How this calculator works
Sidereal time is the hour angle of the vernal equinox, so a sidereal clock tells you which part of the sky is overhead. Greenwich mean sidereal time is computed from the Julian date with a standard polynomial. Apparent sidereal time adds the equation of the equinoxes, a small correction from the nutation of the Earth's axis. Local values add the longitude, which is positive to the east of Greenwich.
Formula
JD = day number + 1721424.5 + (hour + minute/60)/24. With d = JD - 2451545 and T = d/36525, GMST in degrees = 280.46061837 + 360.98564736629 d + 0.000387933 T^2 - T^3/38710000, reduced modulo 360. GAST = GMST + equation of the equinoxes. LMST = GMST + longitude/15 and LAST = GAST + longitude/15, with all times reduced modulo 24 hours.
Worked example
At 0h UTC on 1987-04-10 the formula gives GMST 13h 10m 46.37s, matching the worked example in Meeus, Astronomical Algorithms. At 0h UTC on 2026-11-01 in Toronto, longitude -75.6972, local mean sidereal time is about 21h 38m 24s.
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Frequently asked questions
Why is a sidereal day shorter than a solar day?
The Earth rotates once against the distant stars in about 23 hours 56 minutes 4 seconds. It must turn a little further to bring the sun back to the same place because it has also moved along its orbit. Sidereal time therefore gains about 3 minutes 56 seconds a day against civil time.
What is the difference between mean and apparent sidereal time?
Mean sidereal time uses a smooth model of the Earth's rotation. Apparent sidereal time also includes nutation, the small wobble of the axis, through the equation of the equinoxes. The difference is normally less than about 1.2 seconds of time.
How accurate is this calculator?
It uses the low-precision nutation series, which is accurate to well under an arcsecond and therefore to a small fraction of a second of time. The main limitation is that UT1 can differ from UTC by up to 0.9 seconds, which this page does not apply. For aiming a telescope at a moving object, use an almanac or planetarium software.
Why does longitude shift local sidereal time?
Local sidereal time is the hour angle at your meridian. Every 15 degrees of longitude corresponds to one hour of sidereal time, so moving 15 degrees east adds one hour and moving west subtracts it.