Where the sun rises
The sun rises due east and sets due west only around the equinoxes, in March and September. In summer it rises north of east and sets north of west; in winter it rises south of east and sets south of west (in the Northern Hemisphere). How far it swings depends on your latitude.
The formula
The azimuth is the compass bearing measured clockwise from true north. At sunrise the sun’s center is about 0.833° below the horizon because of refraction and the size of its disk, so the calculator uses:
cos A = (sin δ − sin φ × sin(−0.833°)) ÷ (cos φ × cos(−0.833°))
where φ is the latitude and δ the solar declination, which varies from −23.44° to +23.44° through the year. Sunset is at 360° − A.
How far the direction swings
At the solstices, the sunrise moves this far from due east:
| Place | Latitude | Offset at the solstices |
|---|---|---|
| Equator | 0° | 23.4° |
| Miami | 25.8° N | 26.7° |
| New York | 40.7° N | 32.5° |
| Paris | 48.9° N | 38.4° |
| Anchorage | 61.2° N | about 58° |
Above the Arctic Circle the sun does not rise or set at all for part of the year; the calculator reports polar night or midnight sun.
Example
In New York on November 4, the solar declination is about −16.2°. The sun rises at an azimuth of about 110.8°, roughly 21° south of east, and sets at about 249°.
Uses
- Photography: plan sunrise or sunset shots aligned with a street, a bridge or a mountain.
- Architecture and gardening: know which windows and beds get morning or evening sun in each season.
- Alignments: “Manhattanhenge” happens in late May and mid-July, when the setting sun lines up with Manhattan’s street grid, about 29° north of west. Stonehenge aligns with the midsummer sunrise and midwinter sunset.
Notes
The results use true north. A magnetic compass differs by the local magnetic declination, about 13° west in New York and nearly zero in Paris. Hills on the horizon delay sunrise and shift it slightly toward the south in the morning.