I present a measurement of the W boson mass (M_W) and width (Gamma(W)) using 200 and 350 pb-1 of CDF Run II data respectively. The measurements, performed in both the electron and muon decay channels, rely on a fit to the W transverse mass distribution. We measure M_W = 80413 +/- 48 MeV and Gamma(W) = 2032 +/- 71 MeV which represents the world's single most precise measurements to date.