USNO publish Michael Richmond’s calculator for local apparent sidereal time.
Sidereal time is the hour angle of the vernal equinox, the ascending node of the ecliptic on the celestial equator. The daily motion of this point provides a measure of the rotation of the Earth with respect to the stars, rather than the Sun. Local mean sidereal time is computed from the current Greenwich Mean Sidereal Time plus an input offset in longitude (converted to a sidereal offset by the ratio 1.00273790935 of the mean solar day to the mean sidereal day.) Applying the equation of equinoxes, or nutation of the mean pole of the Earth from mean to true position, yields local apparent sidereal time. Astronomers use local sidereal time because it corresponds to the coordinate right ascension of a celestial body that is presently on the local meridian.