Sidereal Time Calculator
Calculate Greenwich Mean Sidereal Time (GMST) and Local Sidereal Time (LST) for any date, time, and longitude.
Results will appear here.
Formulas Used
Julian Date:
JD = INT(365.25(Y+4716)) + INT(30.6001(M+1)) + D + B − 1524.5 + UT/24
where B = 2 − A + INT(A/4), A = INT(Y/100) (Gregorian calendar correction)
Julian Centuries from J2000.0:
T = (JD − 2451545.0) / 36525
Greenwich Mean Sidereal Time (GMST) at 0h UT:
GMST₀ = 24110.54841 + 8640184.812866·T₀ + 0.093104·T₀² − 6.2×10⁻⁶·T₀³ (seconds)
where T₀ is T evaluated at 0h UT of the given day.
GMST at observation time:
GMST = GMST₀ + UT × 1.00273790935 (sidereal seconds per solar second)
Local Sidereal Time (LST):
LST = GMST + λ / 15 (hours)
where λ is the observer's longitude in degrees (East positive).
Assumptions & References
- All date/time inputs are in UTC.
- Longitude is positive East, negative West (range −180° to +180°).
- The Julian Date algorithm is valid for all Gregorian calendar dates (post 1582-10-15).
- GMST formula is the IAU standard from Meeus, J. — Astronomical Algorithms, 2nd ed. (1998), Ch. 12.
- The factor 1.00273790935 converts mean solar seconds to mean sidereal seconds.
- This calculator computes Mean Sidereal Time; it does not apply the equation of the equinoxes needed for Apparent Sidereal Time (nutation correction ≈ ±1 s).
- Accuracy is sufficient for most observational astronomy purposes (error < 0.1 s over the period 1900–2100).