Local Sidereal Time Calculator

Background.

Sidereal time is the clock the sky keeps. Where a solar clock is set by the Sun, a sidereal clock is set by the distant stars, and because the Earth advances about a degree along its orbit each day the two run at different rates: one solar day carries the sidereal clock forward by 24 hours and 3 minutes 56.6 seconds of sidereal time. That drift is why the constellations rise about four minutes earlier each night, and why an observer who knows the local sidereal time knows immediately which right ascension is crossing the meridian.

This calculator takes a UTC instant and a longitude and returns local and Greenwich sidereal time, both mean and apparent, the equation of the equinoxes that separates them, and the right ascension currently culminating. It is not a time-zone converter, and it is worth being clear about the difference. Converting between time zones is a civil operation on labels: two clocks showing different numbers for the same instant, quantised into political zones. Sidereal time is a physical measurement of how far the Earth has turned relative to the stars. It varies continuously with longitude, ignores zone boundaries entirely, and is defined against a time scale — UT1 — that itself tracks the Earth's slightly irregular rotation.

One convention decides whether your answer is right or on the other side of the planet: longitude is entered east positive, following the IAU and geodetic standard. Nairobi is +36.8219, London is −0.1276, New York is −74.0060, Sydney is +151.2093. Moving east advances local sidereal time, at exactly one hour per fifteen degrees, and moving west retards it by the same amount.

The distinction between mean and apparent sidereal time is small but real. Mean sidereal time is referred to the mean equinox and accounts only for precession. Apparent sidereal time is referred to the true equinox of date and includes nutation, the small nodding of the Earth's axis with an 18.6-year period. The difference between them is the equation of the equinoxes, which oscillates over roughly plus or minus 1.1 seconds. If you are matching against apparent right ascensions from an almanac, use the apparent value; for most amateur purposes the mean value is fine.

About accuracy, and this belongs next to the number rather than buried below it. The expressions used here are the U.S. Naval Observatory's approximate sidereal time formulae, whose own stated error over 2000 to 2100 is at most 0.432 seconds with an RMS of 0.015 seconds. But those formulae are defined on UT1, the time scale that follows the Earth's actual rotation, and what you have entered is UTC, which is an atomic scale kept within 0.9 seconds of UT1 by leap seconds. That input mismatch can contribute up to nine tenths of a second on its own — twice the formula's own error. The dominant uncertainty on this page is not the algorithm; it is the difference between the clock on your wall and the rotation of the Earth. For setting circles, session planning and drift-scan timing, none of this matters. For anything requiring sub-second astrometry, use a source of UT1.

Every coefficient has been cross-checked against a second, independent definition. The USNO expression is a two-part approximation; the IAU 1982 definition of Aoki and colleagues is a rigorous single polynomial from a different lineage. Both are implemented, and they agree to better than a tenth of a second at nine test epochs spanning the whole of the twenty-first century.

What is sidereal time calculator?

Sidereal time is the hour angle of the vernal equinox — in plain terms, a measure of how far the Earth has rotated with respect to the fixed stars rather than with respect to the Sun. It is expressed in hours, minutes and seconds, running from 0 to 24, and one sidereal hour corresponds to 15 degrees of Earth rotation.

A sidereal day is about 23 hours 56 minutes 4.09 seconds of ordinary solar time, roughly 3 minutes 56 seconds shorter than a solar day. The shortfall exists because the Earth must turn slightly more than one full rotation to bring the Sun back to the meridian, having moved about a degree along its orbit in the meantime.

Its practical value is direct: the local sidereal time equals the right ascension of whatever is crossing your meridian at that moment. If the local sidereal time is 20h 26m, an object at right ascension 20h 26m is at its highest point in your sky, and an object at right ascension 8h 26m is on the opposite meridian, below the horizon or near it.

How to use this calculator.

