Sidereal Time Calculator

Sidereal time calculator with a live sidereal clock

A sidereal time calculator tells you where the sky has rotated to: local sidereal time (LST) equals the right ascension of whatever is crossing your meridian at that instant. This one shows Greenwich mean sidereal time (GMST), the apparent versions corrected for nutation (GAST and LAST), and your local mean sidereal time for any longitude — live, updating every second, or for any date and clock time you type. Pick a city to fill the longitude and time zone, or press Use my location.

Below the clock, an hour-angle helper converts a star’s right ascension into its hour angle for your site, says whether it is east or west of the meridian, when it next transits, and — with the declination — its altitude and azimuth right now. Observers use it for manual setting circles, to plan when a target is highest, and to check a mount’s clock. The maths follows Meeus’ Astronomical Algorithms and runs in your browser.

How to use the Sidereal Time Calculator

1. Choose a City, or select “Custom coordinates…” and type the Longitude (east positive, west negative) and the Time zone your clock time is in.
2. Leave Live clock on to follow the current sidereal time, or untick it and enter a Date and Clock time to calculate for any moment.
3. Read the local mean sidereal time and GMST in the panel; the apparent values, the equation of the equinoxes and the UTC instant used are shown below it.
4. In the hour-angle section, type a Right ascension (5h 55m 10s, 5.919 or 88.79°) and optionally a Declination, or pick a preset star or deep-sky object.
5. The helper reports the hour angle, how long until the object transits, and its present altitude and azimuth for your latitude.

Sidereal Time Calculator features

What sidereal time measures

A solar day is 24 hours because the Sun returns to the meridian in that time; but the Earth has moved along its orbit meanwhile, so relative to the stars it completes a turn in only 23 h 56 m 4.09 s — a sidereal day. Sidereal time is the hour angle of the vernal equinox, the zero point of right ascension. When LST is 5h 55m, Betelgeuse (RA 5h 55m) is on the meridian; when LST is 18h 37m, Vega is. Because a sidereal clock gains 3 m 56 s on a civil clock every day, a star transits about four minutes earlier each night, which is why the constellations drift westward through the seasons.

Mean sidereal time uses the slowly moving mean equinox; apparent sidereal time adds the equation of the equinoxes (Δψ cos ε), which oscillates by up to about ±1.1 s over an 18.6-year cycle. Precise transit timing uses the apparent value; planning can use the mean one.

The formula

With JD the Julian Date of the UT instant and T = (JD − 2451545.0)/36525 the Julian centuries since J2000.0, Meeus gives GMST = 280.46061837 + 360.98564736629 (JD − 2451545.0) + 0.000387933 T² − T³/38710000 degrees, reduced to 0–360° and divided by 15 for hours. At J2000.0 itself this returns 280.46061837° = 18h 41m 50.5s, the value this calculator’s self-test checks. Local sidereal time then adds the longitude: LST = GMST + λ/15 with east longitudes positive, so New Delhi (77.2° E) is 5 h 08 m 50 s ahead of Greenwich and New York (74.0° W) is 4 h 56 m behind. The Julian Date converter explains the JD half of the calculation.

Hour angle, transit and altitude

The hour angle H = LST − RA says how far west of the meridian an object is: negative values mean it is still in the east and climbing, positive values that it has passed its highest point. It transits when H = 0, at an altitude of 90° − |φ − δ| for latitude φ and declination δ, so from Mumbai (19° N) Betelgeuse (δ ≈ +7°) culminates 78° up, while from London it reaches 46°. The star chart draws the whole sky for the same moment.