# What FOV would render Ultrawide (21:9) on a 16:9 monitor?

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?

• Too broad. Changes game by game. – Ave Jan 9 '16 at 22:54
• seems like a math question – Aequitas Jan 9 '16 at 23:01
• After looking at the maths I agree with @ardaozkal there's no way to know this as it will change depending on the vertical FOV of the game, and each game would have a different vertical FOV. But I'm not very good at maths, so I may be wrong. Either way I think this questions would be better on the mathematics SE. – Aequitas Jan 9 '16 at 23:08
• Thank you, I originally thought to ask it there, and you're probably right. I was really only interested in it for gaming purposes. A friend of mine swears by his 21:9 monitor, while I've advocated for 4k gaming on the principle that (at the same width and horizontal resolution) 21:9 is essentially letterboxing the 4k screen by chopping it off. The different FOV was the only missing piece, and I was trying to see if there was an easier way than just trial/error. I decided not to ask it in Mathematics because I didn't need exactness, but I appreciate the suggestion and comments! – Atlantic Jan 10 '16 at 4:34

``````r = aspect ratio = w/h
r= 16/9
H = 2arctan(tan(V/2)*w/h)
H = 2arctan(tan(V/2)*r)
``````

for `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`, `w=16` and `h=9`, solve for `V`.

• Thank you for breaking it down for me! This is very helpful. – Atlantic Jan 10 '16 at 4:35
• @Atlantic sorry I had a little maths error, I mistakenly had w/h (ie r) for the vertical fov formula as well, this is obviously not the case and should have been h/w instead. I've fixed it now. – Aequitas Jan 10 '16 at 10:21
• also keep in mind, i'm not an expert and am just guessing, so take it with a grain of salt – Aequitas Jan 10 '16 at 10:22
• Thanks again, @Aequitas. I'm no expert either, and I believe an expert's explanation would be above my head. Your formula was the perfect, simple answer I was looking for, something to give me a ballpark figure and starting point! – Atlantic Jan 12 '16 at 2:42