Solar Geometry Calculator

Calculator Inputs

Example Data Table

Scenario	Latitude	Longitude	UTC	Date	Time	Tilt	Surface Azimuth
South-facing rooftop check	24.8607	67.0011	+5	2026-06-21	13:30	30°	0°
Winter shading review	40.7128	-74.0060	-5	2026-12-21	10:00	45°	-30°
Facade exposure study	34.0522	-118.2437	-8	2026-03-20	15:15	90°	90°

Formula Used

The calculator applies standard solar position relations for local time and site coordinates.

Day number: n = day of year.
Equation of time: EoT = 9.87 sin(2B) − 7.53 cos(B) − 1.5 sin(B), where B = 360(n − 81)/365.
Solar time = clock time + time correction / 60.
Time correction = 4(longitude − standard meridian) + EoT.
Declination: δ = 23.45 sin(360(284 + n)/365).
Hour angle: ω = 15(solar time − 12).
Zenith: cos(θ_z) = sinφ sinδ + cosφ cosδ cosω.
Elevation = 90 − zenith.
Azimuth is derived from atan2 using latitude, declination, and hour angle.
Incidence on a tilted plane uses tilt β and surface azimuth γ with the full beam incidence relation.

How to Use This Calculator

Enter latitude and longitude for the site.
Enter the local date, local time, and UTC offset.
Set the surface tilt from horizontal.
Enter surface azimuth from south. Use negative values for east of south and positive values for west of south.
Set albedo if you want to record site reflectance.
Click the calculate button.
Review the result block above the form.
Use the CSV button for spreadsheet work and the PDF button for a printable report.

Solar Geometry and Sun Position Guide

Understanding Solar Geometry

Solar geometry explains how the sun appears to move across the sky for a specific place and time. It connects astronomy with practical physics. Engineers use it for photovoltaic design. Architects use it for daylight planning. Researchers use it for shading analysis, thermal studies, and seasonal energy estimates.

Why Accurate Angles Matter

Small angle errors can change predicted irradiance, shadow length, and panel orientation decisions. Solar altitude affects available sunlight above the horizon. Solar zenith describes the angle from the vertical. Solar azimuth shows the compass direction of the sun. Incidence angle measures how directly sunlight strikes a tilted surface.

Core Variables in This Calculator

This calculator uses latitude, longitude, date, time, time zone, surface tilt, and surface azimuth. From these values, it estimates day number, equation of time, solar time, declination, hour angle, zenith angle, elevation angle, azimuth angle, sunrise, sunset, solar noon, day length, extraterrestrial irradiance, and the incidence angle on a plane.

How It Helps Real Projects

Solar installers can compare roof orientations before selecting module placement. Students can verify textbook solar position problems. Building designers can test façade exposure during different seasons. Greenhouse planners can check winter sun access. Anyone studying shadows can estimate when the sun becomes too low for reliable collection or lighting.

Interpreting the Results

Higher elevation generally means stronger direct sun potential. A lower zenith angle means the sun is closer to overhead. Solar time often differs from clock time because longitude and the equation of time shift apparent noon. Incidence angle near zero means the surface faces the sun more directly, which usually improves collection.

Use the Calculator Well

Enter accurate coordinates and the correct local time zone offset. Keep sign conventions consistent. Negative latitude represents the southern hemisphere. Negative longitude represents western locations. For surface azimuth, east of south is negative and west of south is positive. Review sunrise and sunset values carefully when working near polar or extreme seasonal conditions.

These metrics also support tracker control, passive solar design, and academic labs. Because the sun angle changes continuously, a time specific calculator gives better insight than fixed monthly assumptions for precision driven decisions in real projects.

FAQs

1. What does a solar geometry calculator measure?

It estimates where the sun appears in the sky for a chosen location and time. Common outputs include declination, hour angle, solar time, zenith, elevation, azimuth, sunrise, sunset, and incidence on a tilted surface.

2. Why is solar time different from clock time?

Clock time follows time zones. Solar time depends on your longitude and the equation of time. Because of that, apparent solar noon often happens before or after 12:00 on a watch.

3. What is the difference between zenith and elevation?

Zenith is measured from the vertical downward to the sun direction. Elevation is measured upward from the horizon. They add to 90 degrees when the sun is above the horizon.

4. How should I enter surface azimuth?

In this calculator, surface azimuth is referenced from south. Enter 0 for due south, negative values for east of south, and positive values for west of south.

5. Why can the incidence angle be large?

A large incidence angle means sunlight strikes the surface obliquely. When the angle approaches 90 degrees or more, the surface is poorly aligned with the beam, so direct collection drops sharply.

6. Can I use this for panel placement?

Yes. It helps compare roof tilt, orientation, and seasonal sun position. It is useful for quick alignment studies, shading reviews, and understanding when direct beam conditions are strongest.

7. What happens near polar regions?

At high latitudes, the sun may stay above or below the horizon all day during some seasons. The calculator checks for this and shows a polar daylight or polar night note.

8. Is albedo used in the sun angle equations?

No. Albedo does not change solar position. It is included as a site parameter because reflected ground conditions matter in broader solar energy assessments and report records.