Sidereal Time Calculator
This sidereal time calculator gives the Greenwich mean sidereal time (GMST), the apparent sidereal time (GAST) and the local sidereal time for your longitude. On 10 October 2026 at 21:00 UT the local mean sidereal time at 13.4° east is 23:11:30. It uses the formulas of the U.S. Naval Observatory.
Example: Year 2,026 · Month 10 · Day 10 · Hour (UT) 21 · Minute (UT) 0 · Longitude 13.4 ° → Local sidereal time: Local mean sidereal time 23:11:30.2. Source: U.S. Naval Observatory, Astronomical Applications: Computing Approximate Sidereal Time – GMST = 6.697375 + 0.065709824279·D_UT + 1.0027379·H + 0.0000258·T² (h), GAST = GMST + eqeq, local sidereal time = Greenwich + longitude/15; max. error 0.432 s for 2000–2100 (read 10.10.2026). Updated: .
How it is calculated
Greenwich mean sidereal time GMST = 6.697375 + 0.065709824279 · D + 1.0027379 · H + 0.0000258 · T² hours, reduced to 0–24 h. D is the number of days from 1 January 2000, 12h UT (Julian Date 2451545.0) to the previous midnight, H the hours of Universal Time since that midnight and T = D ÷ 36525 the centuries since 2000. This is the formula of the U.S. Naval Observatory (USNO). For the local sidereal time the USNO adds the longitude divided by 15 (east positive).
Greenwich sidereal time at 0h UT
| Date (0h UT) | Julian Date | GMST |
|---|---|---|
| 2000-01-01 | 2451544.5 | 06:39:52.3 |
| 2010-01-01 | 2455197.5 | 06:42:09.0 |
| 2020-01-01 | 2458849.5 | 06:40:29.2 |
| 2024-03-20 | 2460389.5 | 11:52:04.5 |
| 2025-06-21 | 2460847.5 | 17:57:46.9 |
| 2026-01-01 | 2461041.5 | 06:42:38.6 |
| 2026-10-10 | 2461323.5 | 01:14:27.2 |
| 2030-01-01 | 2462502.5 | 06:42:46.0 |
The USNO also gives a shorter formula for 0h UT, GMST = 18.697375 + 24.065709824279 · D; it agrees with the table to within 0.1 s. A Julian Date at midnight always ends in .5, because the count starts at noon.
From Greenwich to your longitude
Example: 10 October 2026, 21:00 UT. GMST is 22:17:54.2. At 13.4° east add 13.4 ÷ 15 = 0.893 h (53 min 36 s): local mean sidereal time 23:11:30.2. At 74.0° west subtract 4.933 h: 17:21:54.2.
- Apparent sidereal time (GAST) adds the equation of the equinoxes, at most about 1.1 s; the USNO skips it when an error of about 1 second does not matter.
- Enter Universal Time. Local clock time first has to be converted to UT with your time-zone offset.
- From the factor 1.0027379 follows the length of a sidereal day: 24 h ÷ 1.0027379 ≈ 23 h 56 min 4 s of solar time (calculated).
The day number and the Julian Date of any date are also shown by day of the year; where the Sun stands at a given moment shows the sun position calculator.
Frequently asked questions
How do you calculate local sidereal time?
Compute the Greenwich sidereal time with the USNO formula and add your longitude ÷ 15 (east positive, west negative). Results outside 0–24 h are wrapped around.
What is the difference between mean and apparent sidereal time?
Apparent sidereal time (GAST) includes the equation of the equinoxes, a correction of at most about 1.1 seconds caused by nutation. Mean sidereal time (GMST) leaves it out.
Why is a sidereal day shorter than 24 hours?
Sidereal time runs 1.0027379 times as fast as Universal Time in the USNO formula. 24 h ÷ 1.0027379 gives about 23 h 56 min 4 s.
Do I enter local time or UT?
Universal Time (UT/UTC). The USNO notes that UTC can be used instead of UT1 if an error of about one second is acceptable.
How accurate is the calculator?
For 2000 to 2100 the USNO gives a maximum error of 0.432 s for GAST. Dates from 1900 are accepted, but the accuracy statement covers 2000–2100.
Sources and legal basis
- U.S. Naval Observatory, Astronomical Applications: Computing Approximate Sidereal Time – GMST = 6.697375 + 0.065709824279·D_UT + 1.0027379·H + 0.0000258·T² (h), GAST = GMST + eqeq, local sidereal time = Greenwich + longitude/15; max. error 0.432 s for 2000–2100 (read 10.10.2026)
- U.S. Naval Observatory: Julian Date Converter – JD counts days since noon UT, 1 January 4713 BC; 0h UT1 = fraction .5 (read 10.10.2026)
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