Sunrise, sunset and solar noon
Sunrise and sunset are the moments when the upper edge of the Sun is on the horizon. The air bends sunlight on its way to you, so at sunset you still see the Sun when it is already a little below the horizon. That is why the calculation puts the center of the Sun 0.833 degrees below the horizon at sunrise and sunset, the value used by the NOAA Solar Calculator; the U.S. Naval Observatory uses the same 50 arcminutes, made of 34 arcminutes of refraction and 16 for the radius of the Sun.
Solar noon is the moment the Sun crosses the north and south line in the sky and stands highest for the day. It is rarely 12:00 on the clock: time zones are wide, daylight saving time moves the clock by an hour, and the equation of time, which comes from the tilt of the Earth's axis and its elliptical orbit, moves solar noon earlier or later over the year. The day length is the daylight time from sunrise to sunset. The sun angle at noon is the height of the Sun's center above the horizon at solar noon, without the bending of light by the air.
Civil, nautical and astronomical twilight
Twilight is the time before sunrise and after sunset when the sky is still lit. The U.S. Naval Observatory defines three stages by how far the center of the Sun is below the horizon:
| Twilight | Sun below the horizon |
|---|---|
| Civil | 0.833° to 6° |
| Nautical | 6° to 12° |
| Astronomical | 12° to 18° |
In the calculator, each twilight runs from its dawn, when the Sun rises past that angle in the morning, to its dusk in the evening. In summer at higher latitudes the Sun may not sink 18 degrees below the horizon at all, so astronomical twilight lasts all night and the calculator says so.
Midnight sun and polar night
North of the Arctic Circle and south of the Antarctic Circle, the Sun can stay above the horizon for the whole day around the summer solstice, or below it around the winter solstice. On those days there is no sunrise or sunset, and the calculator shows that the Sun is up all day, or below the horizon all day, with whatever twilight is left. Even in polar night there can be twilight: the U.S. Naval Observatory lists civil twilight in Tromsø, Norway, from 9:31 to 13:53 local time on December 21, 2026, although the Sun does not rise.
How the calculator works
The times come from the equations of the NOAA Solar Calculator, which NOAA's Global Monitoring Laboratory based on Jean Meeus, Astronomical Algorithms. For each date, the calculator finds the Sun's declination and the equation of time, then the hour angle at which the Sun reaches 0.833°, 6°, 12° and 18° below the horizon. It repeats the step with the Sun's position at the event itself for more precision. NOAA states the sunrise and sunset results are accurate to within a minute between 72 degrees north and south latitude, and within 10 minutes closer to the poles. The calculation assumes a flat horizon at sea level, so mountains, buildings and the height you stand at are not included, and the real bending of light changes with the weather.
Times are shown in the time zone of the place, using the time zone database built into your browser, so daylight saving time changes are included. The city list holds the principal locations of the time zones in the IANA time zone database (zone.tab, public domain), with their latitude and longitude to the nearest minute of arc. For any other place, enter its latitude and longitude in decimal degrees or use your location.
How to use the sunrise and sunset calculator
- 1Pick a city, enter a latitude and longitude, or click "Use my location". Check that the time zone is the one you want the times in.
- 2Choose a date. The sunrise, sunset, solar noon, day length and twilight times update right away.
- 3Scroll the table for every day of the month, then copy the result or a link to it.
Frequently asked questions
How are sunrise and sunset defined?
Sunrise and sunset are the moments when the upper edge of the Sun touches the horizon. Because the air bends sunlight, the Sun is still slightly below the horizon at that moment, so the calculation places the center of the Sun 0.833 degrees below the horizon, the value NOAA uses. The U.S. Naval Observatory uses the same 50 arcminutes.
What is the difference between civil, nautical and astronomical twilight?
They differ in how far the Sun is below the horizon. Civil twilight lasts while the center of the Sun is up to 6 degrees below the horizon, nautical twilight up to 12 degrees and astronomical twilight up to 18 degrees, following the definitions of the U.S. Naval Observatory. Dawn is the start of a twilight in the morning, dusk its end in the evening.
Is daylight saving time included?
Yes. Times are shown in the time zone of the place, using the time zone database built into your browser, so daylight saving time is applied on the right dates. You can also pick another time zone, for example to see the times of a trip in your home time.
How accurate are the times?
The equations are the ones behind the NOAA Solar Calculator. NOAA states its sunrise and sunset results are accurate to within a minute between 72 degrees north and south, and within 10 minutes closer to the poles. Real sunrise and sunset can still differ, because the bending of light in the air changes with temperature and pressure, and because hills, buildings or your height above the ground change the horizon.
Is my location sent anywhere?
No. The location button asks your browser for your position only after you click it, and the times are calculated on your device. The coordinates are not sent to Freebiefy or anyone else. If you copy a share link, the place is part of that link.