Roman calendar ancient Greek calendars; and the Gregorian calendar, which refined the Julian system to bring it into still closer alignment with the solar year and is the basis of the current international standard. Roman dates were counted inclusively forward to the next of three principal days: the first of the month (the kalends), a day less than the middle of the month (the ides), and eight days—nine, counting inclusively—before this (the nones). The original calendar consisted of 10 months beginning in spring with March; winter was left as an unassigned span of days. These months ran for 38 nundinal cycles, each
Gregorian calendar always obtained by doubling (the "bissextum" (twice sixth) or bissextile day) until the late Middle Ages. The Gregorian calendar is proleptic before 1582 (assumed to exist before 1582). The following equation gives the number of days (actually, dates) that the Gregorian calendar is ahead of the Julian calendar, called the "secular difference" between the two calendars. A negative difference means the Julian calendar is ahead of the Gregorian calendar. where formula_2 is the secular difference and formula_3 is the year using astronomical year numbering, that is, use for BC years. formula_4 means that if the result of the division is