Badmon

I thought I'd share a formula I have used that matches my own preferences pretty perfectly for a "one size fits all" scope zoom scaling, (an updated "uniform soldier aiming" if you will, for games that use many scope zoom levels).
As many of you agree focal length or "0% monitor match" is the mathematically principled way to scale, with arbitrary monitor distances effectively being just a hack to mitigate the natural slowdown effect that zooming-in creates when using focal length scaling. 
While playing games like Battlefield 4 / 1 or the newer Cod's, I always ended up with the coefficient set to 0% for low-zoom scopes, and then each scope's individual slider gradually increasing in sensitivity the higher the zoom level.
It was always fairly apparent to me that commonly used monitor distances like vertical 100%, 133% or especially 178%, are too fast at low-mid zooms of irons / red dots etc, whereas focal length scaling is always much too slow at high zooms / sniper scopes. I think this experience is also shared by many others.
So I have taken the monitor distance hack a step further to allow what is effectively a dynamic coefficient via a simple calculation based on the start and end FOVs. This is nothing new of course, but unlike other variable methods like Viewspeed or Jedi's trick that also do this, it scales much more broadly by comparison. Converging to focal length scaling for the lowest zooms, and approaching an asymptotic monitor distance limit at an "infinitely high zoom" (or a hard cap).
Here's a graph of the formula with regular 133% vertical monitor distance and focal length scaling for comparison. By replacing the monitor distance coefficient with simply Limit*(1-(ZoomFOV/HipFov)) the coefficient approaches a value of zero when the two FOV's are close together, and gradually approaches the limit the more they diverge.
https://www.desmos.com/calculator/rlrmeml65f

If you enter the hip and zoom vFOV's with the sliders, the graph will calculate a monitor distance based on the variables entered for any games ADS FOV level exposed on this site.
A limit of 2 would mean the maximum monitor distance is 2 for when "zooming to infinity" - the transitional shape would then be like a logit function with the midpoint of 0.5x zoom sensitivity multiplier occurring at exactly half of the base FOV (i.e coefficient of 1 at the midpoint). This value probably makes the most sense, but I personally prefer a limit of 1.5, as seems the most appropriate for the zoom amounts we tend to use in games. As an example, this results in the highest zoom scope I used in BF4 having roughly 130% mdv, and the red dot sights having around 14% mdv when scaled from hipfire. The power could be raised to stay closer to focal length scale before approaching the monitor distance limit, but probably best to leave at or around 1-2.
This is still just an arbitrary solution of course and I am not claiming it is objectively better than any established method, just an approach that very closely approximates my own preference formulaically - with pre-set limit / power of 2 I do believe it would be better for users as a "one click" option than the existing relative / USA with coefficient options.

Cool, I'll let you know when I have a beta version of it up and running so you can verify it
I'll name them Jedi's Trick - Horizontal and Vertical maybe.
I'm working on a lot on new features like swapping input and output with a click (to reverse the calculation) and adding games favorites so they appear in the top of the list, I'll include this in the next update.

0% MM will be enough. No, it will not!
I will try to make this article simple. To make it understandable not just for the regular settlers here. On this site there is a lot of stuff you like a newcomer probably do not understand. They will instruct you to read a instructions which will make you even more confused at the beginning. Because it’s hard to imagine something behind the text or formulas. Most of the time there is a talking about percentage of Monitor Distance ex.: 0% MM. What does it mean? I will show you on example with 100% Monitor distance – vertical (MDV). Converting from Windows to Game.
In Windows desktop measure the distance traveled by the mouse, if the cursor moves across the entire screen, in the vertical axis. In other words, if you move the cursor from the top edge of the screen to the bottom.

I measured 2,7 inches. Now if I want to reach the center from the top edge of the screen. How much distance must mouse travel? A half right => 2,7/2 = 1,35 inches. So if you set a calculator here to match your game for 100% MDV. It means that if you move your mouse vertically about 1,35 inches. The cursor on screen in game will travel exact same monitor distance like in Windows. Ends at the edge of the screen.

Mouse distance 1,35 inches = A half of monitor distance in Windows and game. So at this mouse distance. We can say, that sensitivity is same for both Windows/Game. 
However the sensitivity is same only for one point on the screen = one mouse distance. Any other mouse distance lower or higher from 1,35 inches. Will result in different monitor distance in Game. More or less. Because of 2D/3D projection.

I created a graph that allows me to see the projected path of the cursor on the screen for several mouse distances. So you better understand what's going on. Graph is simulating one quarter of screen. We don't have to simulate the whole screen, because the rest will just be mirrored to this quarter.

Graph on right side is showing cursor path of our example 100% MDV. Dots represents a cursor path. Green simulates a Windows. Red game. But as you can see, mouse sensitivity is same only for one point = one mouse distance = one monitor distance. All other mouse distances will result in a different monitor distance.

Ideally, we want all pairs of points (Green/Red) to become one. But it’s mostly impossible to achieve it. Recently I found out how to find the smallest difference between points for all mouse distances.
Here comes the Jedi’s mouse trick:
Set the monitor distance to 100% MDV and note the 360° distance = 13,1815.
Set the monitor distance to     0% MDV and note the 360° distance = 11,3097.
Manually adjust the sensitivity so that the 360° distance matches the average of both values (13,1815 + 11,3097)/2 = 12,2456. By this you will receive the smallest deviation for all points. I will demonstrate it on a Square graphs (ratio 1:1).
This method looks easy. But it's practically 11 years of development behind it (With pauses of course). 

