Sunrise and Sunset

Sunrise and sunset times, solar noon, day length and civil twilight for a city or coordinates on any date.

What to find:

for a city

by coordinates

Coordinates in degrees: 55.75, 55°45′, 55 45 21, 55°45′ N; southern latitude and western longitude with a minus sign or the letters S / W.

Test yourself

The sunrise and sunset calculator shows the times of sunrise, sunset and solar noon, the day length and civil twilight for any city or point by coordinates on a chosen date.

How it works

First the moment of solar noon is found — when the Sun is highest, corrected for longitude and the equation of time. Then the sunrise hour angle ω:

cos ω = ^{sin(−0.833°) − sin φ · sin δ}/_{cos φ · cos δ}

φ is the latitude and δ the solar declination. The angle −0.833° accounts for atmospheric refraction and the Sun's radius: sunrise is the moment the upper edge of the Sun appears. Sunrise comes ω/15° hours before noon and sunset the same time after.

If cos ω is below −1, the Sun does not set (polar day); above 1, it does not rise (polar night). Civil twilight lasts until the Sun is 6° below the horizon; if it never gets that low, there are white nights.

Example. Moscow, June 21: sunrise about 3:44, sunset about 21:17, the day lasts 17 h 33 min.