Sunrise/Sunset Calculator

Earth's axis is tilted 23.5 degrees relative to its orbital plane. As Earth orbits the Sun, this tilt causes the Sun to appear higher in the sky (and visible for longer) in summer and lower (visible for less time) in winter. At the equator, day length is always close to 12 hours. At higher latitudes, the seasonal variation becomes more extreme — up to continuous daylight or darkness at the poles.

These are three levels of twilight defined by how far below the horizon the Sun is. Civil twilight: Sun 0-6 degrees below horizon (bright enough for outdoor activities without artificial light). Nautical twilight: Sun 6-12 degrees below (bright enough to see the horizon at sea). Astronomical twilight: Sun 12-18 degrees below (dark enough for most astronomical observations). True night begins when the Sun is more than 18 degrees below the horizon.

The midnight sun is the phenomenon where the Sun does not set for a full 24-hour period. It occurs above the Arctic Circle (66.5 degrees N) around the summer solstice and above the Antarctic Circle (66.5 degrees S) around the winter solstice. The number of days with midnight sun increases with latitude, reaching 6 months of continuous daylight at the poles.

The equinoxes give close to 12 hours of daylight but not exactly. This is because: (1) The calculator counts sunrise/sunset when the top edge of the Sun is at the horizon (correcting for the Sun's angular radius of 0.27 degrees). (2) Atmospheric refraction bends sunlight by about 0.57 degrees at the horizon, allowing the Sun to be seen briefly before it actually rises geometrically. These two effects combined add about 10-14 minutes of extra daylight near the equinoxes.

The analemma is the figure-8 pattern traced by the Sun's position in the sky at the same clock time each day throughout the year. It reflects the combination of the equation of time (horizontal variation) and the changing solar declination (vertical variation). If you photograph the Sun at exactly noon every day for a year, the images form an analemma shape in the sky.

Higher altitudes allow you to see the Sun earlier at sunrise (the geometric horizon is farther below the mathematical horizon) and later at sunset. This effect is significant for mountains: at the summit of Everest (8,849 m), sunrise occurs about 15 minutes earlier than at sea level at the same latitude due to the visible horizon being about 335 km away. This calculator does not account for altitude.

Due to the equation of time, the earliest sunrise, the latest sunset, and the longest day (summer solstice) do not all coincide. In the Northern Hemisphere, the earliest sunrise typically occurs about a week before the summer solstice, and the latest sunset about a week after. Similarly, the shortest day is December 21-22, but the earliest sunset is around December 7 and the latest sunrise is around January 4-5.

No — this calculator is specific to Earth and uses Earth's axial tilt (23.5 degrees) and orbital parameters. Other planets have different axial tilts (Mars 25.2 degrees, Uranus 97.8 degrees) and different orbital periods, which would produce very different sunrise/sunset patterns. Mars has longer days (24h 37m) and an 18-month year with its own seasonal structure.

The equation of time is the difference between solar time (measured by the Sun's actual position) and mean solar time (uniform clock time). It has two components: Earth's orbital eccentricity (moves faster near perihelion in January, making solar noon earlier) and axial tilt (Sun moves along the ecliptic rather than the equator, creating seasonal variation in solar day length). The total variation ranges from about -16 minutes in early November to +14 minutes in mid-February.