What is the view perspective angle of most 2.5D isometric games

Question

I examined several quite popular games to determine what perspective angle they are using. For the purpose I created a grid that is 45 and 60 degrees isometric viewed and put it onto a screenshot (of Diablo II in this case). None of these grids fit to the game's perspective. So I tried to find the angle that fits best to the perspective and it is close to 53.5 degrees. However, this number seems like coming from nowhere and I believe there is a strong logic behind the number that defines the perspective angle. I tried 9/16 * 90 degrees and 3/4 * 90 degrees (coming from ratios of screens resolution 16:9 and 4:3) but none of my assumptions seem to be correct. Here are screenshots of what I mean:

60 degrees

45 degrees

Something between the two - 53.5 degrees - quite near to the real number

I really need to know what the real degrees are and where it derives from. Any help is quite appreciated! Thank you!

Answer 1

I believe your intuition was correct, just not your formula.

atan(4 / 3) = 53.1301024 degrees

This ratio can be useful because it forms a Pythagorean triangle, meaning that the length of the diagonal is an exact integer value.

Answer 2

The camera angle used by most "isometric" games is actually 30 degrees (a true isometric view where the x, y, and z axis have the same length is 35.264 degrees). The reason for this angle is so that the width of the tile ends up being twice its height. This way you can get an even 2:1 ratio when drawing the diagonals so the tiles line up neatly without any gaps.