Accelerometer system with automatic calibration composed of: an electronic conditioning and digitizing circuit, a vibrating device driven by said electronic circuit, and a set of groups of accelerometer transducers (1, 2, 3) wherein: a. each group is assembled aligned along the direction of one of the measuring axes of said accelerometer system, and each group is assembled aligned to a different axis from any other group b. each group is composed of at least two accelerometer transducers capable of reading different frequency bands which are partially overlapped c. each group is composed of a first transducer which has a band starting from zero frequency or which is able to autonomously guarantee validity and calibration of the performed reading d. the vibrating system, driven by the electronic circuit, is designed to generate a vibration in the range of overlapping of the two frequency bands of the different accelerometer transducers (1, 2, 3), the accelerometer system further comprising an analysis algorithm which, managed by the electronic circuit, allows reading the digitized signals coming from each group of accelerometers (1, 2, 3) and re-combining them for every axis in a global wide band signal, which, as lower frequency, has value zero or the lower value of the band of the first transducer, and, as maximum value, the maximum frequency value of the accelerometer capable of measuring the frequency band with the highest value, wherein each group of accelerometers (1, 2, 3) is composed of at least two transducers (6, 7) which are capable of reading, in parallel, different frequency bands which are partially overlapped and one of which has a band which starts from zero frequency or which is able to check its actual operation and guarantee its calibration in time; wherein the system is designed to calibrate the whole chain of transducers, either by starting from the warranty provided by the first accelerometer or by reading the acceleration value at zero frequency and comparing it with the gravity acceleration, after having validated the first accelerometer, the analysing algorithm of the system being designed to compare the values read in the overlapping area between the first accelerometer and the immediately following accelerometer, thereby also validating the correct calibration of the second transducer, said comparing being then repeated every time in case of systems with more than two transducers per group of accelerometers (1, 2, 3); and wherein the system is adapted, when one of the transducers of the chain is not adequately calibrated, to automatically self- calibrate itself, and to communicate as output through a suitable digital output, for example an electric, luminous or sound output, its previous incorrect calibration. a. each group is assembled aligned along the direction of one of the measuring axes of said accelerometer system, and each group is assembled aligned to a different axis from any other group b. each group is composed of at least two accelerometer transducers capable of reading different frequency bands which are partially overlapped c. each group is composed of a first transducer which has a band starting from zero frequency or which is able to autonomously guarantee validity and calibration of the performed reading d. the vibrating system, driven by the electronic circuit, is designed to generate a vibration in the range of overlapping of the two frequency bands of the different accelerometer transducers (1, 2, 3),