You can see the difference visually. But we can compare it also with numbers. I will use sum of absolute monitor distance deviations (SoD) for comparing with 0% MM. We don’t care if the deviation is positive or negative. We just need to know absolute deviation. If the SoD value is lower, it means that method has a lower deviation for all monitor distances. It will be not to much precise. Because we are comparing just 9x points on screen. But it’s enough to demonstrate the differences.
Windows to Hipfire:

Windows to AWP Zoom 1:

Hipfire to AWP Zoom 1:

If you do not want to adjust the distance for all points, but maybe only for 40%. Repeat the same procedure, only use 40% instead of 100%. This give you the smallest deviation for all monitor distances in the range of 40% of monitor screen. 
There is many people who are trying to guide me to use 0% MM. No matter what. But they don't understand that they're taking me back 11 years to the exact moment that led to the development of my Mouse sensitivity utility.
I understand that 0% MM is mathematically correct. But when I leave the game back to Windows. I can't hit the icons, and it makes me mad with 0% MM it’s even more noticeable. Because what we are doing in Windows most of the time? We are opening and closing windows. And to close a window you have to move cursor all the way to upper right corner of screen. And there is the biggest deviation for 0% MM. That’s why some people like to use 100% MDH/V. 
Jedi’s mouse trick is a compromise between tracking (0% MM) and flicks (100% MM). 

Beta can be tested here!
There's a few known bugs, in particular with swapping the calculation when using distance.
Note that favorites etc might get reset if necessary, but I hope it's not needed.

Version 3.0 is out
Enjoy a International Students' Day. Which is a sad memory of nazis crime on students in my country.
New method of converting sensitivity which is taking into account all points (all monitor distances) is live :)
- Complete reconstruction of the utility
- Possibility to compare two games / aims
- Option to adjust the monitor distance for "All points" (4000x points)
- The sensitivity ratio is now the average of all monitor distances (4000x distances).
- Language selection added (Czech / English)
- Modified manual and quick start guide
- Source Games (HL2, CS:S, CS:GO, TF2, etc.) renamed to: Counter-Strike: Global Offensive 
- Goldsource Games (HL1, CS 1.6, TF1, etc.) renamed to: Counter-Strike 1.6
- New YouTube video created
Note: A few days before completing this version, I learned how to automate monitor distance adjustment for all points. Because implementation will require a lot of effort, I'll keep it for another time.
download link in video description

Just added a new feature for advanced and advanced plus modes where you can see your pixel to count ratio.

Default mode will show the maximum for any aim, while advanced mode will show details for each aim.
A pixel ratio of 1 means that your crosshair moves exactly 1 pixel for every count:

Going lower means an even smoother movement, like 0.5 pixels/counts:

Or 0.25:

Ideally you should not be over 2, as that theoretically means you are unable to aim directly at something on the pixel you skip. Shown here as 2 pixels/count:

And 4 pixels/count:


Now as mentioned this is theoretical, the reality is that even at 2 pixels/count variations such as bullet spread will in most games far outweigh this pixel you can't aim at. Also for this to have any real impact you have to aim at something 100-150+ meters away without a scope.
So the bottom line is that it certainly doesn't hurt to make sure the pixel ratio is below 1, but it is by no means critical. Over 2 should be avoided.

That was a bug regarding aspect ratio, check again now

If you want something added to this main post, you can add a comment and I'll consider adding it. It doesn't just need to be about these methods, anything of value to general people in one place is the idea.
My aim is to make this as non-technical as possible and so I'll try keep the language as consistent as possible, but there is some language you'll need to know and understand in some form.
Key Language
How to use the calculator
Why there isn't one perfect conversion for 3D games:
When playing a 3D game the information is displayed through a 2D monitor. We encounter the same problem map drawers had many years ago, there's many solutions that go about it in many different ways but all have their benefits and drawbacks. Gnomonic projection is what 3D shooter games use and is what we're all used to and it works by taking points on the sphere through to a camera and where it intersects a plane which is the monitor, we colour the pixel that colour as you can see if you click on the images, look at the car in the CS:GO images. 

This creates distortion at the edges of the image as rays that get closer to the max FOV of 180° get put really far away on the plane so angles on your screen are not preserved for different FOVs (i.e. halfway between your screen and the edge on a 90° FOV isn't 45° in game) what this means is that when you have two different FOVs there will not be two respective sensitivities that match everywhere. This has lead to many methods of converting sensitivities that all have their pros and cons as there is no perfect conversion. The lists of pros and cons below should help you decide.
Conversion Methods:
360° distance:
This is the method most people think of when wanting to convert sensitivity, and is the one people usually try do themselves with some paper measuring the distance and then turning 360° in game and matching sens so the distance is right. This website can do this for you much more accurately but there are some caveats. 
This method matches angles around you in 3D space. So for example every 360° swipe will be the same, and every 180° behind you onto a target will be the same. This is good for general spacial awareness if you know someone's behind you etc.. but it's good for not much else. Plus if you know someone's behind you the other methods as you will see will put you in the right ball park anyway (unless the FOV is very different) and then you can aim more accurately with those other methods as you will see.
This method will only really work if the FOV is exactly the same across the games (but every conversion method would give you the same value anyway) or you're into general spacial awareness,  I give that as a pro of the method but not the sole reason to use it.
Monitor distance:
This method matches your sensitivity perfectly for a specific point(s) on your monitor. You can imagine a ring around your crosshair where it matches but this isn't strictly true. Why is this better than 360 distance? Well when you aim at something, your mind doesn't calculate the angle between you and your target and then aim that much angle, instead we're more bound by how much distance there is on the screen between our crosshair and them. This means you may not be accurate turning around 180° but you'll be more accurate for the targets on your screen around where you've set your perfectly matched 'ring' up. This is good as you'll be better aiming at targets on your screen over different FOV's and also, due to using it matching distance on your monitor, we can use it to convert hipfire sensitivity to ADS sensitivity. Anyone who's tried to use 360 distance on a scope will see what I mean, and why 360° distance is bad for muscle memory aiming at targets near your crosshair.
What about the different percentages??
The percentage is the ratio of the distance from your crosshair to the point on your screen you want to match on and the edge of your monitor. In simpler terms, it's the point from the centre to the edge you want to match. 50% is in the middle of your crosshair and the edge of your monitor, 100% would be matching at the edge of the monitor and 0% would be matching on the crosshair.
This is shown best on the image below, taken from this video which is a very good watch if you want more understanding. 

