This sidereal time calculator is an essential tool in astronomy that helps determine the position of celestial objects relative to Earth’s rotation.
It calculates time based on Earth’s rotation concerning distant stars, rather than the Sun. This distinction is crucial for astronomers and stargazers who need to accurately locate and track celestial bodies.
If you want to observe a particular star at its highest point in the sky (culmination), you would use our local sidereal time calculator to determine when this occurs. For instance, if the star Vega has a right ascension of 18h 36m 56.3s, it will culminate when the local sidereal time matches this value.
Sidereal Time Calculator
| Date | Time (UT) | Location | Longitude | LST |
|---|---|---|---|---|
| 2024-09-08 | 00:00 | London, UK | 0° | 23h 22m 46s |
| 2024-09-08 | 06:00 | Tokyo, Japan | 139.75°E | 11h 01m 31s |
| 2024-09-08 | 12:00 | New York, USA | 74°W | 6h 26m 57s |
| 2024-09-08 | 18:00 | Sydney, AU | 151.2°E | 5h 54m 12s |
| 2024-09-09 | 00:00 | Rio, Brazil | 43.2°W | 20h 20m 03s |
| 2024-09-08 | 03:00 | Cairo, Egypt | 31.25°E | 22h 15m 00s |
| 2024-09-08 | 09:00 | Moscow, Russia | 37.62°E | 14h 45m 30s |
| 2024-09-08 | 15:00 | Los Angeles, USA | 118.25°W | 3h 12m 45s |
| 2024-09-08 | 21:00 | New Delhi, India | 77.1°E | 17h 30m 15s |
| 2024-09-08 | 12:00 | Cape Town, South Africa | 18.42°E | 6h 50m 00s |
| 2024-09-08 | 18:00 | Beijing, China | 116.4°E | 11h 58m 30s |
| 2024-09-08 | 00:00 | Buenos Aires, Argentina | 58.42°W | 20h 10m 00s |
| 2024-09-08 | 06:00 | Bangkok, Thailand | 100.5°E | 11h 25m 30s |
| 2024-09-08 | 12:00 | Berlin, Germany | 13.41°E | 6h 45m 00s |
| 2024-09-08 | 18:00 | Mexico City, Mexico | 99.13°W | 4h 00m 15s |
Sidereal Time Formula
The formula for calculating sidereal time is:
LST = GST + λWhere:
- LST is Local Sidereal Time
- GST is Greenwich Sidereal Time
- λ (lambda) is the observer’s longitude in time units (positive for east, negative for west)
The GST is 14h 30m 00s and you’re observing from a location with longitude 45° West (which is -3h in time units), the LST would be:
LST = 14h 30m 00s + (-3h) = 11h 30m 00sHow do you calculate sidereal time?
- Determine the Julian Date (JD) for the desired observation time.
- Calculate the number of days since J2000.0 (JD – 2451545.0).
- Compute the Greenwich Mean Sidereal Time (GMST) at 0h UT: GMST = 18.697374558 + 24.06570982441908 * D Where D is the number of days since J2000.0.
- Apply the equation of the equinoxes to get the Greenwich Apparent Sidereal Time (GAST).
- Convert GAST to Local Sidereal Time by adding the observer’s longitude.
Let’s calculate the LST for January 1, 2024, at 00:00 UT, for an observer at 30° East longitude:
- JD for 2024-01-01 00:00 UT = 2460310.5
- D = 2460310.5 – 2451545.0 = 8765.5 days
- GMST = 18.697374558 + 24.06570982441908 * 8765.5 = 6.6456 hours
- Assuming negligible equation of equinoxes, GAST ≈ GMST
- LST = 6.6456 + (30° / 15°/hour) = 8.6456 hours or 8h 38m 44s
Local sidereal time formula
The formula for Local Sidereal Time (LST) can be expressed as:
LST = GMST + λ + ΔT + ΔΨ cos(ε)Where:
- GMST is Greenwich Mean Sidereal Time
- λ is the observer’s longitude (positive east, negative west)
- ΔT is the difference between UT1 and UTC
- ΔΨ is the nutation in longitude
- ε is the true obliquity of the ecliptic
Assuming GMST = 15h 30m 00s, λ = 45°E, and neglecting the small corrections (ΔT and nutation terms):
LST = 15h 30m 00s + (45° / 15°/hour) = 18h 30m 00sRelated Tools:
