About Sidereal Time
Sidereal time tracks Earth's rotation relative to the distant "fixed" stars, instead of relative to the Sun the way ordinary clock (solar) time does. Because Earth also travels along its orbit each day, it has to rotate slightly more than 360° to bring the Sun back to the same position in the sky, but only exactly 360° to bring the stars back into the same position. The result is that a sidereal day — one full rotation relative to the stars — lasts 23h 56m 4.0905s, about 3 minutes 56 seconds shorter than the familiar 24-hour solar day. Astronomers use sidereal time to know instantly which stars are on the local meridian (crossing due south, for northern observers), which is essential for pointing telescopes and for celestial navigation.
Greenwich Sidereal Time and Local Sidereal Time
Greenwich Mean Sidereal Time (GMST) is sidereal time measured at the 0° (Greenwich) meridian. Local Sidereal Time (LST) is sidereal time at your own longitude, found by adding your longitude (converted from degrees to hours) to GMST:
LST = GMST + longitude ÷ 15 (east longitude positive, west negative; the division by 15 converts degrees to hours since Earth rotates 15° per hour), reduced to the 0–24 hour range.
The GMST formula used here
This calculator uses the standard polynomial from Jean Meeus's Astronomical Algorithms (also published by the US Naval Observatory), based on the Julian Date (JD) of the observation in Universal Time:
- Compute the Julian Date, JD, for the given UTC date and time.
- Let d = JD − 2451545.0 (days since the J2000.0 epoch) and T = d ÷ 36525 (Julian centuries since J2000.0).
- GMST (in degrees) = 280.46061837 + 360.98564736629 × d + 0.000387933 × T² − T³ ÷ 38710000, reduced modulo 360°.
- Divide by 15 to convert GMST from degrees to hours, and add longitude ÷ 15 for Local Sidereal Time.
Common uses
- Amateur and professional astronomy: knowing which right ascension is currently on the meridian, for telescope pointing and object planning.
- Celestial navigation: relating star positions to time and longitude.
- Astronomy education: illustrating the difference between solar and sidereal time.
- Satellite and orbital mechanics reference calculations that use sidereal (Earth-fixed) time as a baseline.
Precision note
This calculator treats your entered local time and UTC offset as exact and does not apply corrections for polar motion, nutation, or the small difference between UT1 and UTC (which is generally under a second). For everyday astronomy and navigation use, that level of precision is more than sufficient; for professional-grade timing, use IERS UT1−UTC bulletins.