What would I have to set the FOV to in a game to be able to see the same picture horizontally on a 16:9 monitor as I would on a 21:9 monitor?
r = aspect ratio = w/h r= 16/9 H = 2arctan(tan(V/2)*w/h) H = 2arctan(tan(V/2)*r)
V = pi/3 (60 degree vertical FOV),
r = 21/9
H = 1.86 H = 106.6 degrees
Then we solve for the vertical FOV for this horizontal FOV on a 16:9 monitor:
V = 2arctan(tan(H/2)*h/w) V = 2arctan(tan(1.86/2)*(9/16)) V = 2.35 V = 134.5 degrees
So if the game has a 60 degree vertical FOV in 21:9, you would need to set the horizontal FOV to 106.6 degrees and then set the vertical FOV to 134.5 degrees on the 16:9 monitor to get the same horizontal FOV.
So if you wish to render ultrawide on a 16:9 monitor you will need to be able to modify both vertical and horizontal FOV which isn't very common in games. If the game does have it then simply use the maths above substituting in the games
V (in radians) and
r=21/9 and solving. Then using that
h=9, solve for