Sidereal time calculator
Enter a date and time, your offset from UTC and your longitude. The calculator gives Greenwich mean sidereal time and the local sidereal time at your place, in hours, minutes and seconds and in degrees. Local sidereal time is the right ascension now crossing your meridian, which is what you need to find stars with a telescope.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the date and the clock time.
- Enter your offset from UTC, or 0 if the time is already in UT.
- Enter your longitude, east positive and west negative (a trailing E or W also works).
- Read the local and Greenwich sidereal times; the Universal Time and Julian Date used are shown below them.
The clock time minus the offset gives Universal Time, and from it the Julian Date JD. With d = JD − 2451545.0 and T = d ÷ 36525:
GMST = 280.46061837° + 360.98564736629° × d + 0.000387933° × T² − T³ ÷ 38,710,000
reduced to 0–360°. Local sidereal time is LST = GMST + longitude (east positive), again reduced to 0–360°. Dividing degrees by 15 gives hours.
Example
This is the example in Meeus’s book: 10 April 1987 at 19:21:00 UT. The Julian Date is 2446896.30625, and GMST comes out as 128.7378734°, which is 8 h 34 min 57.09 s.
For New York (longitude 74.006° W, written −74.006) at the same moment, which is 14:21 local time with an offset of −5: LST = 128.7378734° − 74.006° = 54.7318734° = 3 h 38 min 55.65 s.
At the J2000.0 epoch, 1 January 2000 at 12:00 UT (JD 2451545.0), GMST is exactly 280.46061837°, or 18 h 41 min 50.548 s.
Tips
- Use your longitude to a few decimal places: 0.1° makes a 24-second difference.
- Remember the sign: places west of Greenwich (the Americas) are negative.
- If your clock time is after midnight in local time but before midnight in UT, the date in UT is the day before; the Universal Time row shows which moment was used.
Frequently asked questions
What is sidereal time?
Time measured by the stars instead of the Sun. One sidereal day, one turn of the Earth relative to the stars, is about 23 h 56 min 4 s of ordinary time, so sidereal time runs about 3 min 56 s a day faster than the clock and the stars rise a little earlier each night.
What is the difference between GMST and LST?
Greenwich mean sidereal time is sidereal time on the Greenwich meridian. Local sidereal time adds your longitude: 15° of longitude east makes it one hour later, 15° west one hour earlier.
How do I use local sidereal time at the telescope?
LST equals the right ascension of the stars crossing your meridian, the north–south line through the sky, at that moment. A star's hour angle is LST minus its right ascension; when the hour angle is 0 the star is at its highest.
Which formula is used?
The IAU 1982 expression for mean sidereal time from the Julian Date, as given in Jean Meeus, Astronomical Algorithms, formula 12.4. The result is mean sidereal time; apparent sidereal time also includes nutation, which differs by about a second at most. The difference between UTC and UT1 (under 0.9 s) is ignored.
Does the calculator handle daylight saving time?
Enter the offset that applies on that date, for example -4 for New York in summer and -5 in winter. With an offset of 0 the time is taken as UT.