Sun Angle Calculator — Solar Altitude & Azimuth

Sun angle is the sun’s elevation angle above the horizon at a given location and time, also called solar altitude. A value of 0° means the sun is exactly at the horizon (rising/setting), 90° means directly overhead (zenith).

With the formula sin α = sin φ · sin δ + cos φ · cos δ · cos H, where φ is latitude, δ is solar declination, and H is the hour angle. This calculator computes δ from the day-of-year number and H from your local solar time.

Solar azimuth is the compass direction of the sun’s position, measured clockwise from north: 0° north, 90° east, 180° south, 270° west. At sunrise the azimuth is near 90° (east) and at sunset near 270° (west).

From the formula cos H0 = −tan φ · tan δ which gives the hour angle when the sun is at the horizon, then converted to local civil time using the equation of time and longitude correction against the timezone meridian. Results are accurate within a few minutes for non-polar locations.

The equation of time is the difference between true solar time and mean solar time, ranging −14 to +16 minutes through the year, caused by Earth’s axial tilt and elliptical orbit. This calculator uses the approximation B = 360°·(N−81)/364.

Solar noon is when the sun reaches its highest point, due south (northern hemisphere) or due north (southern hemisphere). It is almost never exactly 12:00 because of the equation of time and your longitude position within the timezone; in Jakarta, for example, solar noon

Because the sun’s maximum declination is only ±23.44° while Jakarta is at latitude −6.2°, so the smallest distance from zenith is 29.64° and maximum altitude is 60.36°, occurring around June 21. The sun is directly at zenith only possible between the tropics

Shadow length = object height / tan(altitude). Example: a 2-meter pole at 45° altitude casts exactly a 2-meter shadow, and shadow direction is always opposite the sun’s azimuth (azimuth + 180°).

No. Enter the UTC offset in effect at your location on the selected date. If your area uses DST, manually select the summer offset, e.g. UTC+2 for Paris in July.

The model used is a standard astronomical approximation with errors under 0.5° for altitude/azimuth and a few minutes for sunrise/sunset at non-polar latitudes. Atmospheric refraction (about 0.57° at the horizon) is not modeled, so rise/set times

A sun angle calculator computes the sun’s position in the sky (altitude, azimuth, sunrise/sunset) for photography, architecture, and navigation, while a solar panel calculator computes power needs and panel counts. They complement each other

Because solar declination changes through the year, the rising point shifts north or south of true east. Exactly 90° only occurs at equinox; in the northern hemisphere the northernmost rising point occurs at the summer solstice.

Yes, with a caveat: when cos H0 is outside the −1 to 1 range, there is no sunrise/sunset that day (midnight sun or polar night) and the calculator shows this explicitly along with a day length of 24 or 0 hours.

Day length is the duration of daylight from sunrise to sunset, calculated as 2·H0/15 hours with H0 from cos H0 = −tan φ · tan δ. At the equator it is always about 12 hours year-round.