Calculator Inputs
The page stays single column, while the calculator fields adapt to 3, 2, and 1 columns by screen size.
Formula Used
1) Solar declination
δ = 23.45 × sin(360 × (284 + n) / 365)
Here, n is the day of year.
2) Hour angle
ω = 15 × (Solar Time − 12)
Negative values occur before solar noon. Positive values occur after solar noon.
3) Solar zenith angle
cos(θz) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(ω)
φ is latitude and θz is the zenith angle.
4) Incidence angle on a tilted surface
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)
β is tilt and γ is surface azimuth.
5) Beam ratio
Rb = max(0, cos(θ)) / cos(θz)
This compares beam radiation on the tilted plane with beam radiation on a horizontal plane.
How to Use This Calculator
- Enter the site latitude in degrees.
- Choose a calendar date or type the day of year.
- Enter solar time, not standard clock time.
- Enter the surface tilt angle.
- Enter the surface azimuth using the stated sign convention.
- Press the calculate button.
- Review the result panel above the form.
- Use the chart to inspect incidence through the day.
- Download CSV or PDF when you need documentation.
Example Data Table
| Latitude (°) | Day | Solar Time | Tilt β (°) | Azimuth γ (°) | Declination δ (°) | Zenith θz (°) | Elevation α (°) | Incidence θ (°) |
|---|---|---|---|---|---|---|---|---|
| 30 | 172 | 13.00 | 25 | 0 | 23.45 | 14.89 | 75.11 | 23.44 |
| 40 | 81 | 10.50 | 30 | -15 | 0.00 | 44.95 | 45.05 | 18.33 |
| 15 | 355 | 12.00 | 10 | 5 | -23.45 | 38.45 | 51.55 | 28.50 |
These rows help confirm the sign convention and expected angle ranges before using live project values.
Frequently Asked Questions
1) What does the incidence angle show?
It shows the angle between incoming beam sunlight and the panel’s normal line. Smaller angles usually mean stronger direct beam capture.
2) Why should I use solar time?
Solar geometry depends on the sun’s true position, not local clock time. Solar time corrects noon to the sun’s highest daily point.
3) What azimuth sign convention is used here?
The calculator uses south as 0°. East-facing rotations are negative. West-facing rotations are positive. This convention is common in solar engineering texts.
4) Can I use this for trackers?
Yes. Enter the tracker’s current tilt and azimuth position at the selected solar time. Then compare values across positions or export several scenarios.
5) Why can incidence become greater than 90°?
That means the front face is no longer directly illuminated. The sun may still be above the horizon, but beam radiation misses the active front surface.
6) What is the beam ratio Rb?
Rb compares direct beam on the tilted plane with direct beam on a horizontal plane. Values above 1 mean the tilt is favorably aligned.
7) Does this calculator include diffuse or reflected radiation?
No. It focuses on beam geometry only. Use separate irradiance models when you also need sky diffuse, ground reflection, or shading effects.
8) When is this calculator most useful?
It is useful for panel orientation checks, row design studies, training examples, tracker validation, and quick solar geometry comparisons across dates.