Reconstruction of the W mass and width at and above WW threshold at FCC-ee

In the Standard Model theory, the mass of the W boson is predicted with an uncertainty of 4 MeV/c$^{2}$ whereas the current experimental accuracy is of 12 MeV/c$^{2}$. The present uncertainty is currently limiting the sensitivity to possible effects of new physics through the global fit of the electroweak observables. With more than $2 \times 10^8$ W pairs produced at the W threshold energy and above, the FCC-ee collider will be a W boson factory allowing for W mass measurement with unparalleled precision. The W mass can be directly measured at and above the threshold from the kinematic reconstruction of the W-pair decay products. In addition, $e^+e^-$ collisions offer the possibility to derive the W mass from the WW cross-section measured at the pair-production threshold. The precise measurement of the W mass and width, with both methods, is presented in the context of a future experiment at FCC-ee. A statistical uncertainty on the W mass below 1 MeV/c$^{2}$ is expected and the experimental and theoretical systematic uncertainties must be reduced to match such a level of precision