Measure, the symbol, a (without subscript), always refers to the Julian year, aj, of exactly {{safesubst:#invoke:val|main}} seconds.

365.25 days of {{safesubst:#invoke:val|main}} seconds = 1 a = 1 aj = {{safesubst:#invoke:val|main}} Ms

The SI multiplier prefixes may be applied to it to form ka (kiloannus), Ma (megaannus), etc.

Sidereal, tropical, and anomalistic years

{{#invoke:Hatnote|hatnote}}

Each of these three years can be loosely called an astronomical year.

The sidereal year is the time taken for the Earth to complete one revolution of its orbit, as measured against a fixed frame of reference (such as the fixed stars, Latin sidera, singular sidus). Its average duration is {{safesubst:#invoke:val|main}} mean solar days (365 d 6 h 9 min 9.76 s) (at the epoch J2000.0 = January 1, 2000, 12:00:00 TT).<ref>International Earth Rotation and Reference System Service. (2010).IERS EOP PC Useful constants.</ref>

Today the mean tropical year is defined as the period of time for the mean ecliptic longitude of the Sun to increase by 360 degrees.<ref>Richards, E. G. (2013). Calendars. In S. E. Urban & P. K. Seidelmann (Eds.), Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, CA: University Science Books. p. 586.</ref> Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of the seasons; because of the biological and socio-economic importance of the seasons, the tropical year is the basis of most calendars. The modern definition of mean tropical year differs from the actual time between passages of, e.g., the northward equinox for several reasons explained below. Because of the Earth's axial precession, this year is about 20 minutes shorter than the sidereal year. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds, using the modern definition.<ref> {{#invoke:citation/CS1|citation |CitationClass=book }}</ref> (= {{safesubst:#invoke:val|main}} days of 86400 SI seconds)

The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 3 in 2011), and the aphelion, where the Earth is farthest from the Sun (July 4 in 2011). The anomalistic year is usually defined as the time between perihelion passages. Its average duration is {{safesubst:#invoke:val|main}} days (365 d 6 h 13 min 52.6 s) (at the epoch J2011.0).<ref> {{#invoke:citation/CS1|citation |CitationClass=book }}</ref>

Draconic year

The draconic year, draconitic year, eclipse year, or ecliptic year is the time taken for the Sun (as seen from the Earth) to complete one revolution with respect to the same lunar node (a point where the Moon's orbit intersects the ecliptic). This period is associated with eclipses: these occur only when both the Sun and the Moon are near these nodes; so eclipses occur within about a month of every half eclipse year. Hence there are two eclipse seasons every eclipse year. The average duration of the eclipse year is

{{safesubst:#invoke:val|main}} days (346 d 14 h 52 min 54 s) (at the epoch J2000.0).

This term is sometimes erroneously used for the draconic or nodal period of lunar precession, that is the period of a complete revolution of the Moon's ascending node around the ecliptic: {{safesubst:#invoke:val|main}} Julian years ({{safesubst:#invoke:val|main}} days; at the epoch J2000.0).

Full moon cycle

The full moon cycle is the time for the Sun (as seen from the Earth) to complete one revolution with respect to the perigee of the Moon's orbit. This period is associated with the apparent size of the full moon, and also with the varying duration of the synodic month. The duration of one full moon cycle is:

{{safesubst:#invoke:val|main}} days (411 days 18 hours 49 minutes 34 seconds) (at the epoch J2000.0).

Lunar year

The lunar year comprises twelve full cycles of the phases of the Moon, as seen from Earth. It has a duration of approximately 354.37 days. Muslims use this for celebrating their Eids and for marking the start of the fasting month of Ramadan. A Muslim calendar year is based on the lunar cycle.

Vague year

The vague year, from annus vagus or wandering year, is an integral approximation to the year equaling 365 days, which wanders in relation to more exact years. Typically the vague year is divided into 12 schematic months of 30 days each plus 5 epagomenal days. The vague year was used in the calendars of Ancient Egypt, Iran, Armenia and in Mesoamerica among the Aztecs and Maya.<ref>Calendar Description and Coordination Maya World Studies Center</ref> It is still used by many Zoroastrian communities.

Heliacal year

A heliacal year is the interval between the heliacal risings of a star. It differs from the sidereal year for stars away from the ecliptic due mainly to the precession of the equinoxes.

Sothic year

The Sothic year is the interval between heliacal risings of the star Sirius. It is currently less than the sidereal year and its duration is very close to the mean Julian year of 365.25 days.

Gaussian year

The Gaussian year is the sidereal year for a planet of negligible mass (relative to the Sun) and unperturbed by other planets that is governed by the Gaussian gravitational constant. Such a planet would be slightly closer to the Sun than Earth's mean distance. Its length is:

{{safesubst:#invoke:val|main}} days (365 d 6 h 9 min 56 s).

