Equatorial to Horizontal Coordinates
Convert a supplied equatorial position and local sidereal time to geometric altitude and azimuth.
Calculate locally
No account, API or uploaded inputs. All calculations run in this browser.
Worked example
At latitude 45° N, declination 0°, right ascension 0 h and local sidereal time 0 h, the object is on the southern meridian: altitude 45°, azimuth 180°. Six sidereal hours later it reaches the western geometric horizon.
Method and units
Hour angle H = 15 × (local sidereal hours − right ascension hours). Rotate the unit direction into east, north and up components. Altitude = atan2(up, horizontal length); azimuth = atan2(east, north), wrapped to 0–360°. North is 0°, east 90°.
What this result means
Use right ascension, declination and sidereal time with compatible equinox conventions; the local mean sidereal tool is suitable with matching mean-of-date coordinates. No date/longitude lookup, refraction, precession, aberration or topocentric parallax is applied. Azimuth is Undefined at zenith/nadir and geographic poles. Negative altitude means below the geometric horizon.