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Solar Elevation and Azimuth Angle — result sheet
Calculate the Sun's elevation, zenith, and compass azimuth from latitude, solar declination, and hour angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: cos Z = sin φ sin δ + cos φ cos δ cos H; elevation = 90° − Z, with azimuth calculated clockwise from north.
Solar elevation tells how high the Sun is above the horizon, while zenith is its complement. The hour angle is zero at local solar noon, negative before noon, and positive after noon; the azimuth result uses the common clockwise-from-north compass convention.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Observer latitude — °; minimum -90; maximum 90
- Solar declination — °; minimum -90; maximum 90
- Solar hour angle — °; minimum -180; maximum 180
Worked example
| Input | Value |
|---|---|
| Observer latitude | 26.07 |
| Solar declination | 10 |
| Solar hour angle | 0 |
At latitude 26.07°N and declination 10° at solar noon, elevation is about 73.93°, zenith is about 16.07°, and azimuth is 180°.
Assumptions and limits
- Latitude, declination, and hour angle are geocentric angular inputs in degrees; hour angle is local solar time, not a clock-time shortcut.
- Azimuth is reported clockwise from true north and the ideal geometric center of the Sun is used.
- Atmospheric refraction, elevation above sea level, terrain horizon, time-zone conversion, and daylight-saving adjustments are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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