Besselian year

The Besselian year is a tropical year that starts when the (fictitious) mean Sun reaches an ecliptic longitude of 280°. This is currently on or close to January 1. It is named after the 19th-century German astronomer and mathematician Friedrich Bessel. The following equation can be used to compute the current Besselian epoch (in years):<ref> {{#invoke:citation/CS1|citation |CitationClass=book }}</ref>

B = 1900.0 + (Julian dateTT − {{safesubst:#invoke:val|main}}) / {{safesubst:#invoke:val|main}}

The TT subscript indicates that for this formula, the Julian date should use the Terrestrial Time scale, or its predecessor, ephemeris time.

Variation in the length of the year and the day

{{ safesubst:#invoke:Unsubst||$N=Refimprove section |date=__DATE__ |$B= {{ safesubst:#invoke:Unsubst||$N=Refimprove |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} }} The exact length of an astronomical year changes over time.<ref>The Astronomical Almanac Online</ref>{{ safesubst:#invoke:Unsubst||$N=Failed verification |date=__DATE__ |$B= {{#invoke:Category handler|main}}[not in citation given] }}

  • The positions of the equinox and solstice points with respect to the apsides of Earth's orbit change: the equinoxes and solstices move westward relative to the stars because of precession, and the apsides move in the other direction because of the long-term effects of gravitational pull by the other planets. Since the speed of the Earth varies according to its position in its orbit as measured from its perihelion, Earth's speed when in a solstice or equinox point changes over time: if such a point moves toward perihelion, the interval between two passages decreases a little from year to year; if the point moves towards aphelion, that period increases a little from year to year. So a "tropical year" measured from one passage of the northward ("vernal") equinox to the next, differs from the one measured between passages of the southward ("autumnal") equinox. The average over the full orbit does not change because of this, so the length of the average tropical year does not change because of this second-order effect.
  • Each planet's movement is perturbed by the gravity of every other planet. This leads to short-term fluctuations in its speed, and therefore its period from year to year. Moreover, it causes long-term changes in its orbit, and therefore also long-term changes in these periods.
  • Tidal drag between the Earth and the Moon and Sun increases the length of the day and of the month (by transferring angular momentum from the rotation of the Earth to the revolution of the Moon); since the apparent mean solar day is the unit with which we measure the length of the year in civil life, the length of the year appears to decrease. The rotation rate of the Earth is also changed by factors such as post-glacial rebound and sea level rise.

Numerical value of year variation

Mean year lengths in this section are calculated for 2000, and differences in year lengths, compared to 2000, are given for past and future years. In the tables a day is 86,400 SI seconds long.<ref> {{#invoke:citation/CS1|citation |CitationClass=book }}</ref><ref> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref> {{#invoke:citation/CS1|citation |CitationClass=book }} Values in tables agree closely for 2000, and depart by as much as 44 seconds for the years furthest in the past or future; the expressions are simpler than those recommended in the Astronomical Almanac for the Year 2011.</ref><ref> {{#invoke:citation/CS1|citation |CitationClass=book }} Tabulates length of tropical year from −500 to 2000 at 500 year intervals using a formula by Laskar (1986); agrees closely with values in this section near 2000, departs by 6 seconds in −500.</ref>

Mean year lengths for 2000
Type of year Days Hours Minutes Seconds
Tropical 365 5 48 45
Sidereal 365 6 9 10
Anomalistic 365 6 13 53
Eclipse 346 14 52 55
Year length difference from 2000
(seconds; positive when length for tabulated year is greater than length in 2000)
Year Tropical Sidereal Anomalistic Eclipse
−4000 −8 −45 −15 −174
−2000 4 −19 −11 −116
0 7 −4 −5 −57
2000 0 0 0 0
4000 −14 −3 5 54
6000 −35 −12 10 104

Summary

Days Year type
346.62 Draconic, also called eclipse.
354.37 Lunar.
365 Vague, and a common year in many solar calendars.
main}} Tropical, also called solar, averaged and then rounded for epoch J2000.0.
main}} Gregorian, on average.
main}} Julian.
main}} Sidereal, for epoch J2000.0.
main}} Anomalistic, averaged and then rounded for epoch J2011.0.
366 Leap in many solar calendars.

An average Gregorian year is 365.2425 days (52.1775 weeks, {{safesubst:#invoke:val|main}} hours, {{safesubst:#invoke:val|main}} minutes or {{safesubst:#invoke:val|main}} seconds). For this calendar, a common year is 365 days ({{safesubst:#invoke:val|main}} hours, {{safesubst:#invoke:val|main}} minutes or {{safesubst:#invoke:val|main}} seconds), and a leap year is 366 days ({{safesubst:#invoke:val|main}} hours, {{safesubst:#invoke:val|main}} minutes or {{safesubst:#invoke:val|main}} seconds). The 400-year cycle of the Gregorian calendar has {{safesubst:#invoke:val|main}} days and hence exactly {{safesubst:#invoke:val|main}} weeks.


Year sections
Intro  Etymology   Civil year    \"Greater\" astronomical years    Seasonal year    Symbols   See also  References  Further reading  External links  

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