Intercalation

Intercalation 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 a combination of both adjustments. The solar year does not have a whole number of days (it's about 365.24 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 solar calendars, this is often done by adding to a common year of 365 days, an extra day (leap day or intercalary day) about every four years: this makes a leap year of 366 days.

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

In the Julian Calendar as well as in the Gregorian Calendar that improved 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 calendar years whose number is evenly divisible by 100 but not 400, were exempted in order to improve accuracy. Thus, 2000 was the first century year in 400 years to be a leap year.

The solar year does not have a whole number of lunar months either (it's about 12.37 lunations), so a lunisolar calendar must have a variable number of months in a year. This is usually 12 months, but a 13th month (an intercalary or embolismic month) is added to the year every two or three years.

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).