Sidereal Time Calculator
Enter a UTC date and time, then add your longitude to get Greenwich Mean Sidereal Time (GMST), Greenwich Apparent Sidereal Time (GAST), Local Mean Sidereal Time (LMST), and Local Apparent Sidereal Time (LAST). Optionally enter the right ascension of a star or deep-sky object to compute the hour angle for your telescope. All four sidereal outputs are shown in both hours:minutes:seconds and decimal degrees.
Formula
Worked example
For 2025-06-21 20:00:00 UTC at longitude -74.006 deg (New York): JD = 2460843.33333; T = 0.25469...; GMST = 279.47 deg = 18:37:53; LMST = 279.47 - 74.006 = 205.46 deg = 13:41:50; the observer sees stars with RA near 13h 42m crossing the meridian.
What is sidereal time and why does it matter for astronomy?
Sidereal time is a timekeeping system that measures Earth's rotation relative to the distant stars rather than the Sun. Because Earth also orbits the Sun, a solar day (the familiar 24-hour cycle) is about four minutes longer than one full rotation of Earth. That four-minute surplus accumulates to a full day over one year, which is why the night sky shifts by roughly one full hour of right ascension every two weeks. A sidereal day lasts exactly 23 hours, 56 minutes, and 4.09 seconds of solar time. Astronomers care about sidereal time because it tells them directly which region of the sky is overhead at any moment. When your Local Sidereal Time equals the right ascension of a star or galaxy, that object is on your local meridian, the imaginary line running due north-south through the zenith, where it is at its highest point and least affected by atmospheric distortion.
GMST, GAST, LMST and LAST: what each value means
Greenwich Mean Sidereal Time (GMST) is sidereal time calculated for the prime meridian (0 degrees longitude) using the mean position of the vernal equinox, the astronomical reference point defined by the Sun crossing the celestial equator in March. Greenwich Apparent Sidereal Time (GAST) adds a tiny correction called the equation of the equinoxes, which accounts for nutation, a small wobble in Earth's axis caused mainly by the Moon's gravitational pull. The difference between GMST and GAST is usually less than one second of time. Local Mean Sidereal Time (LMST) shifts GMST by your geographic longitude: for every degree east you add four minutes, for every degree west you subtract four minutes. Local Apparent Sidereal Time (LAST) is the most precise value, combining your longitude correction with the nutation correction. For telescope pointing and star-atlas matching, LAST is the correct value to use because it tells you the exact right ascension currently on your meridian.
How to use this calculator for visual and telescope observing
Enter the UTC date and time, not your local clock time. If you know your UTC offset, add or subtract it from your local time before entering it here. Enter your longitude in decimal degrees, east positive and west negative. For example, Los Angeles is about -118.24, Paris is about +2.35, and Sydney is about +151.21. The four sidereal outputs appear immediately, both as hours-minutes-seconds for reading against a star atlas and as decimal degrees for use in programming a mount. To compute the hour angle of a specific target, enter its right ascension in decimal degrees (multiply the hour component by 15 to convert). A negative hour angle means the object has not yet reached the meridian and is rising; a positive hour angle means it has passed the meridian and is setting. Most mounts begin to track badly at hour angles beyond plus or minus 6 hours, so aim to observe near zero.
The Julian Date and why it underlies every sidereal time calculation
The Julian Date (JD) is a continuous count of days and fractions of a day since noon on 1 January 4713 BC in the proleptic Julian calendar, a starting point chosen by historians in the 16th century to precede all recorded history. Because it is a simple decimal number, it is far easier to use in calculations than a calendar date with months of uneven length. The formula for GMST (from Jean Meeus, Astronomical Algorithms, equation 12.4) takes JD as its only input. The related quantity T is the number of Julian centuries (36525 days each) since the standard epoch J2000.0 (2000 January 1 at 12:00 UTC, JD 2451545.0). The quadratic and cubic terms in T in the GMST formula capture tiny long-term changes in Earth's rotation rate. For most practical observing purposes these higher-order terms contribute less than a second, but they matter for precise planning software.
