How to use the sidereal time calculator
- Enter the date, the time of day and the UTC offset that applies to that time, such as -4 for New York in summer or 5.5 for India.
- Enter your longitude in degrees, with east positive and west negative.
- Read the local mean sidereal time in the headline and the Greenwich value below it.
- Open the advanced options to add seconds, or a right ascension to see how far an object is from the meridian.
Formula
JD = Julian date of the instant in UT
GMST (degrees) = 280.46061837 + 360.98564736629 (JD - 2451545.0) + 0.000387933 T^2 - T^3 / 38710000
T = (JD - 2451545.0) / 36525, reduced to 0 to 360 degrees
Local sidereal time = GMST + longitude east, divided by 15 to give hours
Sidereal time is the right ascension currently crossing your meridian. One sidereal day of 24 sidereal hours lasts 23 hours 56 minutes 4.09 seconds of clock time.
The J2000 epoch and an evening in New York
At noon UT on 1 January 2000 (Julian date 2451545.0) the Greenwich mean sidereal time is 280.4606 degrees, which is 18h 41m 50.55s. With longitude 0 the local time is the same.
At 21:00 local time on 10 October 2026 in New York (UTC-4, longitude -74.006) the instant is 01:00 UT on 11 October, Julian date 2461324.54167. Greenwich mean sidereal time is 02h 18m 33.63s, and the local mean sidereal time is 21h 22m 32.19s. An object at right ascension 20h is then 1.376 hours past the meridian.
What sidereal time tells you
Sidereal time measures the rotation of the Earth against the stars instead of the Sun. At any moment the local sidereal time equals the right ascension of the stars on your meridian, the north-south line overhead. An object is highest in the sky when your sidereal time equals its right ascension, which makes this number the quickest way to plan an observing session.
The hour angle of an object is the local sidereal time minus its right ascension. A negative value means the object has yet to cross the meridian, and a positive value means it already has. Enter a right ascension in the advanced options to see this.
Accuracy and limits
The page gives mean sidereal time, using the long-standing polynomial in Julian date. It leaves out nutation, a small wobble that shifts apparent sidereal time by at most about a second, and it treats UT and UTC as the same, which differ by under a second. For finding a target with a telescope or a star chart, that is far finer than needed. It agrees with a modern astronomy library to a few milliseconds near the present.
To plan around sunlight, use the sunrise and sunset calculator; for the Moon, see the moon phase calculator. For where on Earth a bearing points, the bearing and azimuth converter may help. Enter the UTC offset that is in effect on your date, including daylight saving time.
Assumptions and limits
- Dates run from 1800 to 2200 in the Gregorian calendar. Earlier dates would need Julian calendar rules.
- The UTC offset must match the clock you read the time from, including daylight saving time on that date.
- Times are treated as UT; the difference between UT and UTC is under a second and is ignored.
- Longitude is geographic, east positive. Latitude is not needed for sidereal time.
Frequently asked questions
Why is a sidereal day shorter than a solar day?
The Earth also moves along its orbit during the day, so it must turn a little more than one full turn for the Sun to return to the same place. Stars return after one full turn, which takes about 4 minutes less, so sidereal time gains about 4 minutes a day.
What does it mean when sidereal time equals an object's right ascension?
The object is crossing your meridian and is at its highest point in the sky for the night. It is the best time to observe it, because it is shining through the least air.
How do I find the offset from UTC?
Use the number of hours your local clock is ahead of UTC on that date. New York is -5 in winter and -4 in summer, London is 0 in winter and 1 in summer, and India is 5.5 all year.
Is this accurate enough for pointing a telescope?
Yes. The error is a few milliseconds of time, much smaller than the field of view of any eyepiece. Setting circles and mounts are usually less exact than the sidereal time itself.