What's the difference between vertical and horizontal monitor match??
The image above shows the horizontal monitor distance match, going from the centre to the left and right edges of the monitor. Vertical monitor distance match is as if you rotated the scale 90° and fit it on the monitor, so instead of going to the centre to left and right edges it went from the centre to the top and bottom of the monitor.
There's both options as the vertical match is aspect ratio independent (doesn't matter how wide your monitor is compared to how high it is) and therefore easier to talk about as if you have a 4:3 monitor and matched horizontally to the left/right edges of the monitor that would be 100% monitor match, but if you were to talk about the same distance (when converting) to someone with a 16:9 monitor it would be 75% horizontal monitor match. But if you were talking about 100% vertical monitor match it would be the same for both 4:3 and 16:9 monitors. So if you talk to someone about it on the forum you will need to say which you're using, and if horizontal you'll need to give the aspect ratio of your monitor.
Keep in mind there's nothing fundamentally different between them they will both give you the same values if you use the same converted mm% e.g.
100% vertical mm -> horizontal mm (16:9 monitor) 100%*(9/16) = 56.25% So 100% vertical monitor distance match will give you the same sensitivity values as 56.25% horizontal monitor distance match on a 16:9 monitor
30% horizontal mm -> vertical mm (4:3 monitor) 30%*(4/3) = 56.25% So 30% horizontal monitor distance match will give you the same sensitivity values as 40% vertical monitor distance match on a 4:3 monitor
What's the best percentage monitor distance match??
This has been of much debate on this site, and I guess will continue to be as people have different opinions and so I'll try give you it as unbiased as possible.
The best % to hold up mathematically is 0% and from experience myself and should probably be under it's own name you may hear it called zoom ratio but I'll keep it with this section for sake of simplicity. This is the best I've tried after I've gotten used to it. Every other % match is essentially just arbitrary change in sensitivity that may happen to be close to preference, and if you chose it it's down to personal preference, for example 100% 4:3 horizontal monitor distance match (75% 16:9 horizontal monitor distance match) is what CS:GO use for their scoped sensitivity conversions so if you've gotten used to this and you're some pro legendary AWPer, this might be the way to go for you when converting in other games.
One thing to bare in mind when using anything other than 0% everything around the crosshair not on your mm% is essentially not matching at all and you're mind is interpolating the sensitivity, so muscle memory will take longer to build but with 0% you're muscle memory is at the crosshair, so things like micro adjustments when making a big flick (which is what happens in every flick, you're not perfect), and controlling recoil back onto someones head is perfectly matched across all FOV's and this is the massive advantage of low % matches.
The video below will show you what I mean by only certain points match, and that everything other than those points is too fast or too slow as your mind has to guess:
This video shows 1-100% monitor match with the relative feel of speed The only real advantage of larger % matches is when making large flicks out of your view onto a specific point, and the speed feels 'right' but with 0% your flicks will feel slow at first but after a while they'll be really accurate no matter where they are on screen as it's just constant really quick micro adjustments.
Here's some examples showing a low mm % vs a high mm%.
You can see when aiming at the target with the high mm%, the accurate point is further away from the target, so the sensitivities in the middle will be made up by your mind as it has no reference to an accurate sensitivity you converted from.  Your mind would learn these made up sensitivities over time with the larger mm%, but in my mind I'd rather have muscle memory for everywhere on the screen through these small adjustments with a low mm %.
With a low mm% you can see here there's been 4 'micro adjustments' which can make it's way onto the target with multiples of your perfect accuracy. You can imagine this tending down to smaller and smaller intervals as you approach 0%


