Julian Day Number Converter

Formula

How this is calculated

The Julian Day Number (JDN) is a continuous count of whole days starting from noon Universal Time on 1 January 4713 BC in the proleptic Julian calendar. Because it has no months, leap years, or calendar reforms, astronomers use it to compute time intervals between events spanning centuries. The Julian Date (JD) extends this with a fractional part for the time of day, where the integer flips at noon rather than midnight (so JD = ...".0" corresponds to 12:00 UT).

For a Gregorian-to-Julian conversion the tool reads the year, month, day, and the hour, minute and second in Universal Time. It applies the Fliegel–Van Flandern integer formula: an intercalary term a shifts January and February into the previous year, after which fixed multipliers count whole years and the 4/100/400 leap-year cycle of the Gregorian calendar, and the constant 32045 anchors the epoch. The fractional Julian Date then adds (hour − 12)/24 + minute/1440 + second/86400 because the day boundary is noon. The Modified Julian Date (MJD = JD − 2400000.5) re-zeros the count to midnight on 17 November 1858 and is common in space-flight and satellite data.

For the reverse direction the tool takes a (possibly fractional) Julian Date, sets JDN = ⌊JD + 0.5⌋ to recover the civil day, derives the time of day from the remaining fraction, and reconstructs the Gregorian year, month and day with the inverse Richards algorithm. Years use the astronomical convention where 1 BC is year 0 and 2 BC is −1. All times are treated as Universal Time, seconds are rounded to the nearest whole second, and dates before the 1582 Gregorian reform are handled on the proleptic Gregorian calendar.