Julian Date Calculator

Background.

The Julian Date is the continuous day count that astronomy actually runs on. It is a single real number — days elapsed since noon Universal Time on 1 January of the year −4712 in the Julian calendar — chosen so that an ephemeris never has to know about months, leap years, calendar reforms or the difference between February in 1900 and February in 2000. This calculator converts a UTC instant into that number and into every derived form the field uses: the Modified Julian Date, the NASA truncated form, the offset from the J2000.0 epoch, and the Julian-century argument T that goes into precession, nutation and sidereal-time formulae.

This is deliberately not a date calculator. Our Day of the Week and Date Difference pages handle civil calendar questions, and this page does not duplicate them: it returns no weekday name and no interval between two dates. What it does instead is everything those pages cannot. It anchors at noon rather than midnight, because that is where a Julian day starts. It carries the epoch offset and the century argument that ephemeris polynomials consume. It distinguishes Coordinated Universal Time from Terrestrial Time and exposes the leap-second offset between them. It lets you tell it that your date is a Julian calendar date, which matters for every observation recorded before October 1582. And it reports two different Julian Day Numbers, because two conventions genuinely exist and disagree for half of every day.

That last point is worth stating plainly before you read the numbers. 'The Julian Day Number of 29 July 2026' is 2461251 — the integer Julian Date at noon on that date, which is what the Fliegel and Van Flandern algorithm in the Explanatory Supplement computes, and it labels the civil date, so it changes at midnight. But the noon-to-noon Julian day actually containing midnight UTC on 29 July is 2461250, because that day began at noon on the 28th. Both are correct under their own definition, both are in circulation, and this page gives you both with labels rather than picking one silently.

The time scales matter just as much. The clock time you enter is UTC, and no JavaScript date object is ever constructed from it, so no local timezone can shift the answer — the string is parsed field by field and the calculation is pure arithmetic. Terrestrial Time, which is the scale ephemerides are defined on, runs ahead of UTC by 32.184 seconds exactly plus the current leap-second count. That count is 37 seconds and has been since 1 January 2017, with IERS Bulletin C confirming no leap second at the end of 2026 — but it was 32 seconds in the year 2000 and 10 seconds in 1972, so it is an editable input rather than a baked-in constant. One consequence catches people out constantly: J2000.0 is defined as 2000 January 1 at 12:00 Terrestrial Time, which is not 12:00 UTC. Enter noon UTC on that date and the UT-based century comes back exactly zero while the TT-based one does not, because the epoch is 64.184 seconds earlier on the UTC clock.

The calendar select is not decoration either. The Julian and Gregorian calendars have different leap rules, so 29 February 1900 is a real Julian date and not a real Gregorian one — the calculator accepts it in one mode and refuses it in the other. The two calendars had drifted 10 days apart by 1582, 13 by 1900 and will be 14 apart in 2100. Choosing the wrong one silently shifts your Julian Date by that many days, which is the single most common way a historical observation gets mis-reduced.

All arithmetic runs at forty significant digits and is rounded once at the end. One real limit survives that: a Julian Date near 2.46 million, returned as a double-precision number, resolves to about four hundredths of a millisecond, so subtracting two Julian Dates recovers a time difference only to roughly a tenth of a millisecond. That is why the TT − UTC offset is given as its own output rather than left for you to obtain by subtraction, and why days-since-J2000 — a five-digit number that keeps full precision — is the value the downstream formulae actually consume.

What is julian date calculator?

The Julian Date, usually written JD, is the number of days and fractions of a day that have elapsed since 12:00 Universal Time on 1 January −4712 (4713 BC) in the proleptic Julian calendar. Joseph Scaliger proposed the count in 1583 and it was adopted by astronomers precisely because it is free of calendars: any two instants can be subtracted directly to give an interval in days, with no month lengths or leap rules involved.

Because it begins at noon, a Julian Date for a midnight instant always ends in .5. That is intentional: it keeps a single night's observations inside one integer day number rather than splitting them across two.

