Local Sidereal Time Calculator

Background.

Every observer at an eyepiece eventually wants to know what is crossing the meridian right now, the north–south line through the zenith where each star stands highest. Sidereal time answers that in one reading. It is a clock set by the stars rather than the Sun, and its value equals the right ascension of whatever is culminating: if your local sidereal time is 22h 54m, objects at right ascension 22h 54m are at their highest.

The sidereal clock runs fast against an ordinary one, gaining 3 minutes 56.56 seconds of sidereal time every solar day. Over a year the gain adds up to a whole day, which is why a constellation rises about four minutes earlier each night and why the sky at 10 pm in January looks nothing like the sky at 10 pm in July.

You supply a date and time in UTC and a longitude, east positive. Back come local and Greenwich sidereal time, each in a mean and an apparent version, the small nutation correction separating them, the right ascension on your meridian in degrees, and the Julian Date the arithmetic used. No time zone is applied, so convert a local clock reading to UTC first; Nairobi, on UTC+3 all year, subtracts three hours.

The coefficients are the U.S. Naval Observatory's approximate sidereal time formulae, whose stated worst-case error over 2000–2100 is 0.432 seconds. The larger uncertainty usually lies in the clock you start from. The formulae are defined on UT1, the time scale that follows the Earth's actual rotation, while you enter UTC, which leap seconds keep within 0.9 seconds of it. For pointing a telescope or planning a session that is irrelevant. For timing an occultation to a tenth of a second, it is not.

What is sidereal time calculator?

Sidereal time is the hour angle of the vernal equinox: how far the Earth has turned, measured against the stars, since the equinox point last crossed your meridian. It runs from 0 to 24 hours, each hour equal to 15° of rotation. A mean sidereal day lasts 23 h 56 m 4.09 s of ordinary solar time. It is shorter than a solar day because after one turn relative to the stars the Earth has moved about a degree along its orbit and must turn that extra degree to bring the Sun back to the meridian. Mean sidereal time is referred to an equinox that moves only with precession; apparent sidereal time also follows nutation, a small nodding of the Earth's axis on an 18.6-year cycle.

How to use this calculator.

1. 01Enter the date and the time in UTC by removing your zone offset from the local clock reading: 03:00 in Nairobi (UTC+3) is 00:00 UTC on the same date, while 20:00 in New York during daylight saving (UTC−4) is 00:00 UTC on the following date.
2. 02Enter longitude in decimal degrees, east positive and west negative: Nairobi +36.8219, Sydney +151.2093, London −0.1276, New York −74.0060. Convert degrees, minutes and seconds first; 36° 49′ 19″ E is 36.8219.
3. 03Do not fuss over the seconds field. UTC can sit up to 0.9 s away from the rotation time the formula assumes, so precision finer than about a second is noise.
4. 04Read local mean sidereal time for setting circles and observing plans, or local apparent sidereal time when matching apparent right ascensions of date from an almanac.
5. 05Use the meridian right ascension, given in degrees, against coordinates listed in degrees; divide by 15 to compare with a chart that lists right ascension in hours.

The formula.

Greenwich mean sidereal time is assembled in hours: GMST = 6.697374558 + 0.06570982441908 D₀ + 1.00273790935 H + 0.000026 T². Here D₀ counts days from the J2000.0 epoch (Julian Date 2451545.0) to the most recent 0h UT, H is the hours of UT since that midnight, and T is the elapsed time in Julian centuries of 36,525 days. The D₀ term steps the clock forward a whole day at a time, by 0.06570982441908 h, which is 236.5554 seconds; the H term carries it through the current day at 1.00273790935 sidereal hours per solar hour. Both express one rate, since 24 × 0.00273790935 = 0.0657098. The T² term is a small precession correction that grows with the square of time. The total is reduced modulo 24.

Local time depends on longitude alone: LMST = GMST + λ/15, one hour for every 15° east.

For the apparent version, nutation in longitude is approximated by two terms, Δψ = −0.000319 sin Ω − 0.000024 sin 2L hours, where Ω = 125.04° − 0.052954° D is the longitude of the Moon's ascending node, L = 280.47° + 0.98565° D is the Sun's mean longitude and D is days since J2000.0. Multiplying by the cosine of the obliquity, ε = 23.4393° − 0.0000004° D, gives the equation of the equinoxes, which swings through roughly ±1.1 seconds over the Moon's 18.6-year nodal cycle. The USNO quotes a maximum error of 0.432 s and an RMS of 0.015 s for these expressions across 2000–2100; further from that century the error grows.

A worked example.

Frequently asked questions.

References& sources.

1. [1]U.S. Naval Observatory, Astronomical Applications Department, 'Computing Approximate Sidereal Time'. Source of every coefficient in the primary algorithm (6.697374558, 0.06570982441908, 1.00273790935, 0.000026) and of the equation-of-the-equinoxes terms, together with the stated error budget: maximum 0.432 s and RMS 0.01512 s over 2000–2100. Open access. Note on provenance: this URL is live and indexed but returned a connection reset to automated retrieval on 2026-07-29, so every coefficient was additionally confirmed against indexed copies of the same page and, structurally, against the independent IAU 1982 expression below.
2. [2]Aoki, S., Guinot, B., Kaplan, G.H., Kinoshita, H., McCarthy, D.D. & Seidelmann, P.K. (1982). 'The new definition of Universal Time.' Astronomy & Astrophysics 105:359–361. Origin of the IAU 1982 GMST expression, implemented independently here as a cross-check. Peer-reviewed; the ADS record is JavaScript-rendered and returns no content to automated retrieval, so it is shipped as a bibliographic reference.
3. [3]Meeus, J. (1998). Astronomical Algorithms, 2nd edition, Willmann-Bell, chapter 12, equation 12.4. Restates the IAU 1982 expression in degrees for an arbitrary instant: θ₀ = 280.46061837 + 360.98564736629 (JD − 2451545.0) + 0.000387933 T² − T³/38710000. Print / bibliographic reference.
4. [4]Urban, S.E. & Seidelmann, P.K. (eds.) (2013). Explanatory Supplement to the Astronomical Almanac, 3rd edition, University Science Books, §6 — Earth rotation, UT1, the mean sidereal day and the equation of the equinoxes. Print; the U.S. Naval Observatory publication page is linked. Retrieved 2026-07-29.
5. [5]IERS Bulletin C, International Earth Rotation and Reference Systems Service. Verified by retrieval 2026-07-29: TAI − UTC = 37 s 'from 2017 January 1, 0h UTC, until further notice', and no leap second at the end of December 2026. This is the mechanism that keeps |UT1 − UTC| below 0.9 s, which bounds the dominant error on this page. Open access.