Calculator Inputs
Enter either a manual declination or a day number. Enter either solar time or a manual hour angle. Manual values override derived values.
Formula Used
This calculator uses the standard incidence relation for a tilted plane. It assumes the surface azimuth convention
γ = 0° for south-facing surfaces, east negative, and west positive.
Incidence equation:
cos(θ) = sin(δ)sin(φ)cos(β) − sin(δ)cos(φ)sin(β)cos(γ)
+ cos(δ)cos(φ)cos(β)cos(ω)
+ cos(δ)sin(φ)sin(β)cos(γ)cos(ω)
+ cos(δ)sin(β)sin(γ)sin(ω)
Supporting relations:
θ = arccos(cos(θ))cos(θz) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(ω)Solar altitude = 90° − θzω = 15 × (solar time − 12)δ = 23.45 × sin(360 × (284 + N) / 365)
Here, φ is latitude, δ is declination, ω is hour angle, β is surface tilt, and γ is surface azimuth.
How to Use This Calculator
- Enter the site latitude in degrees.
- Enter declination directly, or provide the day number.
- Enter solar time, or enter a manual hour angle.
- Set the surface tilt for the panel or plane.
- Set the surface azimuth using the listed sign convention.
- Click the calculate button to display the result above the form.
- Review the graph, beam factor, daylight estimate, and exported files.
Example Data Table
| Case | Latitude (°) | Declination (°) | Hour Angle (°) | Tilt (°) | Azimuth (°) | Incidence Angle (°) |
|---|---|---|---|---|---|---|
| South-facing noon surface | 35.00 | 15.00 | 0.00 | 25.00 | 0.00 | 5.0000 |
| Morning east-biased plane | 40.00 | -10.00 | -30.00 | 30.00 | -45.00 | 27.8610 |
| Afternoon west-biased plane | 28.00 | 23.45 | 45.00 | 20.00 | 30.00 | 35.8203 |
Frequently Asked Questions
1) What does the angle of incidence mean in solar work?
It is the angle between incoming sunlight and the surface normal. Smaller incidence angles usually mean stronger direct beam collection on the panel or plane.
2) Why does the calculator use solar time instead of clock time?
Solar formulas depend on the sun’s position, not civil clock time. Solar time aligns noon with the sun crossing the local meridian.
3) What if I only know the day of year?
Enter the day number and leave declination blank. The calculator will estimate declination with a common engineering approximation.
4) Which azimuth convention does this page use?
It uses 0° for south-facing surfaces, negative values toward east, and positive values toward west. Keep that convention consistent across comparisons.
5) Why can the beam ratio become zero?
When the sun is below the horizon or the surface turns away from direct sunlight, the direct beam projection becomes zero for practical use.
6) Can I use this for building walls and roofs?
Yes. Any tilted plane can be analyzed, including roofs, façades, skylights, and collectors, as long as tilt and azimuth are defined correctly.
7) Does this calculate diffuse and reflected radiation too?
No. This page focuses on geometry for direct beam incidence. Diffuse sky and ground-reflected components need separate radiation models.
8) Why does incidence angle matter for panel performance?
Direct beam energy is strongest when sunlight strikes closer to perpendicular. Larger incidence angles reduce projected energy on the active surface.