Calculate approximate UTC sunrise and sunset times for any latitude and day of year for astronomy session planning.
Enter your latitude in degrees (north positive, south negative) and the day of year from 1 to 366 — June 21 is day 172 in a non-leap year. The result gives approximate sunrise, sunset, and daylight hours in UTC.
The model estimates solar declination as 23.45° × sin(360/365 × (day − 81)), then solves the sunrise hour angle for your latitude. At 51.5°N on day 172 it predicts roughly 16.4 hours of daylight.
Sunrise and sunset are placed symmetrically around 12:00 UTC, ignoring longitude, the equation of time, and atmospheric refraction — fine for planning observing windows, but expect offsets from your local almanac. At extreme latitudes it flags continuous day or night instead.
The model places solar noon at 12:00 UTC and ignores longitude, so it cannot know your time zone. Treat the daylight-hours figure as the primary output, and shift the clock times by your UTC offset and your position within your time zone.
Count days from January 1 as day 1. Useful anchors: the March equinox falls near day 80, the June solstice near day 172, the September equinox near day 266, and the December solstice near day 355. Values from 1 to 366 cover leap years.
At high latitudes the Sun can stay above or below the horizon all day. When the sunrise hour angle has no solution, the calculator reports polar day (24 hours of daylight) or polar night (0 hours) instead of clock times.
The model uses a simplified solar declination formula and ignores atmospheric refraction and the equation of time, which can shift real events by several minutes up to about a quarter hour. It is intended for planning observing windows, not precise timing.