Julian Date Calculator

Background.

Variable-star observers, satellite trackers and anyone reducing an old eclipse record hit the same snag: months have different lengths, the leap-year rule changed in 1582, and subtracting two calendar dates by hand is error-prone. Astronomy avoids the problem with the Julian Date, a single running count of days and fractions of a day. Noon UTC on 29 July 2026 is day 2,461,251; six hours later it is 2,461,251.25. The interval between any two observations, however far apart, is one subtraction.

Give a date and a UTC clock time and you get that number along with the variants other fields prefer: the Modified Julian Date used in geodesy and observatory logs, NASA's Truncated Julian Date, days since the J2000.0 epoch, and the Julian-century argument T that precession, nutation and sidereal-time formulas take as input.

Two settings decide whether the answer is right. One is the calendar. Anything dated before 15 October 1582, and much that was dated later, was written in the Julian calendar, which since March 1900 has run 13 days behind the Gregorian. Read a date in the wrong calendar and the Julian Date is off by that many days, with nothing in the number to warn you. The other is the time scale. The clock you type is read as UTC with no time zone applied, but ephemerides are computed on Terrestrial Time, which runs ahead of UTC by 32.184 seconds plus the accumulated leap seconds. That count is an editable input, 37 seconds by default, because it has grown by 27 since 1972.

The noon start leaves two habits that surprise newcomers: a midnight instant always gives a Julian Date ending in .5, and the phrase Julian Day Number has two meanings that disagree every morning. Both numbers are reported, each labelled.

What is julian date calculator?

The Julian Date (JD) is the number of days, including the elapsed fraction of the current one, since 12:00 Universal Time on 1 January 4713 BC in the proleptic Julian calendar, written −4712 in astronomical year numbering, which includes a year 0. Its starting point comes from Joseph Scaliger's Julian Period of 1583, which astronomers later turned into a continuous day count. Each day begins at noon so that one night of European observing stays inside a single day number. The other counts are fixed offsets: MJD = JD − 2400000.5, whose day zero is 17 November 1858 starting at midnight; TJD = JD − 2440000.5, zero on 24 May 1968; and the J2000.0 epoch is JD 2451545.0, defined as 1 January 2000 at 12:00 Terrestrial Time. A Julian century is exactly 36,525 days.

How to use this calculator.

1. 01Type the date as your source gives it and set the calendar to match. Use Julian for anything before 15 October 1582 and for later records from countries that changed late; a pre-1582 date left on Gregorian brings a note that the calendar did not exist yet.
2. 02Enter hour, minute and second in UTC, converting local time first: 21:30 in a UTC+3 zone is 18:30 UTC. A leap second, 23:59:60, cannot be entered because the day count has no place for it.
3. 03Leave TAI − UTC at 37 seconds for anything since 1 January 2017. For older instants use the value then in force, such as 32 seconds for 1999 to 2005 or 10 seconds in 1972, or the Terrestrial Time outputs will be off by the difference.
4. 04To log or subtract observations, read JD or MJD. To feed a formula from an almanac or from Meeus, read days since J2000.0 or T, and check whether it wants the UT-based T (sidereal time) or the TT-based one (planetary positions, precession, nutation). The results grid shows four decimals of a day (about 8.6 seconds); the reading line underneath gives six.

The formula.

The conversion follows chapter 7 of Jean Meeus's Astronomical Algorithms. January and February are counted as months 13 and 14 of the previous year, which puts the leap day at the very end of the counting year and keeps the month arithmetic regular. Then JD = ⌊365.25(Y + 4716)⌋ + ⌊30.6001(M + 1)⌋ + D + B − 1524.5. The first term counts the days in whole Julian years from far back. The second counts the days in months already completed: 30.6 reproduces the alternating 31- and 30-day pattern from March onward, and the extra 0.0001 stops a product such as 30.6 × 5 = 153 from slipping to 152.9999 in floating-point arithmetic. D is the day of the month plus the clock time as a fraction of 86,400 seconds. B = 2 − A + ⌊A/4⌋, with A = ⌊Y/100⌋, removes the century leap days the Gregorian calendar drops; for a Julian-calendar date B is zero. The integer method of Fliegel and Van Flandern (1968), reproduced in the Explanatory Supplement to the Astronomical Almanac, gives the same day numbers.

Everything else is a fixed offset or ratio. MJD = JD − 2400000.5, TJD = JD − 2440000.5, days since J2000.0 = JD − 2451545.0, and T = that difference ÷ 36,525. For Terrestrial Time, JD(TT) = JD + (32.184 + TAI − UTC) ÷ 86,400, and the TT-based T is taken from JD(TT). The 32.184 seconds is exact by definition: it makes Terrestrial Time continuous with the older Ephemeris Time scale. No step is approximate, so a wrong answer can only come from the wrong calendar, a clock time that is not UTC, or the wrong leap-second count.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Meeus, J. (1998). Astronomical Algorithms, 2nd edition, Willmann-Bell, chapter 7 ('Julian Day'). Source of the primary conversion algorithm implemented here, including the March-start year shift and the Gregorian century correction B. Print / bibliographic reference — no authoritative free full text exists, so no URL is offered rather than linking a scan of uncertain provenance.
2. [2]Fliegel, H.F. & Van Flandern, T.C. (1968). 'A Machine Algorithm for Processing Calendar Dates.' Communications of the ACM 11(10):657. The pure-integer algorithm, implemented independently here as a cross-check on Meeus's method, with which it agrees across twelve sample dates. Peer-reviewed; the ACM Digital Library copy is paywalled, so it is shipped as a bibliographic reference.
3. [3]Urban, S.E. & Seidelmann, P.K. (eds.) (2013). Explanatory Supplement to the Astronomical Almanac, 3rd edition, University Science Books. Reproduces the Fliegel–Van Flandern algorithm (pp. 617–619 in the 3rd edition; p. 604 in the 1992 edition) and defines JD, MJD and the relationships between UT, TAI and TT. Print; the U.S. Naval Observatory's publication page for it is linked. Retrieved 2026-07-29.
4. [4]IERS Bulletin C, International Earth Rotation and Reference Systems Service. Verified by retrieval 2026-07-29 to state that the difference between UTC and TAI is −37 seconds 'from 2017 January 1, 0h UTC, until further notice', and that NO leap second will be introduced at the end of December 2026. Source of the default TAI − UTC input. Open access.
5. [5]International Astronomical Union, Resolution A4 (1991), defining Terrestrial Time, and the conventional relation TT = TAI + 32.184 s exactly, which makes TT continuous with the earlier Ephemeris Time scale. Bibliographic reference to the IAU resolution text.