Math for nerds:
Here's a link to a geogebra page where you can hopefully better understand the maths and what's going on, with thanks to capta:
https://www.geogebra.org/m/adAFrUq3
View speed:
Viewspeed tries to unify the perceived camera speed across different FOVs while using a constant mouse motion. Since the FOV determines how many degrees are squished onto your screen, higher FOVs naturally look faster as there is more information moving, and low FOVs naturally look slower, and Viewspeed attempts to equalise this. And it does 'feel' right when you use it. But feeling the same in this case doesn't translate to best aim or muscle memory building. It suffers from the same problems as high monitor distance match percentages, aiming close to your crosshair is too fast for varying FOV's
Because viewspeed uses a sine wave (continually varying), when you calculate sensitivities over different FOV ranges, you get a varying equivalent monitor distance match percentages across FOV's. It lies around 60-80% for 16:9 horizontal match.
It's useful If you want to keep the mouse input relatively the same when you change FOV on the fly. It scales based on the chord length. This is the method that you would want to use instead of Monitor Distance Match, if you wanted the 'window to the game world' to influence the sensitivity. Your mouse input will not scale proportionately with the zoom. Instead, you wouldn't scale it at all. The result will be completely wrong for Hipfire, but when comparing sensitivity relatively before and after a change in FOV, it becomes useful. Subconsciously, you would want to scale your mouse input according to the change in image, so you would probably scale your mouse input to some degree, how half-assed of an attempt at doing so, depends on the person. This makes Viewspeed feel too fast. Drimzi made a solution to this in another post, where you specify how much you need to scale your input by, proportionately with the change in image (zoom), or none at all (viewspeed). Which makes a kind of slider between viewspeed and 0% monitor distance match bare in mind this is completely arbitrary.
Maths behind viewspeed - vertical here
I made a geogebra demo, which hopefully makes the maths more clear here: https://ggbm.at/mgw8cke4 Which came from this thread which hopefully has some more insight as to where it came from.
What's the difference between vertical and horizontal view speed??
In the same way vertical and horizontal monitor distance matching varies by the top/bottom edges of the monitor and left/right edges respectfully viewspeed does something similar too. @Drimziis the expert on this forum on this topic it seems, so I'll quote him:
Viewspeed - Vertical : An aperture (monitor) dependent conversion, scaling the sensitivity by the change in Vertical Chord Length. Viewspeed - Horizontal: An aperture (monitor) dependent conversion, scaling the sensitivity by the change in Horizontal Arc Length, as well as the difference between Horizontal Arc and Chord Lengths. The Viewspeed methods don't just change the measurement axis. They are both completely different methods. Viewspeed - Vertical should be using 1:1 measurements rather than Vertical. Horizontal is an older idea that was similar to Monitor Distance Match - Horizontal, but scaled by the difference in Horizontal Arc and Chord lengths.
tldr: So what's the best conversion?
0% monitor distance match (- vertical) unless you're really good and/or are more comfortable another method, even then it's worth trying 0% and seeing how it goes imo. This is the best method for building muscle memory fundamentally, but might not work well practically for really low sens players.
Also remember, don't copy other people's set up because they're good. Unless there's a good reason not to use what you're using for technical reasons, find what works for you. (I'm mainly talking about weird resolutions and stretching)
Other FAQ's
High DPI or Low DPI? (+ pixel skipping) :
This question get asks a lot and is unknowingly the wrong question to be asking. As explained in the key language section, DPI or as I will be changing to the right terminology here, CPI (counts per inch) is the number of counts registered and sent to your computer when you move your mouse 1 inch. Now a count is just telling your computer to move 'some' amount. and more counts coming in means just move that 'some' amount more. So changing DPI (CPI) will directly affect your sensitivity, but in neither a positive or negative manner. It will just make you move more lots of 'some' angle in game or more lots of 'some' distance on the desktop.
So the question should really be how do you decrease that 'some' distance/angle so that you can be more precise.
If you want to get a better understanding of this 'some' distance see this thread there's some nice gif's
Well for games that's by decreasing your sensitivity and then in turn increasing your DPI to keep the overall sensitivity (sometimes referred to as eDPI) the same. So if you half your sensitivity, you double your DPI. So yes, if you want more precision you should decrease your sensitivity and increase your DPI.
This video shows it very well, along with WPS skipping. Keep in mind he talks about pixel skipping, not angle skipping (which is what's happening)
Bare in mind:
This becomes solely placebo after a certain point Increasing your DPI too much can have a negative affect on your accuracy as your mouse starts interpolating to make up counts Some game's minimum sensitivity values mean that if you went too high with your DPI, you couldn't get the right sensitivity to match other games. This starts around 1600 DPI. This will change your desktop sensitivity (read next Q for recommendation) Windows pointer speed (WPS) 6/11 ? :
Windows pointer speed relates the that 'some' distance moved for each count mentioned in the prior question. The reason 6/11 is accepted as the right setting for gaming is that here the multiplier for that 'some' distance is 1, and 1 x anything is itself so this means the data coming from your mouse to motion in non-raw input games is as if windows wasn't messing with the data (even if it is still adding a slight delay/packet loss which is why raw input is the better option).
But 6/11 isn't the ONLY correct option as lots of places seem to state: here is the list of acceptable ones (this post has further correct options but they involve registry edits).
Control panel notch:
6/11 --> 1x count multiplier 4/11 --> 0.5x count multiplier 3/11 --> 0.25x count multiplier 2/11 --> (1/16)x count multiplier 1/11 --> (1/32)x count multiplier Why are these valid options? Well you can multiply all the multipliers by a integer to get back to 1x because they're all fractions in the form 1/n
What this means practically is that even with these options you'll never miss an equivalent spot where 6/11 would be correct, so no skipping.
This means if you use a higher DPI for games to be more precise (skip less angles) but it means your desktop sensitivity feels too high for you, you can chose one of these options to get it back to a desktop sensitivity you'd prefer.
Same desktop sensitivity too (adjustable DPI mouse) ? :
My recommendation here is for if you use 0% monitor distance match for everything, is to convert from your 'best aim' game to desktop as so (using windows desktop), then using this sensitivity to get sensitivities for all games. I'd also recommend using a lower WPS as talked about above if you use a low sensitivity as low DPI values can be output.  Why do this? Well it means that all your sensitivities in all games are the same, and if you wanted to increase your sensitivity in all games, all you'd have to do is increase your DPI, and all the overall sensitivities including desktop will increase perfectly without needing to calculate new sensitivities for each game.
Here's an example converting to windows to get the DPI, then back all your other games, keep in mind the right display scale from your windows monitor settings and WPS benefits from earlier:
keep in mind this only works if you use 0% monitor distance match for everything. If you want to use another method to convert to desktop DPI, you won't be able to convert back to the other games using desktop as the source, you'll need to use the game you converted from with the new DPI value and appropriate sensitivity. 0% will match the speed at the centre of the monitor which is perfect but as the cursor moves to the corners of the monitor it will feel slower as it's physically further away from you. You can reduce this feeling by moving your monitor back or in a perfect scenario have a curved monitor. As an aside this also applies to games, your sitting distance will less affect your perceived sensitivity the further away the monitor is, but there's more of that in the threads below along with the negatives, can't see small details.
You can convert to desktop using other methods like viewspeed, you just won't be able to convert from it to other games. 
Best cm/360°  ? :
There's no one value I can give you for this as at the end of the day it's down to personal preference, but I'll give you a few considerations for practicality. My assumptions here are based on a pretty average FOV for shooter games, around 103°.
First thing to consider is the size of your mouse pad:
My recommendation here is you can do at least 180° on your mouse pad and at most 360°. Why at least 180°, well if there's someone behind you and you start spinning and hit the end of your mouse pad before you can rotate enough to hit them you're pretty much dead if they're any good as you'll have to pick your mouse up move it back and swipe again, plus it gets pretty laborious if you have a large mouse mat. Why max 360°, well in most shooter games your main focus is aim, and if you can do more than a 360° on your mouse pad, you're giving up accuracy everywhere in your view for being able to rotate fully, then some more when you could've just moved that 'some more' distance in the first place.  What kind of games you play:
Some games may require a really high sensitivity for fast moving tracking on a large object, tbh the only thing that comes to mind is Minecraft but I'm sure there's other games out there... A swipe greater than 360° may be favourable here but only if you play only these games or you have a different sensitivity for these games. If you use this in a FPP game, you're using at the detriment of accuracy unless you have a really large mouse pad. Large mouse pad:
I've talked a lot about degrees turned on the mouse pad above, but for people with really large mouse pads they have the freedom to set the sensitivity however they want as following those guidelines may make the sensitivity too low for faster paced games or too low that if you convert with 0% it's hard to play with. The optimal range for this kind of thing seems to be about 30-40cm/360° At the end of the day go with what you are comfortable with but they're just some hopefully useful guidelines.
This thread is useful and goes into some more discussion also about mouse speed
Matching FOV by changing resolution  ? :
In some games, you can't match the hipfire FOV to another game because the FOV slider doesn't go high enough. There is a way around it which and I wouldn't recommend the hassle, but here it is:
By changing your resolution, you can shrink the image down so that your focal length (distance from camera to whole screen) changes to match the other game. You can do this by scaling down your image so you have black bars on each edge and the black bars contain the FOV that you're missing. For example setting overwatch's FOV (103) to the same as CS:GOs(106.26) you can hide the 3.26 degrees you're missing behind black bars on your monitor.

