Accurate measurement of the Sagnac effect for matter waves

A rotating interferometer with paths that enclose a physical area exhibits a phase shift proportional to this area and to the rotation rate of the frame. Understanding the origin of this so-called Sagnac effect has played a key role in the establishment of the theory of relativity and has pushed for the development of precision optical interferometers.The fundamental importance of the Sagnac effect motivated the realization of experiments to test its validity for waves beyond optical, but precision measurements remained a challenge.Here we report the accurate test of the Sagnac effect for matter waves, by using a Cesium-atom interferometer featuring a geometrical area of 11 cm$^2$ and two sensitive axes of measurements. We measure the phase shift induced by the Earth's rotation and find agreement with the theoretical prediction at an accuracy level of 25 ppm. Beyond the importance for fundamental physics, our work opens practical applications in seismology and geodesy.