Measure canthal tilt in 60 seconds

The formula

In a browser, y increases downward. If the outer corner is higher on the screen, its y is smaller. The rise used here is inner y minus outer y, so a higher outer corner produces a positive rise.

angle = atan2(rise, run)

Run is the horizontal distance between the corners. Rise is innerY − outerY after the points have been rotated to remove head roll. A mirror that flips left and right does not flip the sign, because the run is an absolute distance and the rise still compares the two heights.

A numeric example

Suppose the leveled corners are 100 pixels apart and the outer corner is 8 pixels higher. Rise = 8, run = 100. atan2(8, 100) is about 4.6°. That is a positive direction. If the outer corner were 8 pixels lower, rise = −8 and the angle would be about −4.6°.

Why the image horizontal can be wrong

Roll is a lean of the head in the picture plane. Mild roll can be removed by rotating the landmarks back to the face midline. The inner-canthus line is not used for that, because the two inner corners can sit at different heights.^[1]

Pitch is looking up or down. Yaw is turning left or right. Both change perspective. This tool rejects large pitch and yaw instead of pretending to undo them. The automatic points come from MediaPipe Face Landmarker.^[2]

The methodology page records the reference choice, the mirror rule, and the limits.