Sunrise and Sunset Times Calculator

What counts as sunrise and sunset?

In common perception, sunrise occurs when the Sun appears in the morning sky. In astronomy and geodesy, however, sunrise and sunset have exact, rigorous mathematical definitions:

Sunrise is defined as the precise instant when the upper limb (top edge) of the Sun's disk appears to touch the true astronomical horizon. Sunset is the exact instant when the upper limb disappears completely below the horizon.

Crucially, this means the geometric center of the Sun is well below the horizon at both events. By international consensus (US Naval Observatory and HM Nautical Almanac Office), the center of the Sun sits at an altitude of -50 arcminutes (-0.833 degrees) at sunrise and sunset:

• Atmospheric Refraction (34 arcminutes / 0.567°): Terrestrial air density bends light rays downward, lifting the apparent position of the Sun upward by over half a degree on the horizon.
• Solar Disk Semi-Diameter (16 arcminutes / 0.267°): The angular radius of the Sun as seen from Earth. Measuring from the upper edge rather than the center adds 16 arcminutes of advance warning.

Because of this 50-arcminute bonus, even on the equinoxes—when day and night are supposed to be equal—daylight is roughly 7 to 10 minutes longer than nighttime everywhere on Earth.

Solar noon and day length

All sunrise and sunset calculations are anchored around local solar noon—the moment the Sun crosses the observer's local meridian and attains its highest elevation of the day.

Solar noon rarely coincides with 12:00 PM on clock time. Clock noon is distorted by two variables:

Does elevation change sunrise and sunset times?

When an observer stands atop a mountain peak, an ocean cliff, or the observation deck of a skyscraper, the horizon is no longer horizontal; it curves downward beneath eye level.

This angular depression is termed the dip of the horizon:

For example, on the 102nd-floor observatory of the Empire State Building (elevation ~380 meters), the horizon dips by 0.57 degrees. This depression angle allows visitors to see sunrise roughly 3 to 4 minutes earlier than pedestrians on the sidewalk below, and to view sunset 3 to 4 minutes later. On Mount Everest (8,848 m), sunrise occurs over 15 minutes earlier than at sea level at the same latitude.

How sunrise and sunset times are calculated

The half-day length hour angle H₀ from solar noon to sunrise/sunset is derived from spherical trigonometry:

Daylight hours by latitude on the solstices

Reference this benchmark table comparing summer and winter solstice day lengths and sunrise times from the Equator to the Arctic:

Why real sunrise can differ from the calculator

When planning photography, aviation flights, or outdoor recreation, note these real-world exceptions to mathematical sunrise calculations:

• Mountain Topography: Standard calculations assume a smooth, flat horizon at sea level. If your eastern horizon is blocked by a 3,000-meter mountain ridge 15 km away, the actual visual sunrise will be delayed by 20 to 45 minutes until the Sun clears the peaks.
• Polar Singularities: When |cos(H₀)| ≥ 1, the mathematical equation has no solution. If cos(H₀) ≤ -1, the Sun never sets (Midnight Sun). If cos(H₀) ≥ +1, the Sun never rises (Polar Night).
• High-Latitude Twilight Bleed: In locations above 55° latitude (such as Edinburgh, Stockholm, or Edmonton) during midsummer, the Sun never dips more than 12 degrees below the horizon at night, resulting in continuous civil or nautical twilight where the sky never turns truly dark.