Donaldson R F Sunrise & Sunset Calculator
Pick a date and a place to see sunrise, solar noon, sunset, and the three stages of twilight.
How this is worked out
This tool uses NOAA's own published solar-position formulas: the fractional year, equation of time, solar declination and sunrise/sunset hour-angle equations from NOAA Global Monitoring Division, "General Solar Position Calculations". Sunrise and sunset are defined, as in that document, as the moment the sun's upper edge is on the horizon — a solar zenith angle of 90.833°, which bundles the sun's apparent size (about 16 arcminutes) with roughly 34 arcminutes of atmospheric refraction near the horizon. Civil, nautical and astronomical twilight use the standard 6°, 12° and 18° sun-below-horizon definitions.
Because these formulas use a low-order approximation for the sun's position (accurate but not exact), results are normally within a minute of a full ephemeris, widening to a few minutes right around the equinoxes at higher latitudes — the same behaviour published almanacs describe for this class of formula. Above the Arctic/Antarctic Circle, an event can fail to happen at all on a given day (the midnight sun, or a polar night); this tool reports that directly instead of showing a wrong time.
Frequently asked questions
Why is daytime a little longer than night-time on the equinox?
Because sunrise and sunset are measured to the sun's upper edge, not its centre, and atmospheric refraction lifts the sun's apparent position further still — so the "day" side wins by a few minutes even when the sun's centre crosses the celestial equator exactly at the equinox.
What timezone are the times shown in?
Your browser's own local timezone for the date you picked (including daylight saving, worked out for that specific date rather than assumed from today), alongside UTC.
Related tools: Julian Date Converter, Astronomical Distance Converter, Moon Phase.
Source / Last verified: NOAA Global Monitoring Division, "General Solar Position Calculations" (gml.noaa.gov/grad/solcalc/solareqns.PDF), and US Naval Observatory, "Rise, Set, and Twilight Definitions" (aa.usno.navy.mil/faq/RST_defs), both read 27 September 2026. Checked against the US Naval Observatory's own sunrise/sunset/twilight data (aa.usno.navy.mil/data/RS_OneDay) for London and Singapore on several dates, read 27 September 2026: matched to the minute away from the equinoxes, within a few minutes close to them.