calendar (n.)

c. 1200, calender, "the year as divided systematically into days and months;" mid-14c. as "table showing divisions of the year;" from Old French calendier "list, register," from Latin calendarium "account book," from calendae/kalendae "the calends" the first day of the Roman month, when debts fell due and accounts were reckoned.

This is from calare "to announce solemnly, call out," as the priests did in proclaiming the new moon that marked the calends, from PIE root *kele- (2) "to shout." In Rome, new moons were not calculated mathematically but rather observed by the priests from the Capitol; when they saw it, they would "declare" the number of days till the nones (five or seven, depending on the month). The word was taken by the early Church for its register list of saints and their feast days. The meaning "list of documents arranged chronologically" is from late 15c.

The -ar spelling in English is from 17c., to differentiate it from the now-obscure calender "cloth-presser." Related: Calendarial; calendary.