Advanced Solar Geometry Calculator

Solar Geometry Calculator

Enter site coordinates, local time, timezone, and surface orientation. Longitude uses east positive values and west negative values. Surface azimuth uses south as zero, west positive, and east negative.

Date

Local Clock Time

UTC Offset (hours)

Latitude (°)

Longitude (°)

Surface Tilt β (°)

Surface Azimuth γ (° from south)

Daylight Saving Adjustment

Example Data Table

Date	Time	Latitude	Longitude	UTC	Tilt	Surface Azimuth	Altitude	Azimuth	Day Length
2026-06-21	12:00	24.8607	67.0011	+5	25°	0°	Approx. 84°	Approx. 180°	Approx. 13.6 h
2026-03-21	10:30	31.5204	74.3587	+5	30°	-15°	Approx. 49°	Approx. 133°	Approx. 12.0 h
2026-12-21	14:00	33.6844	73.0479	+5	35°	10°	Approx. 29°	Approx. 215°	Approx. 10.1 h

Formula Used

Declination:
δ = 23.45 × sin(360 × (284 + n) / 365)

Equation of Time:
B = 360 × (n - 81) / 365
EoT = 9.87 × sin(2B) - 7.53 × cos(B) - 1.5 × sin(B)

Solar Time:
LSTM = 15 × UTC offset
TC = 4 × (Longitude - LSTM) + EoT
Solar Time = Local Standard Time + TC / 60

Hour Angle and Zenith:
ω = 15 × (Solar Time - 12)
cos(θz) = sinφ × sinδ + cosφ × cosδ × cosω

Altitude and Azimuth:
Altitude = 90 - Zenith
Solar azimuth is shown in degrees clockwise from north.

Sunrise and Day Length:
ωs = acos(-tanφ × tanδ)
Day Length = 2 × ωs / 15

Incidence on Tilted Surface:
The calculator applies the standard tilted-plane incidence equation using latitude, declination, hour angle, surface tilt, and surface azimuth.

How to Use This Calculator

Enter the project date and local clock time.
Add latitude and longitude for the exact site.
Enter the site UTC offset.
Set daylight saving to 1 hour only when applicable.
Enter the panel or surface tilt angle.
Enter surface azimuth using south as zero.
Click the calculate button to generate solar geometry outputs.
Review the chart, results table, and sunrise or sunset estimates.
Use the CSV or PDF buttons to save the report.

Frequently Asked Questions

1. What does solar geometry mean?

Solar geometry describes the sun’s apparent position relative to a location, date, time, and surface orientation. It helps estimate sun angles, daylight hours, and panel exposure.

2. Why is latitude important?

Latitude strongly affects solar altitude, azimuth, and day length. Two sites at different latitudes will have different sun paths even on the same date and time.

3. What is the equation of time?

The equation of time corrects clock-based time to solar time. It accounts for Earth’s orbital shape and axial tilt, which shift apparent solar noon during the year.

4. How is solar azimuth shown here?

This page reports solar azimuth as degrees clockwise from north. Around noon in many northern hemisphere locations, the sun often appears close to south, near 180 degrees.

5. What does surface azimuth mean?

Surface azimuth is the facing direction of the panel or plane. This calculator uses south as zero, west as positive, and east as negative.

6. Why can sunrise or sunset be blank?

At high latitudes, some dates produce continuous daylight or continuous darkness. In those cases, standard sunrise and sunset times may not exist for that day.

7. What is incidence angle?

Incidence angle measures how directly sunlight hits the tilted surface. Smaller incidence angles generally mean the sun is more perpendicular to the panel face.

8. Can I use this for system design?

Yes. It is useful for orientation studies, shading reviews, educational work, and early planning. Final engineering design should also consider weather, shading, and site-specific losses.