Clear-Sky Solar Radiation Calculator

Model clear skies using solar geometry only. Account for elevation, tilt, and reflective ground inputs. Export results to share, compare, and validate calculations easily.

Calculator

North positive, South negative.
East positive, West negative.
Example: Pakistan is +5.
Uses your local clock time at the site.
Higher elevation increases transmittance in the simple model.
Both require the computed zenith angle.
Estimated DHI = fraction × GHI.
0 = horizontal. Use >0 for tilted POA output.
0 = North, 90 = East, 180 = South.
Typical: 0.2 soil, 0.6 snow, 0.1 water.
Integrates clear-sky GHI across the day.
Smaller steps improve accuracy, increase compute time.

Formula Used

1) Solar geometry

The calculator estimates solar declination and equation of time using a compact NOAA-style approximation, then builds true solar time and the hour angle. The zenith angle is computed using: cos(Z) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H), where φ is latitude, δ is declination, and H is hour angle.

2) Extraterrestrial irradiance

The extraterrestrial normal irradiance is: I0n = Gsc × E0, where Gsc = 1367 W/m² and E0 is the Earth–Sun distance correction from day-of-year.

3) Clear-sky global horizontal irradiance

Two options are provided. The Haurwitz model estimates clear-sky GHI from zenith: GHI = 1098 cos(Z) exp(-0.057 / cos(Z)). The simplified transmittance option uses an air-mass attenuation: GHI ≈ I0n cos(Z) τ, with τ ≈ 0.75^m (1 + 2×10⁻⁵·elevation).

4) Tilted-plane (optional)

If tilt is greater than zero, the plane-of-array irradiance uses an isotropic sky model: POA = DNI·cos(θi) + DHI·(1+cosβ)/2 + GHI·ρ·(1-cosβ)/2, where β is tilt, ρ is albedo, and θi is the incidence angle.

How to Use This Calculator

  1. Enter the site latitude and longitude in degrees.
  2. Select the local date and local clock time at the site.
  3. Set the time-zone offset from UTC for the location.
  4. Choose a clear-sky model and a diffuse fraction estimate.
  5. Optional: add tilt, surface azimuth, and ground albedo for POA.
  6. Optional: enable daily total to integrate across the full day.
  7. Click Calculate to see results above the form.

Example Data Table

Latitude Longitude Date Time Model Clear-sky GHI (W/m²)
31.5204° 74.3587° 2026-01-13 12:00 Haurwitz ~650–900
40.7128° -74.0060° 2026-06-21 13:00 Simplified ~800–1050
-33.8688° 151.2093° 2026-12-15 11:30 Haurwitz ~700–1000

Values are typical ranges. Exact outputs depend on geometry and inputs.

Clear-Sky Solar Radiation Guide

1) Clear-sky radiation as a planning baseline

Clear-sky solar radiation is an ideal upper envelope for sunlight when clouds are absent. It helps benchmark sensor data, compare sites, and run best-case energy checks for solar and thermal studies. If measurements stay far below this reference on clear days, shading or dirt is likely.

2) Inputs that most affect the estimate

Latitude, day-of-year, and local time dominate the result because they set the zenith angle. Elevation can slightly raise estimates by reducing atmospheric thickness. Diffuse fraction controls the split between DHI and DNI. Tilt, surface azimuth, and albedo matter when you want irradiance on a sloped surface.

3) Solar geometry outputs you should verify

Zenith, elevation, and azimuth provide quick validation. Elevation should peak near solar noon, while zenith reaches its minimum. When elevation is below 0°, the sun is under the horizon and irradiance becomes 0.

4) Model choices and typical ranges

The Haurwitz option estimates GHI directly from zenith for fast screening. The simplified transmittance option combines extraterrestrial irradiance, air mass, and an altitude adjustment. Under strong sun and clear air, mid-day GHI often lands around 700–1050 W/m² depending on season and latitude.

5) Air mass and why low sun reduces irradiance

Air mass rises quickly as the sun approaches the horizon, increasing attenuation. Values near 1 occur when the sun is high, while values above 5 indicate low-angle sunlight. This is why sunrise and sunset estimates can change sharply within minutes.

6) Diffuse, direct, and tilted-plane components

DHI is set as a fraction of GHI, then DNI is inferred from the remaining horizontal beam component. For tilted surfaces, the tool adds beam on the plane, sky diffuse, and ground-reflected light. Bright ground (higher albedo) can raise plane-of-array totals, especially at steeper tilts.

7) Daily totals and integration step size

With daily totals enabled, the calculator integrates clear-sky GHI across the day. Many locations show roughly 3–7 kWh/m²/day under clear skies, varying with season and latitude. Smaller step sizes (such as 5–10 minutes) better capture the rapid ramps near sunrise and sunset.

8) Interpreting results and limitations

Use these outputs as a clear-sky reference, not an all-weather forecast. Aerosols, water vapor, and thin haze can reduce sunlight even without obvious clouds. For higher precision, tune diffuse fraction using measurements and apply site-specific atmospheric inputs when available.

FAQs

1) What is “clear-sky” solar radiation?

It is an estimate of sunlight intensity assuming no cloud cover. It provides an upper reference curve for a location’s solar resource and is useful for benchmarking instruments, designs, and best-case energy calculations.

2) Why do I need latitude and longitude?

They set the site’s position on Earth, which determines the sun’s path across the sky. Longitude also shifts true solar time relative to your clock, changing hour angle and irradiance at a given local time.

3) How should I choose the diffuse fraction?

Use a small value for very clear conditions and a larger value for hazy conditions. If you have measured GHI and DHI, set the fraction to DHI divided by GHI to match your site and season.

4) Why is irradiance zero at night?

When solar elevation is below 0°, the sun is beneath the horizon and direct sunlight cannot reach the surface. The calculator sets GHI, DNI, and DHI to zero to reflect nighttime conditions.

5) What does plane-of-array (POA) mean?

POA is the irradiance on a tilted surface, such as a solar panel. It combines beam incidence on the panel, diffuse sky light, and ground-reflected light based on tilt, orientation, and albedo.

6) Why do results change with elevation?

Higher elevations generally have thinner air above them, reducing attenuation and increasing transmittance. In the simplified option, elevation slightly boosts the clear-sky estimate to reflect this reduced atmospheric path.

7) How accurate are the daily totals?

They are clear-sky numerical integrations, so accuracy depends on step size and model assumptions. Use smaller steps for better resolution, and remember real daily energy is often lower due to clouds and atmospheric variability.