+ (((4 × J + B) div 146097) × 3) div 4 + C For Julian or Gregorian, continue: D, M, and Y are the numbers of the day, month, and year respectively for the afternoon at the beginning of the given Julian day. Julian Period from indiction, Metonic and solar cycles Let Y be the year BC or AD and i, m and s respectively its positions in the indiction, Metonic and solar cycles. Divide 6916i + 4200m + 4845s by 7980 and call the remainder r. Example i = 8, m = 2, s = 8. What is the year? Julian date calculation As stated above, the Julian date (JD) of any instant is the Julian day number for the preceding noon in Universal Time plus the fraction of the day since that instant. Ordinarily calculating the fractional portion of the JD is straightforward; the number of seconds that have elapsed in the day divided by the number of seconds in a day, 86,400. But if the UTC timescale is being used, a day containing a positive leap second contains 86,401 seconds (or in the unlikely event of a negative leap second, 86,399 seconds). One authoritative source, the Standards of Fundamental Astronomy (SOFA), deals with this issue by treating days containing a leap second as having a different length (86,401 or 86,399 seconds, as required). SOFA refers to the result of such a calculation as "quasi-JD". See also Julian year (calendar) 5th millennium BC Barycentric Julian Date Dual dating Decimal time Epoch (astronomy) Epoch (reference date) Era J2000 – the epoch that starts on JD 2451545.0 (TT), the standard epoch used in astronomy since 1984 Lunation Number (similar concept) Ordinal date Time Time standards Zeller's congruence Notes References Sources Alsted, Johann Heinrich 1649 [1630]. Encyclopaedia , Tome 4, Page 122. American Ephemeris and Nautical Almanac, Washington, 1855–1980, Hathi Trust Astronomical almanac for the year 2001. (2000). U.S. Nautical Almanac Office and Her Majesty's Nautical Almanac Office. . Astronomical almanac for the year 2017. (2016). U.S. Naval Observatory and Her Majesty's Nautical Almanac Office. . Astronomical Almanac Online. (2016). U.S. Nautical Almanac Office and Her Majesty's Nautical Almanac Office. Bede: The Reckoning of Time, tr. Faith Wallis, 725/1999, pp. 392–404, . Also Appendix 2 (Beda Venerabilis' Paschal table. Blackburn, Bonnie; Holford-Strevens, Leofranc. (1999) The Oxford Companion to the Year, Oxford University Press, . Burgess, Ebenezer, translator. 1860. Translation of