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Sidereal Time Calculator

Enter a UTC date, time and longitude to compute the local mean sidereal time.

How it is calculated

The tool takes a UTC date and time and the observer's longitude in degrees, east positive and west negative. It converts the date to a Julian Date JD (Gregorian calendar), then computes Greenwich mean sidereal time with the IAU 1982 polynomial: GMST = 280.46061837 + 360.98564736629 × (JD − 2451545.0) + 0.000387933 T² − T³ ÷ 38710000 degrees, where T is Julian centuries since J2000.0. Local sidereal time is LST = GMST + longitude, both wrapped into 0 to 360°, and hours are degrees ÷ 15. The time is mean sidereal time (no nutation correction) and the clock input must be UTC, not your local time zone. A longitude of 286 gives the same answer as −74.

Worked example

New York, longitude −74°, on 20 March 2026 at 21:30 UTC. The tool finds GMST = 140.9243°. Adding the longitude: 140.9243 − 74 = 66.9243°. Dividing by 15 gives 4.4616 hours, shown as 04h 27m 41.84s. So any object with a right ascension near 4h 28m is crossing the local meridian at that moment. Keep the same clock time but move one day later and LST becomes 04h 31m 38.39s, about 3m 56.55s more.

Try this example →

Common mistakes

  • Entering local clock time instead of UTC. In New York in March the UTC time is hours ahead of the wall clock, and sidereal time moves about 15° per hour, so this shifts LST by whole hours.
  • Using a positive number for western longitudes. West is negative here; New York is −74, not 74.
  • Entering longitude as degrees, minutes and seconds in one field, such as 74.30. Convert to decimal degrees first (74°30′ = 74.5).
  • Treating the result as clock time. Sidereal time gains about 3 minutes 56.55 seconds on a solar day, so the same clock hour has a different LST each night.
  • Expecting apparent sidereal time. The tool gives mean sidereal time, which differs slightly from apparent time by the equation of the equinoxes.

About this calculator

Sidereal time measures the rotation of the Earth relative to the distant stars rather than the Sun, which is why a sidereal day (about 23h 56m 4s) is slightly shorter than a solar day. Greenwich Mean Sidereal Time (GMST) is derived from the Julian date using a polynomial approximation, and Local Mean Sidereal Time (LMST) is GMST adjusted by the observer's longitude — the value that directly equals the right ascension of whatever celestial object is currently crossing the observer's meridian.

This calculator converts a UTC date, time, and longitude into GMST and LMST. Amateur and professional astronomers use LMST to point telescopes using equatorial mounts and to work out which right-ascension objects will be well-placed for observation on a given night, while planetarium software and astronomical almanacs rely on the same GMST calculation as their timekeeping foundation.

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