You can see the focal length is now the same as the images match up. But the bit around the outside would be the hidden FOV.
It's quite hard to imagine this, so here's a geogebra calculator/demo to show what's going on, enter your resolution on the top left and drag around the FOVA and FOVB nodes, notice the blue triangle on the left has a smaller size on the screen, the same focal length and the same FOV as FOVB:
https://www.geogebra.org/classic/wg83gxjc
You can see that this only works for making a smaller FOV bigger, the other way round your rendered image would have to be bigger than your screen so you'd be cropping loads of pixels. The output resolution is in the top left below the input.
Also note for this to work you need to in the Nvidia control panel set the scaling mode to none and make a custom resolution:

Thread references and useful topics:
 

you are totally right ! I read that Note completely wrong LOL. Well shoot I guess I had better get back on 1.072   Thanks !!

Yes I also convert from Windows to games with 0% monitor distance and got 1.072 for my sens. However, I found 400dpi at 1.072 was too high of a 360 so I run 300dpi and its the sweet spot for me at VFOV of 73.74. Also I spotted you use Monitor distance vertical for ads/scope however, I think it's better to use all conversions as monitor distance horizontal 0% or all monitor distance vertical 0% otherwise its kinda messy and confusing. Just my two cents though

@DPI Wizard is it possible to calculare from Windows 1920x1080 to CSGO 1440x1080 (Stretched) ? to have the same horizontal Monitor Distance sensitivity?

50% is the middle ground, the video isn't explaining it very well either and i don't think anyone but only 2 people understand what's really going on.
That's why i will take the time and explain this once and for all!
 
It's a very common mistake to think that you can match your desktop sens with a FPS game, because you cannot.
The best you can do is 50% and i will try to explain why.
 
Every FPS game uses the rectilinear projection methode to visualize the environment, this is because you need to create peripheral vision and the perception of depth but because you are projecting this image on your flat 2D monitor display, it's impossible too create real depth at all.
So to accomplish this perception they are "bending" the image creating a cylindrical shaped image and that's the arc that you see in the video.
 
A high FOV like in FPS games means forcing the image to bend because your display can't project the whole environment with a flat image the only solution is to bend it too create more space. but when you overdue the FOV increase the image will start to distort and somewhat collapse at a certain point. 
It feels like the image is bowed inwards like someone pushes a needle or pin into the center.
That’s why this effect is also called “pincushion distortion” which makes objects at the edge of the display unnaturally large in scale and will tend to misestimate the size and shape of objects, giving misleading visual information since the objects will rescale and significant decrease in size when turning towards them.
 
So, the in-game image is bent and your desktop surface image is not, even so they both are projected on the same evenly sized display. 
This means that the in-game image is in fact larger the the desktop image when it would be projected flat like the desktop image.
 
But since it's projected cylindrical, every object needs to "rescale" to fit on your display and that what's causing the "pincushion" effect and your mouse movement will act by it, meaning that when you turn towards an enemy at the edge of your display, your mouse movement will go faster then your desktop movement and your enemy will look bigger, but once you past the "50%" mark of your display (50% = pixel number x-axis: 480 / y-axis: 540 on a 1920-1080p counting from bodem left) the mouse movement will start to go slower then your desktop movement and your enemy will rescale and be smaler.
 
So your in-game mouse movement is not linear but your desktop mouse movement obviously is, meaning it's impossible to match your desktop mouse movement with your game across the whole line, but only at one point.
50% matching means that you synchronize your desktop mouse movement with your in-game mouse movement at pixel number x-480 and 1440  / y-540.
So the distance your mouse will travel to reach this pixel is the same between game and desktop. (but only at that point!)
Since this is the middle between the center and the edge of your display it's the best you can do too bring the deviation to a minimal across the whole line.
 
