Daily Solar Radiation Calculator

Calculator

Enter location, day, and estimation method

Use the date OR the day-of-year field. Date takes priority when filled.

White theme · Responsive grid

Latitude (°)

North positive, South negative.

Altitude (m)

Used for clear-sky radiation.

Date (optional)

If set, auto-computes day of year.

Day of year (1–366)

Used when date is empty.

Estimation method

Choose based on available data.

Tilted plane estimate

Isotropic model + Erbs split.

Sunshine hours, n (h)

0 to N (day length).

Angstrom a_s

Typical default 0.25.

Angstrom b_s

Typical default 0.50.

Clearness index, Kt

Often 0.2 to 0.8.

Measured GHI value

Enter your daily total.

Measured unit

Conversion uses 1 kWh = 3.6 MJ.

Tilt angle, beta (°)

0 = flat, 90 = vertical.

Ground albedo, rho

Typical: 0.2 grass, 0.6 snow.

Example data table

Sample inputs and typical outputs for a clear day.

Latitude (°)	Day	Altitude (m)	Method	Key input	Hg (kWh/m²/day)	Kt	HT at 25° (kWh/m²/day)
31.52	120	200	Sunshine	n = 9 h	≈ 5.2	≈ 0.55	≈ 5.6
25.20	15	50	Kt	Kt = 0.45	Varies	0.45	Varies
-33.87	300	20	Measured	4.8 kWh	4.8	Derived	Calculated

Exact results depend on solar geometry and your selected options.

Formula used

This calculator combines standard daily solar-geometry with practical radiation models:

Extraterrestrial radiation (FAO-56): computes Ra from latitude and day-of-year using solar declination, Earth-Sun distance, and sunset hour angle.
Angstrom-Prescott: Rs = (a_s + b_s·(n/N)) · Ra, using sunshine hours n and day length N.
Clearness index: Hg = Kt · Ra for quick estimation.
Diffuse split (Erbs, daily): estimates Hd/Hg from Kt; then Hb = Hg - Hd.
Tilt transposition (isotropic sky): HT = Hb·Rb + Hd·(1+cosβ)/2 + ρ·Hg·(1−cosβ)/2 (equator-facing assumption).
Clear-sky: Rso = (0.75 + 2×10⁻⁵·z) · Ra with altitude z.

How to use this calculator

Enter your latitude and altitude. Use negative latitude for the southern hemisphere.
Pick a date, or leave date blank and enter the day-of-year.
Select an estimation method: sunshine hours, clearness index, or measured GHI.
If you want panel-plane energy, enable tilt and enter tilt angle and ground albedo.
Press Calculate. Results appear above this form under the header.
Use the CSV or PDF buttons to export the latest result.

FAQs

1) What does daily solar radiation mean?
It is the total solar energy received per square meter during one day. It is often shown as kWh/m²/day or MJ/m²/day for easy comparison.

2) Which method should I choose?
Use sunshine hours if you have n and local Angstrom coefficients. Use Kt when you only know typical clarity. Use measured GHI when you have sensor or weather data.

3) What is Ra and why is it important?
Ra is extraterrestrial radiation at the top of the atmosphere. It sets an upper limit for what can reach the ground and is the base for Kt and Angstrom estimates.

4) Why does the tool split into diffuse and beam parts?
Tilted surfaces respond differently to direct and diffuse light. Separating them helps estimate panel-plane energy using common transposition models.

5) How accurate is the tilted-plane result?
It uses a simple isotropic sky model and daily correlations. It is useful for planning and comparisons, but detailed design may need hourly data and anisotropic models.

6) What albedo should I use?
Typical values are 0.15-0.25 for grass or soil, 0.3-0.5 for light concrete, and up to 0.6-0.8 for fresh snow. Use local conditions for better estimates.

7) Why can Kt be above 1 sometimes?
Due to measurement noise, local reflections, or model mismatch, calculated Kt can slightly exceed 1. Values far above 1 usually indicate input or unit issues.

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