Solar Radiation Calculator
Estimate the solar radiation reaching a horizontal surface at any location and day of the year. Use this when sizing solar panels, planning agricultural operations, or modeling energy budgets.
About this calculator
Solar radiation at the top of the atmosphere varies slightly throughout the year because Earth's orbit is elliptical. The solar constant (1367 W/m²) is corrected by an eccentricity factor involving the day of year, then reduced by two cosine terms: one for the site's latitude and one for the solar declination angle. The formula is: H = 1367 × (1 + 0.033 × cos(2π × dayOfYear / 365)) × cos(latitude × π/180) × cos(declination × π/180). Declination is the angle between the sun's rays and Earth's equatorial plane; it ranges from −23.45° in December to +23.45° in June. Together, these factors determine how much solar energy strikes a flat surface per unit area under clear-sky conditions.
How to use
Suppose you want solar radiation at latitude 40° on day 172 (June 21), when solar declination is approximately 23.45°. Step 1 — eccentricity factor: 1 + 0.033 × cos(2π × 172 / 365) ≈ 1 + 0.033 × cos(2.96) ≈ 1 − 0.032 = 0.968. Step 2 — cos(40°) ≈ 0.766; cos(23.45°) ≈ 0.917. Step 3 — multiply: 1367 × 0.968 × 0.766 × 0.917 ≈ 928 W/m². This represents peak instantaneous clear-sky irradiance on the summer solstice at 40° latitude.
Frequently asked questions
What is the solar constant and why is it used in solar radiation calculations?
The solar constant (1367 W/m²) is the average power per unit area received from the sun at the outer edge of Earth's atmosphere when the Earth-sun distance equals its mean value. It serves as the baseline for all surface irradiance estimates. Because Earth's orbit is slightly elliptical, the actual extraterrestrial irradiance fluctuates by about ±3.3% over the year, which the eccentricity correction term accounts for. Without this baseline, it would be impossible to scale radiation estimates to real physical units.
How does solar declination affect the solar radiation calculation?
Solar declination is the angle between the sun's rays and Earth's equatorial plane, ranging from −23.45° at the winter solstice to +23.45° at the summer solstice. A higher declination in summer means the sun is more directly overhead at mid-latitudes, increasing the cosine term and boosting calculated irradiance. Conversely, low winter declination produces a smaller cosine value and lower radiation totals. Accurate declination input is therefore critical for seasonal energy planning.
When should I use a solar radiation calculator for agricultural or energy projects?
A solar radiation calculator is most useful during the design phase of solar PV systems, greenhouse siting, and crop evapotranspiration modeling. Engineers use it to determine peak and average irradiance values that drive panel output estimates. Agronomists rely on it to predict crop water demand and photosynthetically active radiation. It is also used in building energy simulations to assess passive solar heating potential throughout the year.