Mouse Tool | Source/Quake & Overwatch Sensitivity Converter
Settings
To see where a specific setting is located in any of the following equations, mouse over it.
Sensitivity
By combining your mouse dpi, windows sensitivity, in-game sensitivity, m_yaw values, and dividing them by 360, you can calculate how many centimeters it takes for you to complete a 360 degree turn. This is called your real sensitivity.
360 / (y * d * w * s)

m_yaw
mouse resolution (dpi)
windows sensitivity multiplier
in-game sensitivity
For those of you who don't use the metric system, the above is how many inches it takes to complete a 360 degree turn.

Note: If you are using accel, then the real sensitivity calculation will give you a "base" sensitivity, which is the sensitivity you would get if you disabled accel.
(360 / (y * d * w * s)) * 2.54

m_yaw
mouse resolution (dpi)
windows sensitivity multiplier
in-game sensitivity
DPI
The mouse resolution determines the smallest angle you can rotate your view by in game, for a given sensitivity. If you want this smallest angle to be small enough so that you can turn your view by 1 pixel (to the pixel next to where your crosshair is), you need to know what angle that distance of 1 pixel represents on your screen. The projection of the 3D world onto the 2D plane of your screen means the pixels located near the crosshair represent much larger angles than those pixels located at the edges of your screen. If the mouse resolution calculated above is bigger than your current dpi, then your smallest rotation will be larger than 1-pixel's worth of rotation.

Please note that this is an estimation of useful dpi. We do not recommend adjusting your setup just to satisfy this value; however, if your current dpi is significantly lower, this may suggest your current setup would benefit from a higher dpi.
(pi * g) / (i * tan(f / 2))

in-game resolution width
real sensitivity (inches/360)
field of view (fov)
Acceleration
The interpretation of real accel can be thought of as the extra sensitivity given per speed of mouse movement. The real accel value calculated above is the number of extra degrees per cm gained by moving the mouse at 1 cm/s.

Note: This is defined for quake 3 style accel (or quake live with cl_mouseAccelStyle 0). Trying to use this for another game engine (i.e. source engine) will not work.
(((d * w) / 2.54)^2 * y * a) / 1000)

mouse resolution (dpi)
windows sensitivity multiplier
m_yaw
cl_mouseaccel
Negative Acceleration
If you move your mouse faster than the above speed you will get negative acceleration. This only will occur in games that use mouse pointer input (WM_MOUSEMOVE/GetCursorPos). In order to tell if your game does this, you need to know what type of input your game uses.

If you find yourself moving your mouse faster than the speed above and getting negative acceleration, make sure to look at what elements of the equation could be causing this issue. If possible, lower your dpi or raise your resolution and see what that does for your new max speed calculation. If your fpsdrops below the value you have in the settings section, your maximum speed before reaching negative acceleration will also decrease, which makes it easier to reach the point of negative acceleration.

Games that use mouse pointer input are not the only cause of negative acceleration. The sensor in your mouse can also effect whether or not you get neg accel past a certain speed. For example, my neg accel value calculated from above is 2.54m/s. However, since I use the wheel mouse optical 1.1a, my sensor will cause me to have neg accel past 1m/s (1.55m/s overclocked).

Some information on other mice and the speed they can handle can be found in ESReality's MouseScore from 2007. There was also a test done specifically on the deathadder at a later date.
(g * fps) / (2 * ((d * w) / 0.0254))

in-game resolution width
frames per second (fps)
mouse resolution (dpi)
windows sensitivity multiplier
Maximum Sensitivity
In order to make sure that your radial movements will be less than a pixels radian value, we can use the following formula, which will calculate the maximum sensitivity before this "skipping" occurs.

It is not recommended to set your sensitivity to these values as lower ones will allow for greater precision, however if your current settings are considerably lower it may suggest that you could benefit from a higher sensitivity.
(360 * tan(f / 2)) / (pi * g * y)

field of view (fov)
in-game resolution width
m_yaw
Maximum Yaw
We can use this formula to find our maximum m_yaw/m_pitch values for a given sensitivity before we start to "skip pixels".

It is not recommended to set your m_yaw/m_pitch to these values as lower ones will allow for greater precision, however if your current settings are considerably lower it may suggest that you could benefit from a higher sensitivity.
(360 * tan(f / 2)) / (pi * g * s)

field of view (fov)
in-game resolution width
in-game sensitivity
Shannon's Law
A low DPI value can cause the reticle to skip over hitboxes.

The overall sampling rate of a mouse (samples per degree) is calculated using the DPI, in-game sensitivity and FOV. If the sampling rate is 2 times bigger than the resolution of your screen for a single degree, then your settings are enough to reach any part of the screen.

The sampling rate must be twice as big as your screen resolution due to Shannon's Law. This means the calculated sample/degree will be halved.
(d * i / 360) / 2

mouse resolution (dpi)
real sensitivity (inches/360)
If the Shannon's Law sample per degree value is higher than your screen's pixel/degree, the input field will turn blue, meaning it's fine. Otherwise, it will turn red.

(Note from the dev: This formula has been listed as inaccurate by user everythingllbeok. Still, Pyrolistical says it is correct)
(rh / rg * h) / f

aspect ratio height
aspect ratio width
in-game resolution height
field of view (fov)