# Is there a math formula to make font the same actual size on a 55“ and 65” monitor hung next to eacother?

So I have a 65" screen and a bunch of 55" screens (1080x1920) in these big panels. They are turned portrait and flush at the top. So I'm trying to figure out if there is math to easily make the font, margins and line breaks look the same across the different size monitors.

I can't just guess and check because the screens are kept off-site.

Any help would be greatly appreciated.

The height of an display is

``````h(d) = d * cos( tan^-1 ( a / b))
``````

Here, `d = 55"` is the diagonal of the screen in inches, and `a = 1920` and `b = 1080` are the horizontal and vertical number of pixels. `tan^-1` is the inverse tangens or arctangens. You can use WolframAlpha to calculate this.

``````h(55") = 26.96"
h(65") = 31.87"
``````

Thus, you get your desired ratio by `h(65") / h(55") = 1.18`.

• or, you can simply divide 65 by 55, which is 1.18. The aspect ratios are the same, so the problem is simple scaling – Yorik Sep 8 '17 at 15:04

If `a` is the aspect ratio (`W/H`) of your display, then

``````D²=W²+H² =>  D²=H²*(1+a²)
``````

hence

``````H=D/sqrt(1+a²)
``````

With two displays:

``````H₁/H₂=(D₁/D₂)*sqrt((1+a₂²)/(1+a₁²))
``````

And if the aspect ratios are the same (`a₁==a₂`), you get the simple:

``````H₁/H₂=D₁/D₂
``````

If you know the physical width and height dimensions of the TV screen then you can just make the working file that size and then export at 1920x1080 pixels.

The left is a 55" TV and the right is 65".

I got the dimensions from Wikipedia - Display size

• That sounds way easier than what I was doing. I figured out the 65" screen is 33.86 pixels per inch and the 55" is 40.08 pixels per inch and then use that to figure out how many inches each object would end up being. – horribly_n00bie Aug 8 '17 at 16:37