Abstract: A measuring system has a freely movable measuring instrument and a computer for processing the measured data. Two measuring devices are in the measuring instrument, each with two acceleration sensors. Two of the sensor each in a common plane and the two measuring planes are at right angles to one another. A measuring wheel is in the measuring instrument for acquiring the length of the displacement path of the measuring instrument. The measuring instrument acquires the shape and length of a surface line of a body and its representation in two spatial planes with a measuring range from 0 to 360° in one plane. Input elements and a display arrangement on the measuring instrument serve to simplify the measuring process and permit direct control and monitoring of the measuring process.