Free Solar Radiation calculator with clear step-by-step results.
Computes extraterrestrial radiation on a horizontal surface from latitude and day of year using solar declination and the sunset hour angle, then scales it by a clearness index to reach ground-level irradiation and applies a tilt factor for an inclined surface.
Solar declination
Declination = 23.45 x sin(360 x (284 + day) / 365)
Ground irradiation
Horizontal = extraterrestrial x clearness index
Around 0.7 for a clear desert sky, 0.5-0.6 for a temperate summer, and 0.3 or lower for an overcast northern winter. It is the ratio of ground to extraterrestrial radiation.
Beyond the polar circles the sunset hour angle becomes undefined for parts of the year - continuous daylight or darkness - and the simple formulation no longer applies.