The FPS Aim Trainer’s “zoom sens auto scale” option goes by focal length. When I first saw the term “focal length” I was interpreting it wrong: I thought it had something to do with a projection in the 3d game world. That’s not it at all - instead imagine that your monitor is a window into the 3d game world, and you are sitting at the correct distance away from your monitor to see the correct FOV. So with a high FOV you are sitting really close in order to see further left/right/up/down past the window, and when you go to a lower FOV (such as zooming in), then you move your eyes further away from the window so that less is shown through the window. Focal length is just the distance from your eyes to the window/monitor (or the distance your eyes *would* be in order to be at the right FOV for the game you are playing).

You can use focal length to come up with a circumference for your view into the 3d game world, and the idea of scaling your mouse sensitivity according to focal length is to maintain the same relative multiples between monitor and mouse for your hipfire and ads/zoom circumferences.

The math to get the relative multiplier on ADS sens relative to hipfire is: __tan(<ADS FOV> degrees / 2)/tan(<Hipfire FOV> degrees / 2)__.

Tammas#3731 put together an interactive desmos calculator that can do this quickly.

A common example is Widowmaker’s scope. Most OW players use 103 16MF9, and Widow’s scope is hard-coded to 30 vML. 30 vML on a 16:9 monitor is 50.9419751° horizontally. So to do focal length scaling, we just do this:

tan(50.9419751 degrees / 2)/tan(103 degrees / 2)= 0.37890917574. (people use 38% or 37.9% when they type it into OW’s options menu)

If you wanted to use this scaling method for Fortnite, then it's slightly more complicated since Fortnite scales your sensitivity as your FOV changes even before your scope sensitivity multiplier from the options menu is applied. Fortnite's hipfire FOV is 80 (and ADS FOV with most weapons is also 80, but it moves the camera forward in space to make it feel like you zoomed in) while the scoped AR uses 40 FOV and the scoped sniper used 15 FOV. The multiplier that Fortnite applies for the scoped AR is 0.5 (40/80), and for the scoped sniper it applies 0.1875 (15/80). So the multiplier we use in the options menu has to keep this in mind too.

tan(40 degrees / 2)/tan(80 degrees / 2)= 0.43376283428 (desired for scoped AR)

tan(15 degrees / 2)/tan(80 degrees / 2)= 0.15689733697 (desired for scoped sniper)

So to get your scoped AR to use the correct multiplier, you'd need to set your scoped sensitivity to __0.86752566856__ (which is 0.43376283428 / 0.5). And to get your scoped sniper to use the correct multiplier, you'd need to set your scoped sensitivity to __0.8367857971733333__ (which is 0.15689733697 / 0.1875).

TLDR: somewhere between 0.836 and 0.867 will get you pretty close to the right scoped sensitivity multipliers, depending on the weapon you are using.