If you would take 100% match it would mean that the synchronization is at the edge of your display.
So the deviation between 0% and 74% will be larger then when you sync at 50%.
100% match will only be more accurate then 50% match once you past the 75% mark,
50% covers more of the spectrum then 100%, and that's why you need to sync at 50% and not at 100% for the most accurate result
 
Amen to that!

You convert using different methods depending on what you want to achieve.
 
360 Distance
360 distance will convert the sensitivity without any FOV compensation. The amount you rotate per mouse count is constant, and so the distance to rotate 360 degrees (or any other amount, like 45, 90, 180) is also constant. Since the FOV determines how many degrees are squished onto your screen, how sensitive the mouse feels will depend solely on the FOV. This method would have the most extreme change in perceived sensitivity when the FOV is changed.
My opinion: It is useful for converting hipfire sensitivity if you prefer to keep 180 degree flicks, but I would never recommend to use this for zooming/aiming. You will need to master all aiming styles, as low FOV will require micro finger movement and high FOV will require arm movement.
 
Viewspeed
Viewspeed V2 converts the sensitivity using the Sine trigonometric function for FOV compensation. The intended outcome is to make the perceived camera speed constant for all FOV while using a constant mousing motion. Since the FOV determines how many degrees are squished onto your screen, higher FOVs naturally look faster as there is more information moving, and low FOVs naturally look slower, and Viewspeed attempts to equalise this.
My opinion: The perceived sensitivity may be a little too high for low FOVs and too low for high FOVs. I don't think the perceived camera speed should be kept constant, as it is natural for it to change with the FOV. It can improve visual comfort, but I don't think this benefits muscle memory.
 
Monitor Distance Match
Monitor Distance Match converts the sensitivity by comparing the horizontal angle values of the FOV, and lets the user define a percentage of the horizontal FOV to match to. Rather than matching the distance for a constant angle like 360 distance, it matches to a dynamic value instead, your FOV, which is an angle on your screen. The result is a screen-space distance match, where the distance to rotate to a point on the screen is constant, but the discrepancy to rotate to any other point will depend on the FOV. This method is the same as Battlefield's Uniform Soldier Aiming system, except you define the point using a multiplier of the vertical angle in Battlefield, and a percentage of the horizontal angle in Monitor Distance Match. The method of comparing the angle values is also commonly used by most games, so you can replicate most games using this method. Example, CSGO divides the horizontal 4:3 angles, so 75% (for 16:9) will copy this.
My opinion: Matching to the square (1:1) aspect ratio's angle is the best distance match. You can find the percentage of this using a calculator, e.g. 1080/1920 * 100 = 56.25%. The benefit for this method is that you can specify a max radius required to move your mouse to aim within your FOV, which can give the sense of comfort, let you use a very low sensitivity, and master one aiming style (such as wrist only, arm only, etc.), but I wouldn't recommend this method for muscle memory. I think the logic behind this method is also flawed, it holds up for camera pitch distance, but camera yaw distance depends entirely on the camera pitch, if you look up or down, the distance to reach a predetermined point will fail.
 
Zoom Match (0% Monitor Distance Match)
Zoom Match converts the sensitivity using the tangent trigonometric function for FOV compensation. The sensitivity scales proportionately with the zoom / focal length, so if the camera zooms in 2x, the sensitivity will also scale by 2x. Screen distances and camera speed are not preserved. This method will have the largest discrepancy in 360 distance when comparing high and low FOVs.
My opinion: This will be the best method for muscle memory, but can also be the least comfortable and requires a higher sensitivity in general. You need to master aiming with all aiming styles. High FOVs will require micro finger movement, and low FOVs will require arm movement.

Means your monitor is 12.25" tall, your input output ratio is roughly 1 : 4.53, and the CPI to achieve 1:4.53 ratio is 399.37. You move your mouse 1 cm, your cursor moves 4.53 cm. You move your mouse 1 inch, your cursor moves 4.53 inch. 1 inch of mouse movement equals 400 pixels, and in-game, 400 pixels worth of rotation.
You wanted the calculator to tell you the perfect value to use as an input, and this will be the most informative thing the calculator could tell you before you settle on a sensitivity without actually testing anything. The outcome is the game is tied to your 2d movement, and all you need to do is change the CPI to achieve that perfect ratio.

Yes, dividing it is not the best way to do it.
Here's what you do, you do not need to change your sensitivity for this:
Right click UserActionBindings key [0] and click Duplicate. Do this two times so you get two new keys.

Expand key 0, 1 and 2 and confirm that they are all identical (all should have the ActionName MoveForward etc). For key 0 change:
ActionName = Turn
KeyBind1 - Keyname = MouseX
KeyBind1 - Keyname = None For key 1 change:
ActionName = LookUp
KeyBind1 - Keyname = MouseY
KeyBind1 - Keyname = None
InputScale = -1.428571
Note that numbers in this file are localized to your locale, so use comma or period according to your settings. In the end the content of the file should look like this:

  Export it to cloud and you're good to go!   
 

I'm sorry I've been sparse with the updates to this thread. This is largely because it's very time-consuming to make illustrations which are really needed to explain the progress I'm making. I'm old.... I've been doing it with pen and paper and such I might just get a camera and put pics of some of that here, rather than just nothing.

 
Theoretically, 0% is perfect. For the image, on the screen. But what we see, is not what is on the screen. What we see, is on the inside of our eye. This is why 0% feels 'slow'. It does not account for the last step in the game world being projected from the monitor to our eye. We do not have any formula which do so, and accordingly, 0% is the most correct theory we have as of right now.



As per the science nerdery posted above, we know that we do not measure distance between two points, in the real world or the game world, directly - as we would with say, a ruler, or by pixels on screen. We measure it by means of deriving the distance from the angle between two points.

