What this calculator does
Sidereal time measures the Earth rotation against the stars rather than against the Sun. A sidereal day is about 23 hours 56 minutes 4 seconds, roughly four minutes shorter than a solar day, because the Earth has to turn slightly further each day to bring the Sun back to the same place.
Its practical use is simple: the local sidereal time equals the right ascension currently crossing your meridian. If the sidereal time reads 18:36, then objects at right ascension 18h 36m are due south (or due north from the southern hemisphere) and at their highest point in the sky.
The formula
Greenwich mean sidereal time is 280.46061837 degrees plus 360.98564736629 degrees for each day elapsed since the J2000.0 epoch, which is noon UTC on 1 January 2000. That second coefficient is slightly more than 360 because of the four minute daily difference. Adding your longitude, east positive, gives local sidereal time in degrees, and dividing by 15 converts it to hours.
| Term | Meaning |
|---|---|
| Sidereal day | One rotation relative to the stars, 23 h 56 m 4 s. |
| J2000.0 | The reference epoch, noon UTC on 1 January 2000, from which the day count runs. |
| GMST | Greenwich mean sidereal time, the value at zero longitude. |
| Right ascension | The celestial equivalent of longitude, measured in hours. It matches local sidereal time on your meridian. |
The inputs explained
| Field | What to enter |
|---|---|
| Date (UTC) | Date in UTC, not local time. The two differ either side of midnight. |
| Time (UTC, 24h) | Time in UTC on the 24 hour clock. Convert from your local clock time first, allowing for daylight saving if it applies. |
| Longitude (east positive, west negative) (°) | Your longitude in degrees, east positive and west negative. London is roughly 0, New York about −74, Sydney about +151. |
When to use it
Planning an observing session
Knowing the sidereal time tells you which part of the sky is best placed, since objects near your current sidereal time are highest and least affected by atmosphere.
Setting a telescope setting circle
Equatorial mounts with manual setting circles are aligned using sidereal time, since the hour angle of a target is the sidereal time minus its right ascension.
Understanding why the stars shift
The four minute daily drift is why a given constellation rises four minutes earlier each night, and two hours earlier each month.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is the sidereal time at different longitudes?
The same instant seen from five longitudes.
| Longitude | Local sidereal time | Greenwich sidereal time (GMST) | Local sidereal time in degrees |
|---|---|---|---|
| -120° | 3:50:10 | 11:50:10 | 57.54° |
| -75° | 6:50:10 | 11:50:10 | 102.54° |
| 0° | 11:50:10 | 11:50:10 | 177.54° |
| 15° | 12:50:10 | 11:50:10 | 192.54° |
| 151° | 21:54:10 | 11:50:10 | 328.54° |
Questions
Why is a sidereal day shorter than a solar day?
Because the Earth is orbiting the Sun as it rotates. After one full rotation relative to the stars, it has moved about a degree along its orbit, so it must turn roughly four minutes further to bring the Sun back overhead. That extra turn is the difference between the two days.
What is sidereal time used for?
It tells you which right ascension is on your meridian, so it identifies what is best placed for observing. Equatorial telescope mounts with setting circles use it directly, since hour angle equals sidereal time minus right ascension.
Do I enter local time or UTC?
UTC. The calculation is built on the count of days since the J2000.0 epoch in UTC, so a local clock time will give a wrong answer by however many hours your zone is offset, plus another hour if daylight saving is in force.
What is the difference between mean and apparent sidereal time?
Mean sidereal time ignores nutation, the small wobble in the Earth axis. Apparent sidereal time includes it, and the two differ by at most about a second. This calculates the mean value, which is what setting circles and observation planning use.
For the moon phase on a given night, see the moon phase calculator. For wind components, see the crosswind calculator.