The Modified Julian Date, MJD = JD − 2400000.5, was introduced to shed five leading digits and to move the day boundary back to midnight, which suits geodesy and satellite work. NASA's Truncated Julian Date, TJD = JD − 2440000.5, does the same job with an epoch in 1968. J2000.0 is the reference epoch of the modern celestial reference system: JD 2451545.0, or 2000 January 1 at 12:00 Terrestrial Time.

How to use this calculator.

1. 01Enter the date. If your source is an observation from before October 1582, switch the calendar select to Julian first.
2. 02Enter the time of day in UTC. If your record is in local time, convert it before entering — nothing on this page applies a timezone.
3. 03Leave TAI − UTC at 37 seconds for any instant since 2017; set it to the value in force at the time for older instants.
4. 04Read JD or MJD for archiving and for differencing two observations.
5. 05Read days since J2000.0 and the Julian centuries T if you are feeding an ephemeris or sidereal-time formula.
6. 06Check which T you need: the UT-based one for sidereal time, the TT-based one for precession, nutation and planetary positions.
7. 07Read the note if your date is before 1582 — it will tell you when you are working in a proleptic calendar that did not yet exist.

The formula.

Meeus's algorithm works by shifting the year to start in March, so that the awkward leap day falls at the end rather than the middle. If the month is January or February the year is decremented and twelve is added to the month; the term ⌊365.25(Y+4716)⌋ then counts whole Julian years from a distant epoch, ⌊30.6001(M+1)⌋ counts the days in the completed months of the shifted year, and B applies the Gregorian century correction — zero for a Julian calendar date.

Work through the default. For 2026 July 29 the month exceeds two, so nothing shifts. A = ⌊2026/100⌋ = 20, so B = 2 − 20 + ⌊20/4⌋ = −13. Then ⌊365.25 × 6742⌋ = 2462515 and ⌊30.6001 × 8⌋ = 244, giving JD = 2462515 + 244 + 29 − 13 − 1524.5 = 2461250.5. Subtracting 2400000.5 gives MJD 61250 exactly — a whole number, because the instant is midnight and MJD begins at midnight. Days since J2000.0 is 9705.5, so T is 9705.5 ⁄ 36525 = 0.2657221082. With TAI − UTC at 37 seconds, TT − UTC is 69.184 seconds and the TT-based century is 0.2657221301.

THE INDEPENDENT CHECK. A completely different algorithm — Fliegel and Van Flandern's 1968 integer method, reproduced in the Explanatory Supplement to the Astronomical Almanac — is implemented alongside Meeus's and the test suite asserts they agree on twelve dates. Those dates deliberately include 28 February and 1 March 1900, which a wrong century-leap rule breaks, and 29 February 2000, which a wrong four-hundred-year rule breaks. Two further anchors that come from neither algorithm are also checked: MJD 0 must be 1858 November 17 at 0h, and TJD 0 must be 1968 May 24 at 0h. Both come out exactly.

ROUNDING STAGE, AND A REAL PRECISION FLOOR. Nothing is rounded part-way through; all arithmetic runs at forty significant digits and rounding happens once at the return boundary — eight decimal places for Julian Dates, and fifteen significant digits for the two century values, because T legitimately ranges from about 10⁻⁸ to about 20 and a fixed decimal place would flatten the small end to zero. What survives is a hard limit of the number format itself: a Julian Date near 2.46 million has a double-precision resolution of about 0.04 milliseconds, so differencing two Julian Dates recovers an interval only to roughly a tenth of a millisecond. The TT − UTC offset is therefore reported as its own output rather than left to be obtained by subtraction.

APPROXIMATION REGIME. There is none. This is exact integer and decimal arithmetic. The only modelling choices are which calendar the entered date belongs to and what the leap-second offset was at the time — and both are yours to set.

INVALID DOMAIN. A month outside 1 to 12 is rejected. So is a day beyond the true length of that month in the calendar you selected, which is why 29 February 1900 is accepted as a Julian date and refused as a Gregorian one. Hours must be 0 to 23, minutes and seconds 0 to 59, and TAI − UTC between 0 and 60 seconds. A leap second, 23:59:60, has no Julian Date at all: JD is a smooth count of days and simply has no room for a sixty-first second.

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 in this module and asserted equal to Meeus's method across twelve test dates — this page's second-authority check. 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.