Sidereal Time Calculator (local & Greenwich sidereal time from date, time, longitude)

Understanding the sidereal time calculator — concept and principle

This calculator converts a local date, clock time, time zone and longitude into Greenwich mean sidereal time and local mean sidereal time, and the right ascension currently on your meridian. Amateur astronomers use it to know which stars and objects are well placed and to set up telescopes.

How it is calculated

UT = local time − time-zone offset

GMST = 6.697375 + 0.065709824279 D₀ + 1.0027379 H + 0.0000258 T² hours (mod 24)

LMST = GMST + east longitude ÷ 15

Right ascension on the meridian (°) = LMST × 15

• D₀ is the days from 2000 Jan 1, 12h UT to the previous 0h UT, H the UT hours, T the centuries since 2000 (USNO approximation).

The principle

Clocks follow the Sun, but the stars return to the same place about 3 minutes 56 seconds earlier each day, because Earth also moves along its orbit. A sidereal day is about 23 h 56 min 4 s. Sidereal time measures Earth's rotation against the stars, and the local sidereal time equals the right ascension of stars crossing your meridian. Adding the longitude shifts Greenwich time to your location, at 15° per hour.

Worked example

Default inputs: 10 Nov 2026, 21:00:00 local, UTC+9, longitude 126.978° E (Seoul).

1. UT = 21:00 − 9 h = 12:00, on Tue, Nov 10, 2026.
2. The USNO formula gives GMST = 15:18:39.
3. LMST = 15:18:39 + 126.978 ÷ 15 h (8 h 27 min 55 s) = 23:46:33.
4. Right ascension on the meridian = 356.639°.

How to read the result

Objects with right ascension close to the local sidereal time are crossing your meridian and are highest in the sky. At about 23:47 LST, objects near RA 0 h, such as the Andromeda region, are well placed. Each hour of clock time adds slightly more than an hour of sidereal time.

Common mistakes

• Forgetting daylight-saving time in the time-zone offset.
• Using west longitude as positive.
• Confusing sidereal time with solar time.

Frequently asked questions

Why is a sidereal day shorter than a solar day?

Earth moves along its orbit, so it must turn a little more each day to face the Sun again.

What is right ascension?

The celestial equivalent of longitude, measured in hours eastward.

How accurate is this formula?

About 0.1 s for 2000–2100, apart from the up to about 1 s difference between mean and apparent time.

Why use local sidereal time?

It tells you directly which right ascension is on your meridian.

Sources: U.S. Naval Observatory, Astronomical Applications Department, "Computing Approximate Sidereal Time"