# Abbe error

Abbe error, named after Ernst Abbe, also called sine error, describes the magnification of angular error over distance. For example, when one measures a point that is 1 meter away at 45 degrees, an angular error of 1 degree corresponds to a positional error of over 1.745 cm, equivalent to a distance-measurement error of 1.745%.

In machine design, some components are particularly sensitive to angular errors. For example, if the shaft of a lathe is angled slightly, the part will have errors in diameter far down the part.

Abbe error can be detrimental to dead reckoning.

Formula:

$\epsilon = h \sin \theta$

$\epsilon$ the error.

$h$ the distance.

$\theta$ the angle.