Mouse Movement

Mouse movement represents the instant displacement of the cursor on the screen (in pixels) : (${\textstyle dx,dy}$).

When it comes to Minecraft, mouse movement represents the instant rotation of the camera (in degrees) : (${\textstyle \Delta x,\Delta y}$).

Sensitivity

Sensitivity (s) is a parameter that changes how fast the camera should turn.

This setting can be changed in the Controls menu.

• The default sensitivity is "100%" (${\textstyle s=0.5}$)

• The lowest vanilla sensitivity is "0%" (${\textstyle s=0.0}$)
• The highest vanilla sensitivity is "200%" (${\textstyle s=2.0}$)

In 1.8, ${\textstyle \Delta x}$ is calculated as:

$\Delta x=1.2dx\times (0.6s+0.2)^{3}$

${\textstyle \Delta y}$ is obtained in the same way, and is multiplied by -1 if "Invert Mouse" is ON.

With default sensitivity (${\textstyle s=0.5}$), one pixel of mouse movement translates into 0.15° of rotation.

This means that the camera moves in increments of 0.15°: to turn 45°, you would need to move your mouse by 300px.

Furthermore, s isn't bounded by [0,1], and can take any value (even negative).

You can manually edit the value of mouseSensitivity in the options.txt file (found in the .minecraft folder)

Remarkable values

Since it's possible to set the sensitivity to any value we want, it might be interesting to adjust the sensitivity to match specific rotation increments.

To get the required sensitivity for the desired increment ${\textstyle \delta }$, you can use the inverse formula:

$s={\frac {{\sqrt[{3}]{\frac {\delta }{1.2}}}-0.2}{0.6}}$

s	${\textstyle \delta }$
-0.3333333	0°
0.3946504	0.1°
0.5	0.15°
0.6546926	0.25°
0.9115013	0.5°
1.2350600	1°
5.2452746	45°
8.5221547	180°

Yaw and Pitch

... [WIP]