A workpiece measuring apparatus for measuring a workpiece (9, 9x) on a machine tool (1, 101), comprising: a numerical control apparatus for controlling the machine tool (1, 101); a measuring head detachably mounted on a main spindle of the machine tool (1, 101), for measuring the workpiece on the machine tool; a transceiver for sending and receiving signals and data between itself and said measuring head; a control device for controlling said workpiece measuring apparatus; and a predictive system; wherein said workpiece measuring apparatus comprises: a programmable controller for acquiring positional data of said measuring head, with respect to measured points on the workpiece, in at least two-axis directions including a first axis direction and a second axis direction, along which said measuring head scans said workpiece, at predetermined time intervals (ΔT) from said numerical control apparatus; and a pulse output unit for outputting timing pulses at pulse intervals corresponding to said predetermined time intervals (ΔT) to said transceiver; said pulse output unit outputs said timing pulses at the same time that said programmable controller acquires the positional data of said measuring head; and said measuring head measures said workpiece according to a measurement command (f) which is output positively earlier than the timing of the predetermined time intervals (ΔT) by a time difference (n) which is preset by the predictive system and which is kept in timed relation to the timing pulses; whereby a first time at which said programmable controller acquires the positional data of said measuring head and a second time at which said measuring head measures the workpiece in response to the measurement command (f) synchronize. a numerical control apparatus for controlling the machine tool (1, 101); a measuring head detachably mounted on a main spindle of the machine tool (1, 101), for measuring the workpiece on the machine tool; a transceiver for sending and receiving signals and data between itself and said measuring head; a control device for controlling said workpiece measuring apparatus; and a predictive system; wherein said workpiece measuring apparatus comprises: a programmable controller for acquiring positional data of said measuring head, with respect to measured points on the workpiece, in at least two-axis directions including a first axis direction and a second axis direction, along which said measuring head scans said workpiece, at predetermined time intervals (ΔT) from said numerical control apparatus; and a pulse output unit for outputting timing pulses at pulse intervals corresponding to said predetermined time intervals (ΔT) to said transceiver; said pulse output unit outputs said timing pulses at the same time that said programmable controller acquires the positional data of said measuring head; and said measuring head measures said workpiece according to a measurement command (f) which is output positively earlier than the timing of the predetermined time intervals (ΔT) by a time difference (n) which is preset by the predictive system and which is kept in timed relation to the timing pulses; whereby a first time at which said programmable controller acquires the positional data of said measuring head and a second time at which said measuring head measures the workpiece in response to the measurement command (f) synchronize. a programmable controller for acquiring positional data of said measuring head, with respect to measured points on the workpiece, in at least two-axis directions including a first axis direction and a second axis direction, along which said measuring head scans said workpiece, at predetermined time intervals (ΔT) from said numerical control apparatus; and a pulse output unit for outputting timing pulses at pulse intervals corresponding to said predetermined time intervals (ΔT) to said transceiver; said pulse output unit outputs said timing pulses at the same time that said programmable controller acquires the positional data of said measuring head; and said measuring head measures said workpiece according to a measurement command (f) which is output positively earlier than the timing of the predetermined time intervals (ΔT) by a time difference (n) which is preset by the predictive system and which is kept in timed relation to the timing pulses; whereby a first time at which said programmable controller acquires the positional data of said measuring head and a second time at which said measuring head measures the workpiece in response to the measurement command (f) synchronize.