Solar Radiation on Tilted Surface Calculator
Calculate total solar irradiance on a tilted surface.
Find beam, diffuse, and reflected radiation components to optimize solar panel tilt angle and azimuth.
Total Irradiance on a Tilted Surface (GT) GT = Beam (Ib_t) + Diffuse (Id_t) + Reflected (Ir_t)
Angle of Incidence (theta) The angle between incoming sunlight and the surface normal. cos(theta) = cos(beta)cos(Z) + sin(beta)sin(Z)cos(gamma_s - gamma) Where:
- beta = surface tilt from horizontal (0° = flat, 90° = vertical)
- Z = solar zenith angle = 90° - solar altitude
- gamma = surface azimuth (0° = south in northern hemisphere)
- gamma_s = solar azimuth
Beam Component on Tilted Surface Ib_t = Ib × cos(theta) / sin(altitude)
Where Ib is the beam (direct) component of GHI: Ib ≈ GHI - Id (diffuse) Diffuse fraction approximated from GHI (isotropic sky model): Id ≈ GHI × 0.15 to 0.40 (higher for cloudy/overcast)
Diffuse Component (Isotropic Model) Id_t = Id × (1 + cos(beta)) / 2
Ground-Reflected Component Ir_t = GHI × albedo × (1 - cos(beta)) / 2 Default albedo = 0.20 (grass/soil). Snow albedo can reach 0.80.
Optimization Tips
- For maximum annual yield, tilt ≈ latitude
- South-facing (northern hemisphere) maximizes annual output
- A 20–30° tilt gives similar annual yield to optimal, with better summer performance