# What's the simplest way of calculating total radiation on a tilted surface knowing time, date and geographical location?

I am working on a model and must calculate the total solar radiation in W/m² on an inclined plane.

I need a function to calculate this value given longitude, latitude, date, time, tilt angle, and azimuth. The funtion can assume a clear sky.

1. Can someone direct me to an example where the above is calculated? All the resources I found so far do not provide an example of a complete calculation from start to finish.

2. Would it be simpler to calculate from first principles or would interpolating from an existing database be the way to go?

• I don't quite understand what you require. Do you need the derivation of the function to calculate irradiance for any point on earth, or just the data for it?
– noah
Commented Apr 24, 2022 at 11:09
• @noah I was looking for the derivation, but in some cases with a complex function like this it might be easier to interpolate from existing data. So if the latter option is easier, I'd like to be pointed to some resources I can use. But the actual derivation is what I am originally after. Commented Apr 25, 2022 at 12:25
• The irradiance at the surface is a very complex function if you want to have accurate data, so if what you need is to have a good approximation of the real irradiance, you'll have to use measurement data as your base anyway. If this is just an exercise to calculate it in a simplified way, then measurement data is not really the way to go, and you could start from first principles (which might be way off in some places). I assume you need the former, ist that right?
– noah
Commented Apr 25, 2022 at 12:30
• @noah I have some texbooks showing how to calculate the AST and sunset/sunrise times but there is a gap between those calculations and how to determine the total (direct and diffuse) radiation on an inclined plane. If you could direct me to a resource it would be much aopreciated. Commented Apr 26, 2022 at 9:23