1. 01Enter the date and time in UTC. If you have a local clock time, convert it first — this page applies no time zone of its own.
2. 02Enter your longitude in degrees, EAST POSITIVE. Western longitudes are negative.
3. 03Read the local mean sidereal time; that is the number to set a right-ascension circle to.
4. 04Use the local apparent value instead if you are matching against apparent right ascensions from an almanac.
5. 05Read the meridian right ascension to see immediately what is culminating.
6. 06Ignore digits below about a second: the UTC-versus-UT1 mismatch is worth up to 0.9 s on its own.

The formula.

The expression is built in two parts. The term in D₀ carries sidereal time forward one whole day at a time, at 0.06570982441908 hours per day — that is the 3 minutes 56.6 seconds by which the sidereal clock gains on the solar clock. The term in H then advances it through the current day at 1.00273790935 sidereal hours per hour of Universal Time. The T² term is a small secular correction for precession. Adding longitude divided by fifteen converts Greenwich time to local time, at one hour per fifteen degrees.

Work through the default. For 2026 July 29 at 00:00:00 UTC the Julian Date is 2461250.5, so D₀ = D = 9705.5 and H = 0. Then 0.06570982441908 × 9705.5 = 637.7467008994 and the T² term contributes 0.0000018358, giving 644.4440772932 hours; reducing modulo 24 leaves 20.4440772932 hours, or 20h 26m 38.68s. For Nairobi at longitude +36.8219° the local value is 20.4440772932 + 36.8219⁄15 = 22.8988706265 hours, which is 22h 53m 55.93s.

The equation of the equinoxes on that date works out to +0.585 seconds: the nutation terms give Δψ = 0.000177199 hours, and multiplying by cos ε with ε = 23.4354178° gives 0.000162578 hours. Apparent sidereal time is that much later than mean.

THE INDEPENDENT CHECK. A completely different definition of the same quantity — the IAU 1982 expression of Aoki and colleagues, a rigorous single polynomial rather than a two-part approximation — is implemented alongside and cross-checked in the test suite. At the same instant it gives 20.444077285 hours against the USNO 20.4440772932, a difference of 3 × 10⁻⁵ seconds. Across nine epochs from 2000 to 2099 the two never differ by as much as a tenth of a second, well inside the USNO's own published 0.432-second bound. There is also a structural check: the IAU polynomial's constant term at J2000.0 is 280.46061837°, which is 18.697374558 hours, exactly twelve hours more than the USNO constant of 6.697374558. That twelve-hour gap is the noon-versus-midnight offset between the Julian Date epoch and the Universal Time day, and asserting it catches an entire class of half-day errors.

A UNIT TRAP WORTH NAMING. Two numbers describe how much shorter a sidereal day is, and they are not interchangeable. The sidereal clock gains 236.5554 seconds OF SIDEREAL TIME over one solar day — that is the D₀ coefficient times 3600. A sidereal day is 235.9095 seconds OF SOLAR TIME shorter than a solar day, since 86400 − 86164.0905 = 235.9095. The two differ by the factor 1.00273790935. The first version of this page's structural test asserted the solar figure against a sidereal measurement and failed by 0.65 seconds; nothing in the formula was wrong, the test's units were. Both are now asserted, with the conversion written out.

ROUNDING STAGE. Nothing is rounded part-way through; all arithmetic runs at forty significant digits and rounding happens once at the return boundary. The hours-minutes-seconds string is display formatting of the same unrounded value, and a test parses it back and confirms it agrees with the decimal output.

APPROXIMATION REGIME AND WHERE IT BREAKS. Valid across 2000 to 2100 at the accuracy quoted, and usable either side with degrading accuracy — at 2200 the two algorithms still track to within 5 seconds. The nutation series here has two terms and is good to a few milliseconds of time against the full IAU 2000A series. This is entirely adequate for setting circles, planning and drift-scan timing, and entirely inadequate for VLBI or microarcsecond astrometry.

INVALID DOMAIN. Gregorian dates only, with the correct leap rule enforced, so 29 February 2026 is refused and 29 February 2028 accepted. Hours must be 0 to 23, minutes and seconds 0 to 59, and longitude within ±180°, with exactly ±180 accepted (they are the same meridian and the calculator returns the same answer for both).

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 in this module as the second-authority 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.