How this calculator works
The NOAA fractional-year approximation supplies solar declination and the equation of time. Longitude and the entered UTC offset convert clock time to true solar time, giving the hour angle. Spherical geometry then gives elevation and azimuth. This tool uses a geometric centre-of-Sun elevation, without atmospheric refraction. Enter the offset that actually applies on your date, using the daylight-saving option only when the standard offset excludes that hour. The hourly table replaces a chart.
Formula
gamma = 2 pi/N (day_of_year-1+(hour-12)/24). True solar minutes = local minutes + equation_of_time + 4 longitude_degrees - 60 UTC_offset. sin(elevation) = sin(phi)sin(delta)+cos(phi)cos(delta)cos(hour_angle).
Worked example
At latitude 0 degrees, longitude 0 degrees on 2026-03-21 at 12:00 UTC, this approximation gives solar elevation about 88.03 degrees. The small offset from zenith includes equation-of-time and declination effects.
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Frequently asked questions
Which direction is azimuth measured from?
Clockwise from true north: east is 90 degrees, south is 180 degrees and west is 270 degrees.
Does the tool know my time zone rules?
No. Enter the standard UTC offset and the daylight-saving adjustment for the date and place.
Why does sunrise use another elevation?
Observed sunrise includes the solar disc and atmospheric refraction. This page gives geometric centre-of-Sun position.