Sunrise & Sunset Calculator

Implements the simplified NOAA solar position equations: from a date and a (lat, lng) pair, it derives the solar declination and hour angles for each event. Civil twilight = sun 6° below the horizon (when artificial light starts being needed), nautical = 12° (horizon still visible at sea), astronomical = 18° (the sky is fully dark). When the sun never crosses the relevant altitude — polar day or night — the row is left blank and a note appears.

Sunrise is defined as the moment the sun's upper edge touches the horizon, not its centre, and the standard calculation folds in about 34 arcminutes of atmospheric refraction on top of that. Both corrections push the event earlier than pure geometry predicts, by several minutes at temperate latitudes. The refraction figure is an average for standard conditions, so unusual temperature layering near the horizon shifts the real time by a minute or two, and that is the floor on how accurate any such prediction can be.

The blank rows near the poles are a real answer rather than a failure. Above the Arctic and Antarctic circles the sun can stay up or stay down for days, and the twilight thresholds fall out one at a time as you move poleward: a place can have no astronomical night for months while still getting a proper sunset. Saint Petersburg's white nights are exactly that.

The model treats the observer as being at sea level on a smooth horizon. Altitude brings sunrise forward and pushes sunset back, a mountain or a building to the east delays it, and neither is something a latitude and longitude can express. Times are also solar rather than legal: a country whose clocks sit far from their natural meridian, or one on a single time zone spanning a wide span of longitude, will see the calculated time differ from the official tables by more than the rounding.

Day length is derived from the same two events, so it inherits every caveat above.