How to Measure Canthal Tilt

Five steps

1. Take a front-facing photo with the camera at eye level. Both corners need to be visible.
2. Find the medial canthus, the inner corner next to the nose.
3. Find the lateral canthus, the outer corner toward the ear.
4. Establish a face-relative horizontal. This site uses a line perpendicular to the facial midline. A 3D head-pose roll is used only when it agrees with that midline.^[1]
5. Calculate the signed angle. Positive means the outer corner is higher in the image.

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°.

Manual measurement demo

Drag the two points. The drawing uses the same signed angle as the scanner.

Why the image horizontal can be wrong

Roll is a lean of the head in the picture plane, like tilting the camera. 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.

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.

Camera height, pitch, yaw, roll, and expression can all change the apparent angle. A clinical photograph in the cited series also built its horizontal from the facial midline rather than from the photo frame.^[1] The automatic points come from MediaPipe Face Landmarker.^[2]

The methodology page records the reference choice, the mirror rule, and the limits. Compare directions on the positive versus negative page.