Sunrise Sunset Calculator

Determining sunrise and sunset times relies on spherical astronomy and celestial mechanics. The core logic begins by converting your calendar date into a fractional day of the year (dayum). The calculator then utilizes latitude (Phi) and longitude (longi) to find the sun's declination angle and equation of time. The hour angle of the sun at rising and setting is computed using trigonometric functions that account for the solar zenith angle, standard atmospheric refraction (roughly 34 arcminutes), and the sun's semi-diameter. Finally, daylight duration (daylength) is calculated by finding the absolute difference between the sunset (sunset) and sunrise (sunrise) timestamps.

Imagine you want to calculate the sunrise and sunset times for a location at latitude 40.7128$°$ N, longitude 74.0060$°$ W (New York City) on the 172nd day of the year (around the summer solstice). First, the input latitude (Phi) and longitude (longi) are processed with their respective signs. The tool evaluates the solar declination for day 172, which is approximately 23.44$°$. By applying the hour angle formula and adjusting for local time zone offsets (timzon), the raw sunrise is determined to be roughly 5:25 AM, and sunset occurs around 8:30 PM local time. The resulting total day length (daylength) comes out to approximately 15 hours and 5 minutes.

Always ensure your latitude and longitude use the correct directional signs (positive for North and East, negative for South and West) to prevent inverted calculations. Keep in mind that standard time zones should be adjusted manually if your region observes Daylight Saving Time, unless your input parameter automatically incorporates seasonal shifts. Finally, pay attention to the difference between standard calculations and refraction-adjusted values (sunriseref), as atmospheric bending extends daylight by several minutes each day.