Epact

The epact (Latin: epactae, from Ancient Greek: ἐπακται ἡμεραι epaktai hēmerai 'added days') was originally the term used by medieval computists for the age of a phase of the Moon, in days since the new moon, as determined on 22 March of a given year. In the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January. Its principal use is in determining the date of Easter by computistical methods. It varies (usually by 11 days) from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days. Epacts can also be used to relate dates in a lunisolar calendar to dates in the common solar calendar. A solar calendar year has 365 days (366 days in leap years). A lunisolar calendar year has 12 lunar months which typically alternate between 30 and 29 days for a total of 354 days: to resynchronise with the solar year, a thirteenth leap month is added. This is because a lunar year lasts a little over 354+1⁄3 days and consequently a leap year arises every second or third year rather than every fourth.) If a solar and lunar year start on the same day, then after one year the start of the solar year is 11 days after the start of the lunar year. These 'excess' days are called epacts, and have to be added to the lunar year to complete the solar year; or from the complementary perspective they are added to the day of the solar year to determine the day in the lunar year.