| Date (UTC) | Time (UTC) | Longitude (°) | RA (HH:MM:SS) | LST (HH:MM:SS) | Hour Angle (±HH:MM:SS) |
|---|---|---|---|---|---|
| 2026-01-12 | 00:00:00 | 0.00 | 05:34:32 | 7:26:01 |
+01:51:29 |
| 2026-06-01 | 21:00:00 | 74.35 | 16:29:24 | 8:38:49 |
+02:09:25 |
| 2026-03-20 | 12:00:00 | -122.42 | 10:12:45 | 5:42:27 |
+05:29:42 |
| 2026-10-10 | 03:30:00 | 31.24 | 02:31:49 | 6:49:59 |
+04:18:10 |
| 2026-12-15 | 18:15:00 | 10.00 | 23:59:59 | 0:32:40 |
+00:32:41 |
The hour angle (H) measures how far an object is from the local meridian, expressed in time units (hours). It is defined by:
- H = LST − RA
When you provide date/time and longitude, the calculator estimates Greenwich Mean Sidereal Time (GMST), then converts it to Local Sidereal Time (LST):
- LST = GMST + (longitude / 15) (longitude in degrees, converted to hours)
- All sidereal-time values are wrapped into a 0–24 hour range.
The hour angle can be shown as 0–24 hours or as a signed value within −12 to +12 hours, which many observers prefer.
- Select a method: use date/time and longitude if you do not know LST, or choose LST directly if you already have it.
- Enter the object’s right ascension. Choose the input format (HH:MM:SS, decimal hours, or degrees).
- If using date/time: enter the date, time, and your longitude. If you enter local time, provide the offset from UTC.
- Choose the hour-angle range (−12..+12 or 0..24), then press Calculate.
- After calculation, use Download CSV or Download PDF to save the result.
1) What hour angle represents
Hour angle tells how far a celestial object is from your local meridian. It is measured in time, where one hour equals fifteen degrees of rotation. Negative hour angle means the target is east of the meridian and has not culminated yet. Positive hour angle means it is west and already passed transit.
2) Right ascension as a sky coordinate
Right ascension works like longitude on the celestial sphere but uses hours, minutes, and seconds. The scale wraps at twenty four hours. Converting is simple: degrees divided by fifteen gives hours. This calculator accepts RA in HH:MM:SS, decimal hours, or degrees, then normalizes the value for clean results.
3) Local sidereal time links your location to the stars
Local sidereal time is the right ascension currently on your meridian. When LST equals a target’s RA, the target is transiting, so its hour angle is near zero. Because Earth rotates relative to the stars, sidereal time advances about four minutes per solar day compared to civil time. This makes LST a powerful planning tool.
4) Core relationship used in this calculator
The core computation is H = LST − RA. This tool can display H as a signed range from minus twelve to plus twelve hours, or as a wrapped value from zero to twenty four hours. The signed form is helpful when you want an east or west indicator, while the wrapped form matches some catalogs and telescope controllers.
5) Converting UTC to sidereal time
If you do not know LST, the calculator estimates Greenwich Mean Sidereal Time from the Julian Date. GMST is then shifted by observer longitude to obtain LST. East longitudes add time; west longitudes subtract time. Using UTC avoids daylight saving confusion, but a local time option is included with a numeric offset.
6) Why longitude matters
Two observers at different longitudes see the same star transit at different clock times. A fifteen degree longitude change corresponds to one hour of sidereal time shift. Entering longitude accurately improves hour angle. For best practice, use a value within the range minus one hundred eighty to plus one hundred eighty degrees and keep sign conventions consistent.
7) How observers use hour angle
Hour angle supports pointing models, mount alignment checks, and deciding when to image. Large absolute hour angle often means the target is near the horizon, where refraction and extinction can increase. Many observatories set constraints such as observing within two to four hours of transit for higher signal and steadier tracking.
8) Accuracy and verification tips
Small differences can appear between calculators because models may use mean or apparent sidereal time, different Earth rotation terms, or rounding choices. For typical observing plans, the results here are practical. If you need higher precision, compare against a trusted almanac and keep the same epoch, time standard, and coordinate format across all tools.
1) What does a negative hour angle mean?
It means the object is east of the local meridian and has not reached transit yet. Many mounts treat negative values as “before culmination” for planning and alignment checks.
2) Should I use UTC or local time?
UTC is recommended because it avoids daylight saving changes. If you use local time, enter your offset from UTC so the calculator can convert to UTC internally.
3) Why is hour angle measured in hours?
Earth rotates 360 degrees in about 24 sidereal hours. That makes 15 degrees per hour, so time units directly represent sky rotation and are convenient for pointing.
4) How do I convert RA from degrees to hours?
Divide degrees by 15 to get hours. For example, 45° becomes 3 hours. The calculator can also accept degrees directly and convert automatically.
5) What longitude sign should I use?
Use east as positive and west as negative. For example, Karachi is positive, while California is negative. Staying consistent prevents LST shifts in the wrong direction.
6) Why do my results differ from another site?
Different tools may use slightly different GMST formulas, rounding, or apparent sidereal time corrections. Small differences are normal, especially near the minute or second level.
7) When is hour angle closest to zero?
Hour angle is near zero when the target is transiting your local meridian. That is typically the best time for high elevation, reduced air mass, and steady tracking.