This is a terrible thing to attempt to explain without pictures, but I'll try, because it offers us two interesting insights. Firstly, it offers some validity to 'monitor matching', and secondly, offers some hint as to why it is that we seem to prefer to monitor match at the kind of percentages which we do. If none of this makes any sense, I'll do some cruddy mspaint to explain it

Firstly, let's picture our monitor from above or from the side (it doesn't really matter, but I do it from the side because the games use VFOV) so we have a straight line. Now we need to measure our monitor and our seating position (assuming that your eyes are directly in line with the centre of the screen, which for the purpose of FPS games, they should be). We can use the following formula to find our actual FOV of the monitor. I sit 32.5cm from a 1440p 27" monitor (I can hear my mother telling me that's unhealthy), so mine looks like this:
widthpx = 2560
heightpx = 1440
diagcm = 27*2.54
viewdistance = 32.5  <-- ^--- Yep, centimetres because science. Also I'm Aussie You can use inches, just don't *2.54 in the line above.
heightcm = (diagcm/sqrt(widthpx^2+heightpx^2))*heightpx
actualfov = 2(arctan((heightcm/2)/viewdistance))
= 54.70173510519102597649

Unsurprisingly, valve know their stuff (see links above) and I have adjusted my workspace to bring my FOV close to the natural 55-60 degree FOV where our eyes and brain treat the image as important (beyond this is our peripheral vision where we do not see so much detail but mostly movement, again see links above)

So, now we can envision that there is a triangle formed between our eyes (well, our eye. We don't need to worry about stereo for this, so we just use the dominant eye) and the edges of the screen, and the angle from the eyes is as calculated above. Cool. But, let's imagine that angle is increased to say 80degrees (my hipfire FOV). In order for the triangle to meet the edges of the screen, our eyes should be much closer.... and if they are (ie, we move our head closer to the monitor), we see NO distortion. The distortion of the image is NOT caused by the projection. It is caused by the fact that our head doesn't move, to match the focal point of the projection.

Here, we start to uncover the real reason WHY we feel the need to change mouse sensitivity when zooming, at all. It's about the amount of angle our eyes need to move, to cover the same amount of angle in the game world. This is distinct from, the distance our eyes move, to cover the distance between two points. Our brain doesn't work that way. It thinks of all distances as angles, which makes sense really, since it's all a matter of feedback from our eyes telling our brain how much they rotated.

Now, if we take a few FOVs (in my testing I've been using actual, hipfire, 4x and 8x zoom) and measure out the distances to the focal points, we will have one very close to the monitor (hipfire), one where we sit(actual), one some distance behind where we sit (4x), and one very far behind us (8x). Guess what the ratios between those distances are? zoom ratio. Great And we already know, that Zoom Ratio/0% gives us perfect movement in the centre of the screen.

So, why does it fail? Let's say, that we see a target which is half-way to the edge of our monitor. Let us not make the mistakes of the past and think of this as pixels or cm or inches, it is an angle. Our brains all agree on this In my case (using the same formula above and dividing the screen by half again), that's angle= 2(arctan((heightcm/2/2)/viewdistance)) ~=29.00degrees from the centre of the screen.

So, now let's put this into effect using our hipfire, 4x and 8x zoom. Our eyes move 29degrees, how far do we need to rotate in game, to aim at this target? (yes, it can be simplified mathematically, but for the purpose of conversation...) We can calulate the focal distance from our screen, for a given FOV, using the following formula: 
opticallycorrectdistance=(heightcm/2)/(tan(fov/2))
So, I'll do that for my 3 example FOVs:
 
hipdistance=(heightcm/2)/(tan(80/2))
= 20.03463865597708287603
 
fourdistance=(heightcm/2)/(tan(14.8/2))
= 129.4379759752501060469
 
eightdistance=(heightcm/2)/(tan(7.45/2))
= 258.21347922131382533488



And now we can just use the same formula above, with these distances, to calculate how far that ~29 degrees of eye movement amounts to, in the game world:
 
actualfov = 2(arctan((heightcm/2/2)/hipdistance))
= 45.52095254923326167504
 
actualfov = 2(arctan((heightcm/2/2)/fourdistance))
= 7.43098865714869079575
 
actualfov = 2(arctan((heightcm/2/2)/eightdistance))
= 3.72894033006548981691


Ok that's well and good, but why is it important? This quick example, when we compare the results to those of 0%MM/zoom ratio,demonstrates that as our FOV decreases, the effect of the distortion on angular displacement decreases. So what? well, this tell us that the most important adjustment to our mouse sensitivity, is that made between the widest FOV - which is going to be hipfire - and our actual FOV of the screen from our eyes. As the FOV becomes smaller (higher zoom in game) the distortion is lower and lower and less and less meaningful.

So, since we can NEVER make a perfect adjustment of sensitivity for all parts of the screen, because the distortion is not constant across the screen; but we can make an adjustment which is perfect for one part of the screen (this is why there is a percentage in monitor matching and a coefficient in BF and a zoom sensitivity in OW etc)... Which part of the screen is most important? If we say, the centre, then we use zoom ratio. But almost all agree, that 0% feels 'slow', and we know that is because of the angles vs distance thing. If we are CSGO or BF1 defaults, we use 4/3 aka 75% because muh feels. If we're the average OW pro, we use 18%. Why does everyone disagree? Well, if you take the hipfire FOV of a player, and his actual FOV, and work out your ratio from there....suddenly it all begins to line up with what 'muh feels' has been telling us all along.

Sure, ANY variation from the optically correct distance from screen, for a given FOV, will introduce distortion; and that distortion will ensure that our mouse sensitivity will never be correct to any given point on the screen..... but the lower our FOV gets, the more zoomed in we get, the less of a difference it makes. The big difference, is that between our wide hipfire FOV, and our actual FOV of the screen.

