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In this paper, a new wearable sensing system based on a piezoresistive FlexiForce sensor has been developed. The sensor can be attached to any common chest strap. A compact 3D casing has been designed and printed with a 3D printer. This casing integrates the sensor and all auxiliary elements of the system: microcontroller, battery, Bluetooth module, connections, battery charger, and acquisition circuit. To the best of our knowledge, this is the first study presenting a FlexiForce respiration sensor that includes all system elements in a single compact casing. The source files with the design of the casing have been published as supplementary material to be reused by any interested researcher. The sensing system was tested with twenty-one subjects for different breathing rates. Two different algorithms were developed to obtain the respiratory rate from the voltage signals recorded by the sensor. Statistical tests were performed to determine the optimal computation time window and algorithm. This approach is also novel in this field. Low error values were obtained for a time window of 27\u2009s with an algorithm based on the calculation of time between zero-crossings (4.02%) and with an algorithm based on counting them (3.40%). To promote research transparency and reusability, the dataset with the recorded data and the source code of the algorithms and statistical tests have also been published. 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