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Sunrise & Sunset Calculator

Calculators · Added

Sunrise and sunset from a date and a pair of coordinates, computed with NOAA's solar position algorithm in your browser. No location is requested and nothing is sent anywhere — the Sun's position is a polynomial, not a lookup.

North positive

East positive

Include daylight saving if it applies on that date

How to use the sunrise & sunset calculator

  1. 1Choose the date, and enter coordinates or pick a city.
  2. 2Set the UTC offset for that date, including daylight saving if it applies.
  3. 3Read the sunrise, sunset and day length.
  4. 4Check the twilight table if you need the light rather than the Sun itself.

Examples

Midsummer in London

Input
21 June, 51.5074 / −0.1278, UTC+1
Result
Sunrise 04:43, sunset 21:21, and 16h 38m of daylight

Midwinter above the Arctic Circle

Input
21 December in Tromsø
Result
The Sun does not rise — reported as polar night rather than as a failure

About the sunrise & sunset calculator

The equation of time

Solar noon is almost never at 12:00, and the gap has two causes. The obvious one is longitude: the Earth turns 15° an hour, so a place at the eastern edge of a time zone sees noon well before one at the western edge.

The subtler one is the equation of time, which swings about ±16 minutes across a year because the Earth's orbit is elliptical and its axis is tilted. It is why the earliest sunset of the year is not on the shortest day — in mid-northern latitudes it falls a couple of weeks earlier — and why a sundial and a clock only agree four times a year.

Day length does not change evenly

Around the solstices the day length barely moves — a few seconds either side — which is what the word solstice means: the Sun standing still. Around the equinoxes it changes fastest, by several minutes a day in mid-latitudes and much faster nearer the poles.

That is the cosine curve of the Sun's declination showing through, and it is why the second half of January feels like it is getting lighter quickly while late December does not, even though both are the same distance from the solstice.

Frequently asked questions

Why is sunrise not when the Sun's centre reaches the horizon?
Two corrections push it earlier. Sunrise is defined as the upper limb appearing, which is 0.266° before the centre arrives, and atmospheric refraction bends light over the horizon so you see the Sun while it is still about 0.567° below it. Together those give the 90.833° zenith angle this uses.
What is the difference between the three twilights?
How far the Sun is below the horizon. Civil twilight runs to 6° and is when there is still enough light to work outdoors. Nautical runs to 12° and is named for the point where the sea horizon becomes too faint for sextant work. Astronomical runs to 18°, past which the sky is as dark as it is going to get.
Why does it sometimes say there is no sunrise?
Because at high latitudes there are dates when the Sun genuinely does not rise or does not set. The hour angle equation then asks for the arccosine of a number outside −1 to 1, which has no solution — and that is the right answer. Reporting polar day or polar night is correct; returning a plausible-looking time would not be.
How accurate is it?
NOAA states about a minute between 72° north and south, degrading beyond that as the Sun's path flattens against the horizon. It assumes sea level and a flat horizon, so local terrain matters more than the algorithm does: a hill to the east delays sunrise by more than any refinement would change it, and altitude brings it forward by roughly a minute per 1.5 km.

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