I realized that my spreadsheets had an error where I was calculating target distances with the zoom sensitivity ratio relative to the 16:9 magnification instead of relative to the 4:3 magnification like CS:GO does. All three spreadsheets have been updated.
One consequence of this correction is that the Scoping and Scope 2x/4x/8x/15x sensitivities will now all be different values, even if you are using zoom_sensitivity_ratio_mouse 1, since PUBG's sensitivity scaling is relative to 16:9 instead of 4:3 like CS:GO.

Yeah it makes sense to wait.
Here is my method for converting CS:GO sensitivity to PUBG, and it should work for other Source games. Where it gets interesting is that I preserve the behavior of the scoped mouse sensitivity from CS:GO and its zoom_sensitivity_ratio_mouse. While Valve's method for handling scoped sensitivity is far from perfect, as has been discussed ad nauseam on this forum and other places, it is the behavior that feels most natural to me now after years of playing CS:GO and TF2. After refining this method and trying it out extensively in-game, I'm extremely satisfied with how familiar and seamless the aim feels across all scopes/FOVs. All the other methods I've tried that use Viewspeed or various Monitor Distances just did not feel right across all scopes/FOVs.
Note, this method was made for people who primarily stay in third person except to engage in gunfights. This will need a little tweaking once first person only servers come out. Also note that I've included corrected magnifications for the 8x and 15x scopes, as discussed a few posts above. Edit: these steps are now obsolete, check this post for updated instructions.
 
1) Convert your CS:GO 360° rotation to PUBG Hipfire using the calculator. For me, 1 sensitivity @ 900DPI = 46.1818cm per 360°, which gives 0.009900 for PUBG Hipfire. The reason that I've used PUBG's third person (Hipfire) for 360° rotation conversion is because it is the mode you will almost always be in when you need to do large flicks. If you hear gunfire coming from 100m directly behind you, for instance, almost everyone will turn the 180° in third person, because the camera angle and increased FOV help you locate where the gunfire is coming from. Then once you have located the enemy, you switch to ADS or scope in to engage them, for the increased clarity from the zoomed in FOV and lower spread/deviation. So the muscle memory you have built in CS:GO for snapping to precise angles aligns best with PUBG's third person (Hipfire).
2) Hipfire is named Normal in the config file. For VehicleDriver and Targeting in the config file, use the same sensitivity that you calculated in step 1 for Hipfire, since they are all the same FOV.
3) Go to this Google spreadsheet and then "File" > "Download as" so you can have a copy to edit. In the green boxes, edit the red text to enter your personal CS:GO cm per 360° from the calculator and zoom_sensitivity_ratio_mouse (my values are just there as an example).
4) To make zoomed FOV sensitivity behave like CS:GO and other Source games with zoom sensitivity ratio, the target 360° rotation for PUBG Scoping is calculated in cm by starting with the Hipfire 360° rotation and multiplying it by the FOV magnification, then dividing by the zoom sensitivity ratio. This way, the change in a zoomed FOV's sensitivity changes according to the FOV in the exact same way as with the various zoom levels in CS:GO. Sniper rifles' first zoom, AWP second zoom, SSG 08/G3SG1/SCAR-20 second zoom, and AUG/SG 55 zoom are all different magnifications and FOVs in CS:GO, but are all controlled by the same zoom_sensitivity_ratio_mouse value.
5) EDIT - For these last 2 steps, only pick PUBG as the first game in the calculator, don't pick CS:GO for the first game and PUBG as the second game to convert. To get your PUBG Scoping sensitivity, pick Scoping under Aim in the calculator, enter your DPI, and manually alter the sensitivity value until the green 360° rotation value in the CALCULATIONS box is as close to the spreadsheet's Scoping target 360° rotation as possible. Keep in mind that the game only uses six decimal places (0.xxxxxx) for config values, so don't waste your time getting more exact than that. This might sound like it would take forever, but it goes quickly once you get a method down.
6) Scope 2X/4X/8X/15X  target 360° rotations are all calculated similarly to Scoping in step 4, but they are calculated relative to Scoping 360° rotation. So just repeat step 5 for the remaining sensitivities, matching the calculator's green 360° rotation values to the spreadsheet's target 360° rotation values. Make sure to change the calculator's Aim selection for each Scope level, as the same sensitivity value gives different 360° rotations for each of the Aim choices.
 
When you are all done, you should end up with a list of values similar to mine below. You will need to look up how to edit PUBG's config file if you are not familiar with it, and you will probably have to make it Read-only or the game will probably revert your values at some point in time. I suggest making a backup of the config file in case this ever happens.
Normal: 0.009900 VehicleDriver: 0.009900 Targeting: 0.009900 Scoping: 0.008749 Scope2X: 0.007732 Scope4X: 0.007732 Scope8X: 0.008532 Scope15X: 0.009665

Your sensitivities should all be the same since your zoom sensitivity ratio is 1, like this:
Normal: 0.010890 VehicleDriver: 0.010890 Targeting: 0.010890 Scoping: 0.010890 Scope2X: 0.010890 Scope4X: 0.010890 Scope8X: 0.010890 Scope15X: 0.010890 I agree that the zoomed sensitivities feel really high when scaling with zoom sensitivity ratio 1. I would suggest that you experiment with lowering it in CS:GO, which would also make the PUBG scopes less sensitive, relatively, using my method. Maybe start with 0.978753, which is the ratio you get if you convert CS:GO Hipfire to AWP zoom level 1 using viewspeed conversion. I think around 0.9 is a really good compromise that still allows you to make all the reasonable flicks you need to make, but still not so fast that it feels out of control.

Thanks for dealing with my derpiness

I will add specific support for stretched resolutions in the next update.