Solar Elevation Azimuth and Shadow Calculator
Estimate geometric sun position and a vertical object’s level-ground shadow from entered date, clock time and coordinates.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use NOAA fractional-year approximations for declination and equation of time. Convert the entered civil clock to true solar time, evaluate spherical sun geometry, and divide vertical height by tangent of elevation.
True solar minutes=clock minutes+equation of time+4×longitude−60×UTC offset; shadow=height/tan(elevation)
Worked example
Near 40°N, 105°W at local noon UTC−7 on the June solstice, the sun is approximately 73° above the horizon. A 2 m vertical object casts a shadow about 0.6 m long on level ground.
Assumptions and input details
Approximate geometric model for 2000–2099 and latitude −89.9° to +89.9°. Azimuth is clockwise from true north: east=90°, south=180°. Longitude is east-positive, unlike some older calculators. UTC offset is entered explicitly; no DST or timezone lookup. No refraction, terrain, elevation, buildings or solar-disk correction. At/below the geometric horizon there is no finite direct-sun ground shadow. Near the horizon, shadows are highly sensitive to model errors. Azimuth is undefined at exact zenith/nadir. Not for surveying or navigation.
References: NOAA: general solar position equations
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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