A positioning device for positioning a stage relative to a tool mounted on a carrier device includes two intersecting linear axes disposed one above the other for pre-positioning the stage. A first magnetic levitation unit is configured to support the stage on one of the linear axes, the stage being actively movable for fine positioning in six degrees of freedom. A measuring head and first and second 6-DOF encoders are configured to determine a position of the stage relative to the carrier device. The measuring head is mounted on the other linear axis. The first 6-DOF encoder is disposed between the carrier device and the measuring head and the second 6-DOF encoder is disposed between the measuring head and the stage. A second magnetic levitation unit disposed on the other linear axis is configured to actively move the measuring head in the six degrees of freedom.