A method and an apparatus for determining the dimensional accuracy of workpiece surfaces, for example, of essentially cylindrical workpiece surfaces, wherein a measuring sensor scans the workpiece surfaces in accordance with a predetermined relative movement pattern between sensor and workpiece. The sensor is a pneumatic measuring head, so that the measuring procedure can be incorporated in the production process. The pneumatic measuring head travels over the workpiece surface along a continuous path which covers the surface area of the workpiece. The pneumatic measuring head is maintained at a constant basic or measuring distance from the workpiece surface, so that the measuring range of the measuring head is not exceeded when the measuring head travels over the workpiece surface. The measuring head continuously produces measurement signals, so that the measure procedure can be directly integrated in the production sequence.