Star Altitude and Azimuth Calculator
ANA›Life Services Authority›National Calculator Authority›Star Altitude and Azimuth Calculator
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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).
Observer Latitude (°)
Positive = North, Negative = South (-90 to 90)
Observer Longitude (°)
Positive = East, Negative = West (-180 to 180)
Date and Time (UTC)
Enter date and time in UTC
Right Ascension — Hours (0–23)
Right Ascension — Minutes (0–59)
Right Ascension — Seconds (0–59.99)
Orion's Rigel: RA = 05h 14m 32s, Dec = −8° 12′ 06″
Declination — Degrees (−90 to 90)
Declination — Arcminutes (0–59)
Declination — Arcseconds (0–59.99)
Negative declination: degrees field carries the sign
Calculate Results will appear here.
function staCalc() { var resultDiv = document.getElementById('sta-result');
// --- Read inputs --- var lat = parseFloat(document.getElementById('sta-lat').value); var lon = parseFloat(document.getElementById('sta-lon').value); var dtStr = document.getElementById('sta-datetime').value; var raH = parseFloat(document.getElementById('sta-ra-h').value); var raM = parseFloat(document.getElementById('sta-ra-m').value); var raS = parseFloat(document.getElementById('sta-ra-s').value); var decD = parseFloat(document.getElementById('sta-dec-d').value); var decAM= parseFloat(document.getElementById('sta-dec-m').value); var decAS= parseFloat(document.getElementById('sta-dec-s').value);
// --- Validation --- var errors = []; if (isNaN(lat) || lat 90) errors.push("Latitude must be between −90° and 90°."); if (isNaN(lon) || lon 180) errors.push("Longitude must be between −180° and 180°."); if (!dtStr) errors.push("Please enter a valid date and time."); if (isNaN(raH) || raH 23) errors.push("RA hours must be 0–23."); if (isNaN(raM) || raM 59) errors.push("RA minutes must be 0–59."); if (isNaN(raS) || raS = 60) errors.push("RA seconds must be 0–59.99."); if (isNaN(decD) || decD 90) errors.push("Declination degrees must be −90 to 90."); if (isNaN(decAM) || decAM 59) errors.push("Declination arcminutes must be 0–59."); if (isNaN(decAS) || decAS = 60) errors.push("Declination arcseconds must be 0–59.99.");
if (errors.length > 0) { resultDiv.innerHTML = '' + errors.join('') + ''; return; }
// --- Convert RA to decimal degrees --- var raDecimalHours = raH + raM / 60.0 + raS / 3600.0; var raDeg = raDecimalHours * 15.0; // 1 hour = 15°
// --- Convert Declination to decimal degrees --- // Sign is carried by decD; arcmin/arcsec always positive var decSign = (decD 180) H -= 360; // range [−180, 180]
// --- Convert to radians --- var latR = lat * Math.PI / 180.0; var decR = decDeg * Math.PI / 180.0; var HR = H * Math.PI / 180.0;
// --- Altitude (a) --- // sin(a) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H) var sinAlt = Math.sin(latR) * Math.sin(decR) + Math.cos(latR) * Math.cos(decR) * Math.cos(HR); sinAlt = Math.max(-1, Math.min(1, sinAlt)); var altRad = Math.asin(sinAlt); var altDeg = altRad * 180.0 / Math.PI;
// --- Azimuth (A) — measured from North, clockwise --- // cos(a)·sin(A) = cos(δ)·sin(H) // cos(a)·cos(A) = sin(δ)·cos(φ) − cos(δ)·cos(H)·sin(φ) var cosAlt = Math.cos(altRad); var sinAz, cosAz, azDeg; if (Math.abs(cosAlt) 0) { visibility = "Above the horizon ✓"; if (altDeg ' + 'Altitude' + fmt(altDeg,4) + '° (' + dms(altDeg) + ')' + 'Azimuth' + fmt(azDeg,4) + '° (' + compass + ')' + 'Hour Angle (H)' + fmt(H,4) + '°' + 'Local Sidereal Time' + fmt(LST/15,4) + ' h (' + fmt(LST,4) + '°)' + 'GMST' + fmt(GMST/15,4) + ' h' + 'Julian Date' + fmt(JD,5) + '' + 'RA (decimal)' + fmt(raDecimalHours,4) + ' h = ' + fmt(raDeg,4) + '°' + 'Declination (decimal)' + fmt(decDeg,4) + '°' + 'Visibility' + visibility + '' + ''; }
#### 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.
- Declination sign is set by the degrees field; arcminutes and arcseconds are always positive.
- Azimuth is measured from North, clockwise (standard astronomical convention).
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