Surface measuring apparatus for measuring a surface of a workpiece has a probe including a probe arm bearing a probe element for contacting workpiece surface to be measured. Surface measuring apparatus also has a feed apparatus for moving probe element relative to workpiece to be measured. Probe arm is detachably connectable or connected to a movable part of feed apparatus via a mechanical interface having a first part and a second part, which in installed position of probe arm are connected to one another with static determinacy on movable part of feed apparatus, and one of the parts is associated with probe arm and the other part is associated with feed apparatus. At least one alignment protrusion is on first part as an installation alignment aid, which in installed position of probe arm contactlessly or essentially contactlessly engages in an alignment recess formed on second part.