Astronomy and time
Julian date, MJD, GPS week, Unix time and sidereal time converter
Convert between UTC, Julian Date, Modified Julian Date, Unix time and GPS week and seconds, with leap seconds, TT and Greenwich sidereal time.
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Showing the worked example. Results update as you type.
Result
- Sidereal time uses UT1 ≈ UTC (they differ by less than 0.9 s), the IAU 1982 GMST expression and a low-precision nutation, good to about 0.01 s of time.
Method and limits
The Julian Date counts days and fractions since noon on 1 January 4713 BC (Julian calendar). It is computed from the calendar date with Meeus’s algorithm (chapter 7), using the Julian calendar before 15 October 1582 and the Gregorian calendar from then on. The Modified Julian Date is JD − 2,400,000.5, so it starts at midnight; MJD 0 is 17 November 1858. Unix time counts seconds since 1970-01-01T00:00:00Z without leap seconds (JD = Unix/86,400 + 2,440,587.5).
Leap seconds: TAI − UTC has been a whole number of seconds since 1972 (10 s then, 37 s since 1 January 2017). IERS Bulletin C 72 (6 July 2026) confirmed no leap second at the end of December 2026, so the table is complete to at least 30 June 2027. GPS time runs from 6 January 1980 without leap seconds, so GPS − UTC = TAI − UTC − 19 s (18 s now); a GPS week has 604,800 seconds and receivers broadcast the week number modulo 1024 (rollovers on 22 August 1999 and 7 April 2019). Terrestrial Time is TAI + 32.184 s.
Sidereal time uses the IAU 1982 expression GMST = 280.46061837° + 360.98564736629° (JD − 2451545.0) + 0.000387933° T² − T³/38,710,000 (Meeus eq. 12.4, T in Julian centuries), with UT1 ≈ UTC. Apparent sidereal time adds the equation of the equinoxes, Δψ cos ε, from a low-precision nutation.
Worked examples (Meeus): Sputnik 1’s launch, 1957 October 4.81 UT (19:26:24), is JD 2436116.31; 333 January 27, 12h is JD 1842713.0; at 1987 April 10, 0h UT, GMST is 13h10m46.3668s and GAST 13h10m46.1351s (this page: 46.131 s with its low-precision nutation); at 19:21 UT the same day GMST is 8h34m57.0896s. GPS week 2048 began on 7 April 2019 at 00:00:00 GPS time, 23:59:42 UTC on 6 April.
Limits
Julian Dates here are UTC-based, as is usual for civil times; add TT − UTC for ephemeris work. A leap second (23:59:60) cannot be entered because Unix time and UTC-based Julian Dates have no value for it. Sidereal times can be off by up to 0.9 s of UT1 − UTC plus about 0.01 s from the nutation series.
References
- Meeus, J. (1998). Astronomical Algorithms, 2nd ed., chapters 7 and 12 (Willmann-Bell)
- US Naval Observatory: Julian date converter
- IERS Bulletin C 72 (6 July 2026), as forwarded to the tz mailing list
- IERS: Bulletin C and the leap second table
- IS-GPS-200: GPS interface specification (GPS time, week number)
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