How does scale eccentricity or bearing runout affect angular error?

Scale mounting eccentricity error is the offset of the scale center, relative to the actual axis of rotation. Bearing runout, or wander, reflects the change in the radius of rotation through a revolution. Both affect angular error. They can be additive or subtractive, depending on the orientation of the two errors.

Angular error = arctan (eccentricity-error/radius) degrees
Note: sometimes scale concentricity is specified

Eccentricity = concentricity/2

Angular error = acrtan (runout-error/radius) degrees
Note: be sure the errors and radius are the same units

For a shortcut to get angular error in arcsecs, use the following formula:
Angular error = eccentricity/runout-error(um)*412.5/diameter(mm) arcsecs

Click for more information on eccentricity error and examples.