Star Altitude and Azimuth Calculator
Calculate the altitude (elevation above horizon) and azimuth (compass bearing) of any star given your location, the date/time, and the star's equatorial coordinates (Right Ascension and Declination).
Formulas Used
1. Julian Date (JD) — Meeus, Ch. 7:
JD = ⌊365.25(Y+4716)⌋ + ⌊30.6001(M+1)⌋ + D + B − 1524.5
where B = 2 − A + ⌊A/4⌋, A = ⌊Y/100⌋ (Gregorian correction).
2. Greenwich Mean Sidereal Time (GMST) — Meeus Eq. 12.4:
T = (JD − 2451545.0) / 36525
GMST = 280.46061837 + 360.98564736629·(JD−2451545) + 0.000387933·T² − T³/38710000 (degrees)
3. Local Sidereal Time (LST):
LST = GMST + λ (observer longitude in degrees)
4. Hour Angle (H):
H = LST − α (Right Ascension in degrees, where α[°] = RA[h] × 15)
5. Altitude (a):
sin(a) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H)
6. Azimuth (A) — measured from North, clockwise:
sin(A) = cos(δ)·sin(H) / cos(a)
cos(A) = [sin(δ)·cos(φ) − cos(δ)·cos(H)·sin(φ)] / cos(a)
A = atan2(sin A, cos A), normalized to [0°, 360°)
where φ = observer latitude, δ = star declination, H = hour angle.
Assumptions & References
- All date/time input is treated as UTC (no timezone conversion).
- Coordinates are J2000.0 equatorial (ICRS); precession and proper motion are not applied — error is <1° for dates within ~50 years of 2000.
- Atmospheric refraction is not applied; near the horizon (alt < 5°) the true apparent altitude will be slightly higher than calculated.
- The GMST formula is accurate to ~0.1 s over the period 1900–2100 (Meeus, "Astronomical Algorithms", 2nd ed., Ch. 12).
- Julian Date algorithm: Meeus, Ch. 7 (valid for all Gregorian dates).
- Altitude/Azimuth transformation: Meeus, Ch. 13; also Montenbruck & Pfleger, "Astronomy on the Personal Computer".
- Right Ascension is entered in hours, minutes, seconds (0h–23h 59m 59.99s).
- Declination sign is set by the degrees field; arcminutes and arcseconds are always positive.
- Azimuth is measured from North, clockwise (standard astronomical convention).