The Solar Elevation Angle is the angle between the sun's rays and the horizontal plane, ranging from 0° (sun at horizon) to 90° (sun directly overhead). It is a crucial parameter in solar energy, architecture, photography planning, and agriculture.
The Solar Azimuth Angle is the compass direction of the sun's horizontal projection. North = 0°, East = 90°, South = 180°, West = 270°, measured clockwise from North.
δ = 23.45° × sin(360° × (284 + N) / 365) (Cooper's equation for declination)
sin(h) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(ω)
cos(A) = (sin(δ) - sin(h)sin(φ)) / (cos(h)cos(φ))
Where: N = day of year, φ = latitude, δ = declination, ω = hour angle, h = elevation, A = azimuth
1. Enter the date and local time, or click "Use Current Time" to auto-fill.
2. Enter the latitude and longitude of your observation location (decimal degrees). You can also click a city preset.
3. Select the correct timezone (UTC offset).
4. Click "Calculate Sun Position" to get the elevation, azimuth, sunrise, and sunset times.
5. The visualization above shows the sun's position in the sky.
A negative solar elevation means the sun is below the horizon — it has either not risen yet or has already set. A larger negative value means the sun is deeper below the horizon.
This tool uses standard astronomical formulas with an accuracy of about ±5 minutes. Actual times are affected by altitude, terrain, and atmospheric refraction (which typically advances sunrise and delays sunset by about 2-3 minutes).
The optimal tilt is usually equal to your local latitude. For winter optimization, add 10-15°; for summer, subtract 10-15°. Use this tool to understand seasonal sun elevation changes.
Solar noon (maximum elevation) doesn't always fall at 12:00 clock time because of the longitude offset from the time zone meridian and the "equation of time" — a difference between solar time and clock time caused by Earth's elliptical orbit and axial tilt, with deviations up to ±16 minutes throughout the year.