The roughness of an area of the surface of a workpiece (W) is measured by bringing a height measuring device (10) to points on the surface and using the device to measure the height of each point relative to a datum level defined by a skid (17) while the device (10) is stationary relative to the surface. The points are arranged in a repetitive pattern in two dimensions across the area. The movement between the points is brought about by orthogonally arranged stepping motors (20,22).