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Find sunrise, sunset, solar noon, and day length for any city or coordinates.
Sunrise is the moment the upper edge of the Sun first appears above the horizon, calculated from the observer's geographic coordinates and the date using solar geometry equations.
| Event | Date | Day Length |
|---|---|---|
| Summer Solstice (N. Hem) | June 20-21 | ~16h 00m (NYC) |
| Winter Solstice (N. Hem) | Dec 21-22 | ~9h 15m (NYC) |
| Spring Equinox | Mar 19-21 | ~12h 00m |
| Autumn Equinox | Sep 22-24 | ~12h 00m |
Formula
cos(HA) = [cos(90.833°) − sin(lat) × sin(dec)] ÷ [cos(lat) × cos(dec)] | Sunrise = Solar Noon − (HA × 4 min/°)HA = Hour Angle — degrees the Sun must travel from solar noon to the horizon
lat = observer latitude in degrees (positive = North)
dec = solar declination — the Sun's angular distance north or south of the equator
90.833° = accounts for atmospheric refraction and the Sun's apparent radius
Worked Example
New York (40.71°N), June 21
Did you know? The equation of time — the difference between true solar time and clock time — varies by up to ±16 minutes throughout the year. This is why solar noon rarely falls at exactly 12:00 PM. The effect is caused by Earth's elliptical orbit and its 23.5° axial tilt.
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