Sidereal time vs solar time: key comparisons
| Property | Sidereal | Solar (Civil) |
|---|---|---|
| Day length | 23 h 56 min 4.09 s | 24 h 0 min 0 s |
| Reference direction | Distant stars (vernal equinox) | The Sun |
| Repeats per year | 366.25 sidereal days | 365.25 solar days |
| Rate vs solar | Gains ~4 min per day | Standard civil time |
| Used for | Telescope pointing, RA matching | Everyday scheduling |
| GMST origin | Greenwich meridian, mean equinox | Greenwich meridian, mean Sun |
| GAST vs GMST | Includes nutation (~1 s) | Not applicable |
| LST = GMST when | Observer is at 0 deg longitude | Observer is at UTC+0 |
Differences between sidereal and solar timekeeping in everyday astronomy.
Frequently asked questions
Why do I need to enter UTC instead of my local time?
Sidereal time is a universal astronomical quantity tied to the rotation of Earth. The GMST formula takes a Julian Date in Universal Time (UTC) and produces a result valid for the Greenwich meridian. If you enter local time without converting it, the result will be offset by the number of hours in your time zone. To convert, find your UTC offset (for example, UTC-5 for Eastern Standard Time) and add or subtract it from your local time. Online time zone converters make this straightforward.
What is the difference between LMST and LAST, and which should I use?
LMST (Local Mean Sidereal Time) uses the mean vernal equinox, an idealized point that ignores the small wobble of Earth's axis called nutation. LAST (Local Apparent Sidereal Time) adds the equation of the equinoxes, a correction that accounts for nutation and gives the true position of the vernal equinox at the moment in question. For casual visual observing and star-hopping, LMST is precise enough. For automated telescope mounts, astrometry software, and precision timing, use LAST because star catalogs give coordinates relative to the true equinox.
What does the hour angle tell me?
The hour angle (HA) is the angular distance, measured in hours and degrees westward along the celestial equator, between your local meridian and the hour circle passing through the object. An HA of zero means the object is exactly on your meridian and at its highest point in the sky, the ideal moment to observe it. A negative HA (for example, -02:30) means the object is 2.5 sidereal hours east of the meridian and has not yet reached its peak. A positive HA (for example, +04:00) means the object passed the meridian 4 sidereal hours ago and is now in the western sky.
How long is a sidereal day compared to a solar day?
A sidereal day lasts 23 hours, 56 minutes, and 4.09 seconds of solar (clock) time, approximately 3 minutes and 56 seconds shorter than a 24-hour solar day. The difference arises because Earth must rotate slightly more than 360 degrees each solar day to bring the Sun back to the same position in the sky, since Earth has also moved along its orbit. Over one year, this accumulates to one extra sidereal day, so Earth completes 366.25 sidereal rotations but only 365.25 solar days per year.
Why does the night sky shift by about 2 hours per month?
Because the sidereal day is about 4 minutes shorter than the solar day, the sky advances by 4 minutes each night relative to the clock. Over 30 nights that accumulates to about 2 hours (30 times 4 minutes equals 120 minutes). This is why constellations visible in the south at midnight in January are already setting by 10 pm in March, and why astronomers plan seasonal observing programs around which right-ascension region culminates at a convenient hour.
How do I convert right ascension from hours:minutes:seconds to decimal degrees?
Multiply the hours component by 15, the minutes component by 0.25, and the seconds component by 0.004167, then add the three results. For example, RA 05h 34m 32s = (5 x 15) + (34 x 0.25) + (32 x 0.004167) = 75 + 8.5 + 0.1333 = 83.63 degrees. The relationship is simply 360 degrees divided by 24 hours, giving 15 degrees per hour, because the sky appears to rotate 360 degrees in 24 sidereal hours.
Is this calculator precise enough for telescope alignment?
Yes for most amateur telescopes. The GMST formula used here is from Jean Meeus, Astronomical Algorithms, which is accurate to well under a second of time for dates within a century of J2000.0 (the year 2000). The nutation correction for GAST uses two dominant terms and is accurate to about 0.5 arcseconds. That level is more than sufficient for visual observing, GOTO mounts, and most astrophotography. For high-precision astrometry, radio telescope pointing, or satellite tracking, use the IAU SOFA library or the U.S. Naval Observatory online data service.