Calendar year

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A calendar year begins on the New Year's Day of the given calendar system and ends on the day before the following New Year's Day, and thus consists of a whole number of days. The astronomer's mean tropical year, which is averaged over equinoxes and solstices, is currently 365.24219 days. As this is not an integer, solar calendars have strategies to adjust for the 0.24219 remainder. Neither is it a whole number of lunar months (being about 10 or 11 days more than 12 lunations) so lunisolar calendars also must include adjustments to resynchronise with the seasons. Pure lunar calendars ignore the solar cycle and instead have an invariant year of twelve lunar months that drifts through the seasons.

The Gregorian calendar year, which is in use as civil calendar in most of the world, begins on January 1 and ends on December 31.^[1] It has a length of 365 days in an ordinary year but, in order to reconcile the calendar year with the astronomical cycle, it has 366 days in a leap year. With 97 leap years every 400 years, the Gregorian calendar year has an average length of 365.2425 days.

Other formula-based calendars can have lengths which are further out of step with the solar cycle: for example, the Julian calendar (a solar calendar) has an average length of 365.25 days; the Hebrew calendar (a lunisolar calendar) has an average length of 365.2468 days. The Lunar Hijri calendar ("Islamic calendar") is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days.^{[lower-alpha 1]}

A year can also be measured by starting on any other named day of the calendar, and ending on the day before this named day in the following year.^[2] This may be termed a "year's time", but is not a calendar year.

The calendar year can be divided into four quarters,^[3] often abbreviated as Q1, Q2, Q3, and Q4. Since they are three months each, they are also called trimesters. In the Gregorian calendar:

• First quarter, Q1: January 1 – March 31 (90 days or 91 days in leap years)^[4]
• Second quarter, Q2: April 1 – June 30 (91 days)
• Third quarter, Q3: July 1 – September 30 (92 days)
• Fourth quarter, Q4: October 1 – December 31 (92 days)

In some domains, weeks are preferred over months for scheduling and reporting, so they use quarters of exactly 13 weeks each, often following ISO week date conventions. One in five to six years has a 53rd week which is usually appended to the last quarter. It is then 98 days instead of 91 days long, which complicates comparisons.

In the Chinese calendar, the quarters are traditionally associated with the 4 seasons of the year:

• Spring: 1st to 3rd month
• Summer: 4th to 6th month
• Autumn: 7th to 9th month
• Winter: 10th to 12th month

The calendar year can also be divided into three quadrimesters (from French quadrimestre),^[5] lasting for four months each. They can also be called the early, middle, or late parts of the year. In the Gregorian calendar:

• First quadrimester, early year: January 1 – April 30 (119 days or 120 days in leap years)
• Second quadrimester, mid-year: May 1 – August 31 (122 days)
• Third quadrimester, late year: September 1 – December 31 (121 days)

The calendar year can also be divided into two semesters,^[6] lasting six months each and often being abbreviated as S1 and S2. In the Gregorian calendar:

• First semester, S1: January 1 – June 30 (181 days or 182 days in leap years)
• Second semester, S2: July 1 – December 31 (184 days)

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