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Sun Angle Calculator

NOAA approximate solar-position equations for a non-leap year of 365 days. Include daylight saving in the supplied UTC offset. Elevation excludes atmospheric refraction and horizon obstructions.

NOAA approximate solar-position equations for a non-leap year of 365 days. Include daylight saving in the supplied UTC offset. Elevation excludes atmospheric refraction and horizon obstructions.

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Result

Enter your values and run the tool to see your result.

How to use this tool

Check the units, enter your values, and run the tool. Results follow the assumptions and method below.

Calculation method

Geometric solar elevationasin(min(1,max(-1,(sin(latitude*pi/180)*sin((0.006918-0.399912*cos((2*pi/365*(day-1+(hour-12)/24)))+0.070257*sin((2*pi/365*(day-1+(hour-12)/24)))-0.006758*cos(2*(2*pi/365*(day-1+(hour-12)/24)))+0.000907*sin(2*(2*pi/365*(day-1+(hour-12)/24)))-0.002697*cos(3*(2*pi/365*(day-1+(hour-12)/24)))+0.00148*sin(3*(2*pi/365*(day-1+(hour-12)/24)))))+cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+(hour-12)/24)))+0.070257*sin((2*pi/365*(day-1+(hour-12)/24)))-0.006758*cos(2*(2*pi/365*(day-1+(hour-12)/24)))+0.000907*sin(2*(2*pi/365*(day-1+(hour-12)/24)))-0.002697*cos(3*(2*pi/365*(day-1+(hour-12)/24)))+0.00148*sin(3*(2*pi/365*(day-1+(hour-12)/24)))))*cos(((hour*60+(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+(hour-12)/24)))-0.032077*sin((2*pi/365*(day-1+(hour-12)/24)))-0.014615*cos(2*(2*pi/365*(day-1+(hour-12)/24)))-0.040849*sin(2*(2*pi/365*(day-1+(hour-12)/24)))))+4*longitude-60*zone)/4-180)*pi/180)))))*180/pi
Solar zenith angleacos(min(1,max(-1,(sin(latitude*pi/180)*sin((0.006918-0.399912*cos((2*pi/365*(day-1+(hour-12)/24)))+0.070257*sin((2*pi/365*(day-1+(hour-12)/24)))-0.006758*cos(2*(2*pi/365*(day-1+(hour-12)/24)))+0.000907*sin(2*(2*pi/365*(day-1+(hour-12)/24)))-0.002697*cos(3*(2*pi/365*(day-1+(hour-12)/24)))+0.00148*sin(3*(2*pi/365*(day-1+(hour-12)/24)))))+cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+(hour-12)/24)))+0.070257*sin((2*pi/365*(day-1+(hour-12)/24)))-0.006758*cos(2*(2*pi/365*(day-1+(hour-12)/24)))+0.000907*sin(2*(2*pi/365*(day-1+(hour-12)/24)))-0.002697*cos(3*(2*pi/365*(day-1+(hour-12)/24)))+0.00148*sin(3*(2*pi/365*(day-1+(hour-12)/24)))))*cos(((hour*60+(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+(hour-12)/24)))-0.032077*sin((2*pi/365*(day-1+(hour-12)/24)))-0.014615*cos(2*(2*pi/365*(day-1+(hour-12)/24)))-0.040849*sin(2*(2*pi/365*(day-1+(hour-12)/24)))))+4*longitude-60*zone)/4-180)*pi/180)))))*180/pi
Solar declination(0.006918-0.399912*cos((2*pi/365*(day-1+(hour-12)/24)))+0.070257*sin((2*pi/365*(day-1+(hour-12)/24)))-0.006758*cos(2*(2*pi/365*(day-1+(hour-12)/24)))+0.000907*sin(2*(2*pi/365*(day-1+(hour-12)/24)))-0.002697*cos(3*(2*pi/365*(day-1+(hour-12)/24)))+0.00148*sin(3*(2*pi/365*(day-1+(hour-12)/24))))*180/pi
Equation of time(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+(hour-12)/24)))-0.032077*sin((2*pi/365*(day-1+(hour-12)/24)))-0.014615*cos(2*(2*pi/365*(day-1+(hour-12)/24)))-0.040849*sin(2*(2*pi/365*(day-1+(hour-12)/24)))))

References