Solar Zenith & Azimuth

Answer: Solar zenith measures the angle between the sun and the direction directly overhead. Solar azimuth identifies its horizontal direction. With a clockwise-from-true-north convention, east is 90° and south is 180°. Solar elevation equals 90° minus zenith. State the coordinate convention and timestamp before using these angles to compare site surveys, shading models or array orientations.

Reading the angles

NOAA’s solar glossary explains this north-based convention and the elevation–zenith relationship. True north and compass north are different references. Do not apply a compass bearing without checking local magnetic declination.

Software may use another reference direction or sign. Also distinguish the sun’s azimuth from an array’s fixed azimuth: one varies through the day; the other describes the installation. A sun path diagram combines solar directions across times and dates.

Solar noon is different from clock noon

Solar noon is the sun’s passage across the observer’s meridian. The corresponding clock time depends on longitude, the time zone and the equation of time; daylight saving adds another clock adjustment. A noon photograph and a solar-noon model therefore need matching timestamps.

At upper meridian transit, the sun is to the north or south depending on latitude and solar declination. It is not always south throughout the Northern Hemisphere: tropical locations can have the noon sun to the north during part of the year. When the sun is exactly overhead, its horizontal projection has no direction, so azimuth is undefined. The equation of time changes when solar noon occurs, rather than moving the meridian to the east.

Calculating solar zenith

A geometric relationship is:

cos(zenith) = sin(latitude) × sin(declination) + cos(latitude) × cos(declination) × cos(hour angle)

Declination describes the sun’s angular position north or south of the equatorial plane. Hour angle is referenced to solar noon, rather than civil 12:00. Use consistent angular units in trigonometric functions. NOAA’s calculation equations show how longitude, time-zone offset and the equation of time enter the calculation.

A useful solar-noon simplification is zenith = absolute value of (latitude − declination). For an illustrative latitude of 40° north and assumed declination of −23.44°, geometric noon zenith is 63.44° and elevation is 26.56°. This is a worked geometric example, not an observation for a particular date or site.

Near the horizon, distinguish geometric angles from apparent angles corrected for atmospheric refraction. Calculations also need a documented convention for the sun’s center versus its disk when interpreting sunrise and sunset.

Using the angles in a shading review

For an ideal vertical object above level ground, a simple shadow-length calculation is:

Shadow length = object height / tan(solar elevation)

Illustrative calculation: A 2 m vertical object with the sun at 30° elevation casts a shadow approximately 3.46 m long. At 60° elevation, the length is approximately 1.15 m. In the north-based convention, a sun bearing of 150° gives an opposite shadow bearing of 330°.

This geometry assumes an unobstructed direct beam and level receiving surface. A sloping roof, complex tree canopy, different receiving elevation or neighboring structure needs a suitable three-dimensional model. A shadow’s length alone does not tell you how much annual energy is lost.

For row spacing, distinguish vertical rise, module length, horizontal projection and row pitch. Specify the dates and hours you intend to evaluate. Winter’s lower sun means a larger zenith angle, not a smaller one. December is not winter in the Southern Hemisphere, and a single noon check does not establish shade-free operation throughout a design window.

Position angles do not establish annual output

The angle of incidence describes the relationship between incoming direct sunlight and the module’s surface normal. Sun position contributes to it, alongside panel tilt and orientation. Annual production also depends on weather, diffuse and reflected irradiance, obstructions and electrical losses. Sandia’s PV Performance Modeling Collaborative places sun position within the PV modeling workflow.

Do not infer a universal east-facing penalty, tracker gain or optimal tilt from these angles alone. Compare project-specific tilt and azimuth scenarios using consistent weather and loss assumptions. Financial value additionally depends on when energy serves load or earns export compensation.

A practical check before comparing models

1. Confirm latitude and longitude, including their sign conventions.
2. Record date, local time, time zone and daylight-saving treatment.
3. Confirm true-north reference, azimuth origin and direction of measurement.
4. Identify geometric or apparent solar angles and any horizon model.
5. Check obstruction dimensions and the receiving surface, then compare equivalent timestamps.
6. Keep solar position separate from irradiance, shading loss and energy-output results.

Use the sun-angle calculator for an initial exploration and check its assumptions before relying on a result. For a project evaluation, review the shading-analysis workflow and confirm which inputs and outputs are available for your site.