Intercalation

Intercalation is the insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons.
The solar year does not have whole number of days, but a calendar year must have a whole number of days. The only way to reconcile the two is to vary the number of days in the calendar year.

In many calendars, this is done by adding to a common year of 365 days, an extra day (leap day or intercalary day): this makes a leap year of 366 days.

The Decree of Canopus, which was issued by the pharaoh Ptolemy III, Euergetes of Egypt in 239 BC, decreed a leap year system.

In the Gregorian calendar, the intercalary day is February 29. The leap year in the Gregorian calendar occurs conventionally every four years, if the year is divisible by four (i.e. 2004 was a leap year, as will be 2008 and as was 1996). However, since this assumes that the solar year is 365.25 days long (it is actually 365.242199 days long), this simple system of one extra day every day every four years results in an error of +11 minutes per year. To adjust for this error, the system of one leap year every four years is interrupted if the year can be evenly divided by 100 (i.e. there was no leap year in the year 1900, nor will there be one in the year 2100). This system flawed as well though, being too short. Accordingly, a final adjustment adds a leap-year every year that can be evenly divided by 400 (i.e. 1600 was a leap year, as was 2000, and 2400 will also be a leap-year). This results in an error of 27 seconds per year, and produces an extra day every 3236 years.

The solar year does not have a whole number of lunar months either, so a lunisolar calendar must have a variable number of months in a year. This is usually 12 months, but sometimes a 13th month (an intercalary or embolismic month) is added to the year.

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

The determination of whether a year has intercalation may be calculated (Julian, Gregorian and Hebrew calendars), or determined by observation (Iranian calendar).

See also

*Calendar
*Bahá'í calendar
*Julian calendar
*Gregorian calendar
*Iranian calendar
*Hebrew calendar
*Hindu calendar
*Chinese calendar
*Islamic calendar (intercalation is prohibited)
*Leap second