Solar Elevation and Azimuth

Solar elevation and direction

Elevation is measured upward from the horizon. Azimuth increases clockwise from north, with east at 90°, south at 180° and west at 270°. The calculation transforms solar coordinates into the local horizontal frame.

Choosing the inputs

True solar time is not civil clock time. Solar noon is defined as 12. Obtain declination from a verified source for the observation time. At an equinox, solar noon at latitude 40° north gives elevation 50° and azimuth 180°. This tool does not derive inputs from a date, longitude or time zone. Atmospheric refraction and obstructions are excluded. When the sun is directly overhead, a unique azimuth cannot be assigned.

Compare morning and afternoon

For a teaching example, set latitude and declination to zero and true solar time to 8. The hour angle is 15 × (8 − 12) = −60°. The elevation relation reduces to sin α = cos 60° = 0.5. Elevation is 30° and azimuth is 90°, due east. With the same inputs at solar time 16, elevation is again 30° and azimuth is 270°, due west. These are geometric examples, not positions calculated from a calendar date.

Do not treat clock notation as a decimal number. For example, 8 hours 30 minutes is 8.5 hours, not 8.30 hours. Check the latitude sign against the hemisphere and the declination sign against the source definition. Entering longitude in either field does not give a valid position.

Solar elevation is neither panel tilt nor the incidence angle on a surface. An inclined surface also requires its orientation and tilt. Ensure that compared azimuths use the same north reference. Terrain, buildings and horizon obstructions may hide the Sun even when its geometric elevation is positive. This result alone is not a shading or energy yield calculation.

Frequently asked questions

How do you calculate solar elevation angle?

At example latitude 40° north, declination 0° and true solar time 12, the solar position equation gives a geometric solar elevation of 50°. True solar time differs from civil clock time, and apparent elevation can differ because atmospheric refraction and surrounding obstructions are excluded from this geometric calculation.

Calculate with these values