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Solar Radiation

Free Solar Radiation calculator with clear step-by-step results.

About Solar Radiation

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.

Formulas

Solar declination

Declination = 23.45 x sin(360 x (284 + day) / 365)

Ground irradiation

Horizontal = extraterrestrial x clearness index

Worked example

With the default values below, Solar Radiation returns Daily irradiation on the tilted surface of 32.12. Change any input above and every figure here is recalculated in your browser.

Inputs used

Latitudeaccepts -66–66 degrees
45 degrees
Day of the yearaccepts 1–366
172
Clearness indexaccepts 0.05–0.85
0.55
Surface tilt from horizontalaccepts 0–90 degrees
35 degrees

Results

Daily irradiation on the tilted surface
32.12 MJ/m2
Daily irradiation on the horizontal
23.06 MJ/m2
Extraterrestrial irradiation
41.93 MJ/m2
Daylight hours
15.43 h

Step by step

  1. 1Values used
  2. 2Solar declination
  3. 3Ground irradiation
  4. 4Daily irradiation on the tilted surface= 32.12 MJ/m2
  5. 5Daily irradiation on the horizontal= 23.06 MJ/m2
  6. 6Extraterrestrial irradiation= 41.93 MJ/m2
  7. 7Daylight hours= 15.43 h

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What clearness index should I use?

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.

Why does the calculator stop at 66 degrees latitude?

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.

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