Polaris Observation Calculator
Determine the true azimuth of a survey line from a hour-angle observation of Polaris — no elongation timing required.
Field aid, not a certified result. Verify against a known control point where possible, and use current Polaris coordinates from an up-to-date star almanac for best accuracy — the values below are an editable approximation.
Observation time
Station position
Polaris coordinates from current almanac
Field observation
Fill in every field above to compute the true azimuth.
Brass = Polaris · Line = line azimuth
Show calculation steps
| Julian Date (UT) | – |
| Greenwich Mean Sidereal Time | – |
| Local Sidereal Time | – |
| Local Hour Angle of Polaris | – |
How the Polaris observation method works
Quick answer: Because Polaris sits less than a degree from the celestial pole, its azimuth is always close to true north but not exactly on it. Observing it at any known time — not just at elongation — lets you compute its exact azimuth from your latitude, longitude, and the star’s right ascension and declination, then transfer that azimuth to your survey line using a measured horizontal angle.
The method rests on the hour angle of Polaris at the moment of observation: LHA = Local Sidereal Time − Right Ascension. Local Sidereal Time comes from the Greenwich Sidereal Time at that instant (derived from the date and UT) plus your longitude. Once the hour angle is known, a standard spherical-astronomy formula converts hour angle, declination, and latitude into Polaris’s azimuth — the direction you’d have to point to see it, measured clockwise from true north.
In the field, you measure a horizontal clockwise angle from your reference line to Polaris with a total station or theodolite. Subtracting that angle from Polaris’s computed azimuth gives the true azimuth of your line — a full azimuth determination without waiting for elongation, when Polaris briefly stops moving sideways and is easiest to time precisely.
Why the Polaris coordinates need updating
Because Polaris is so close to the celestial pole, ordinary precession — the slow wobble of Earth’s axis — moves its right ascension noticeably from year to year, even though its declination barely changes. Surveying almanacs republish updated Polaris coordinates regularly for exactly this reason; plugging in stale values from years ago will shift your computed azimuth.
Frequently asked questions
Why not just assume Polaris is due north?
Polaris is about 0.6–0.7° from the true celestial pole, so its azimuth swings slightly east and west of north over each sidereal day. For rough work that’s negligible, but for a precise azimuth determination it needs to be calculated, not assumed.
Do I have to observe at elongation?
No. Elongation (when Polaris appears to pause sideways) is convenient because timing errors matter less there, but this hour-angle method works at any time of night as long as you know the exact observation time and Polaris’s current coordinates.
How accurate does my observation time need to be?
Very. Because sidereal time advances about 15 arcseconds of hour angle per second of clock time, even a few seconds of timing error can shift the computed azimuth by a measurable amount — use a synchronized, accurate time source.
Where do I get current Polaris right ascension and declination?
From a current star almanac, ephemeris, or surveying software with an updated star catalog. Values drift measurably year to year due to precession, so figures from several years ago will introduce error.
What sign convention should I use for longitude?
East longitudes are positive and west longitudes are negative in this calculator, which is the convention needed to correctly compute Local Sidereal Time from Greenwich Sidereal Time.
Does this replace a licensed survey control check?
No. This is a field calculation aid. Always verify azimuth results against known control where available and follow the standards required for your jurisdiction and project.
