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Some of the names for guns are incorrect i believe

Putting DNAMTE's ideas into math. 360/hfov * desktop distance * chord /arc = 360° distance We are playing CS:GO which has 106.26 horizontal FOV, on a 2560x1440 monitor, with a 400 DPI mouse. We can find our horizontal desktop distance by doing the following: Resolution Width / DPI * 2.54 = desktop distance (cm) 2560 / 400 * 2.54 = 16.256 cm The arc we can calculate by doing the following: chord + chord * (fovradians - 2 sin(fovradians/2))/(2 sin(fovradians/2)) Our FOV in radians can be calculated like so: hfov * π / 180 = fov (radians) 106.26 * π / 180 = 1.85459... radians The full arc calculation is: 2560 + 2560 * (1.85459 - 2 sin(1.85459/2))/(2 sin(1.85459/2)) = 2967.34 So we have a chord distance of 2560 and an arc distance of 2967. When the game is 2967 pixels wide, you can see why it is distorted to fit into 2560 pixels. Now we have our two distances we can convert it to a 360° distance and find our perfect sensitivity for our given FOV. 360/hfov * desktop distance * chord /arc = 360° distance 360/106.26 * 16.256 * 2560/2967.34 = 47.51372 cm This concludes that with 2560x1440 and a 400 DPI mouse, the perfect sensitivity to match the desktop pointer speed will be 47.51372 cm 360° distance. This is accomplished using 2.186936 sensitivity, equal to 875 eDPI as a reference point when comparing sensitivities to other players. The full formula without using rounding would be like so: 360/106.26 (2560/400×2.54)×2560/(2560 + 2560×(106.26×π/180 - 2 sin(1/2 (106.26×π/180)))/(2 sin(1/2 (106.26×π/180)))) = 47.5137... Simplified down to: (4 π z sin(x/2))/x^2 where x = fov radians and z = desktop distance (4 π (2560/400×2.54) sin(1/2 (106.26×π/180)))/(106.26×π/180)^2 = 47.5137...