About the Sidereal Time Calculator
This sidereal time calculator converts an ordinary date and clock time into local sidereal time (LST) — the right ascension that is crossing your meridian at that moment. Enter the date, your local time and UTC offset, and your longitude, and it returns LST and Greenwich mean sidereal time (GMST) in hours, minutes and seconds, plus the Julian Date.
Amateur astronomers use LST to point setting circles on an equatorial mount, to work out when a target transits (is highest in the sky), and to plan observing sessions. Enter a target’s right ascension and the calculator also gives its hour angle: negative means it is still rising toward the meridian, positive means it has passed it.
Sidereal time is calculated from the IAU expression published in Meeus’s Astronomical Algorithms, which is accurate to a fraction of a second for dates within a few centuries of 2000. It returns mean sidereal time; apparent sidereal time differs by at most about 1.2 seconds because of nutation. Longitudes east of Greenwich are positive and west are negative.
How to use the sidereal time calculator
- 1Enter the date and your local clock time.
- 2Enter your UTC offset (including daylight saving if it applies).
- 3Enter your longitude — negative for west of Greenwich.
- 4Optionally enter a target’s right ascension in decimal hours.
- 5Read local sidereal time and the target’s hour angle.
Formula and method
Sidereal time measures Earth’s rotation relative to the distant stars rather than the Sun. Because Earth also moves along its orbit, a sidereal day is about 23 h 56 m 4 s, so sidereal time gains roughly 3 minutes 56 seconds on clock time every day. The calculator converts your local time to Universal Time using the UTC offset, finds the Julian Date, and evaluates the IAU mean-sidereal-time polynomial (T is Julian centuries since J2000.0).
Adding the observer’s east longitude (in degrees) gives local sidereal time, which is divided by 15 to convert degrees to hours. The hour angle of a target is LST minus its right ascension, wrapped into −12 to +12 hours. UT1 is approximated by UTC, a difference of under 0.9 s.
- θ₀
- Greenwich mean sidereal time (degrees)
- JD
- Julian Date of the moment in Universal Time
- T
- Julian centuries since J2000.0 = (JD − 2451545) / 36525
- LST
- Local sidereal time
- HA, RA
- Hour angle and right ascension of the target
Worked examples
Meeus example 12.a — 10 April 1987, 0h UT at Greenwich
JD 2446895.5 is 4,649.5 days before J2000. The polynomial gives θ₀ = 197.6932°, which divided by 15 is 13h 10m 46.37s — matching the worked example in Meeus’s Astronomical Algorithms.
Meeus example 12.b — 10 April 1987, 19:21 UT
19 h 21 m later, sidereal time has advanced 19.35 × 1.0027379 hours, wrapping past 24 h to 8h 34m 57.09s, as in the textbook.
London, 1 January 2026 at 21:00 GMT
GMST is 3h 46m 05.6s; London’s longitude of −0.1276° subtracts 30.6 seconds, giving LST 3h 45m 35s. The Orion Nebula (RA 5.588 h) is still 1.83 sidereal hours east of the meridian.
New York, 15 January 2026 at 22:00 EST (UTC−5)
22:00 EST is 03:00 UT on 16 January, when GMST is 10h 42m 16.5s. Subtracting 74.006° ÷ 15 = 4h 56m gives LST 5h 46m 15s, so the Orion Nebula has just crossed the meridian.
Frequently asked questions
What is sidereal time?+
Sidereal time is timekeeping based on Earth’s rotation relative to the stars. Local sidereal time equals the right ascension of the stars on your meridian, so an object with RA 5h 35m is highest in the sky when LST is 5h 35m.
How long is a sidereal day?+
About 23 hours 56 minutes 4.09 seconds of ordinary time. Because Earth moves along its orbit, it must rotate an extra degree each day to bring the Sun back to the meridian, which makes the solar day about 4 minutes longer.
What is the difference between local and Greenwich sidereal time?+
Greenwich sidereal time applies at longitude 0°. Local sidereal time adds your longitude converted to time (15° = 1 hour): east longitudes are ahead of Greenwich, west longitudes behind.
What is hour angle?+
Hour angle is how far an object is from your meridian, measured in hours westward: HA = LST − RA. A negative value means it is still rising toward the meridian; a positive value means it has already transited and is moving west.
What is the difference between mean and apparent sidereal time?+
Apparent sidereal time includes the equation of the equinoxes caused by nutation of Earth’s axis, a correction of at most about ±1.2 seconds. Mean sidereal time, shown here, is more than accurate enough for pointing a telescope.