I would like to convert a rectangular beam shape given in Horizontal and Vertical beam angle, into solid angle representing the surface area in steradians of projected light. For example a light projection that has a 120° H beam by 5° Vertical beam pattern.
It would be helpful if this could be represented in a geometric form that can be used in an Excel Spreadsheet that allows one to input a horizontal beam angle and a vertical beam angle and then output the area in steradians. Given that a sphere has $4\pi$ sr and a hemisphere is $2\pi$ sr I was approaching this for example above that 120°=3.1414 sr or 1/3 of a sphere, and 5°= 0.00597 sr, I thought if there are 120 sections of 5° vertical sections this becomes a total area of 0.7164 sr. Then second guess I thought that there are only 24 vertical sections that are 5 degrees wide in the total horizontal area of 120° area. That yields only 0.1435 sr which seems unbelievably small. I came to the conclusion I need help and found this forum trying to find the solution.
I reviewed many questions that are similar. This is my first post, and I'd appreciate any help and guidance trying to figure where I have gone wrong in the application. Thank you in advance