A precision measurement of the mass and width of the W boson is presented. The W bosons are produced in proton antiproton collisions occurring at a centre of mass energy of 1.96 TeV at the Tevatron accelerator. The data used for the analyses is collected by the Collider Detector at Fermilab (CDF) and corresponds to an average integrated luminosity of 350 pb-1 for the W width analysis for the electron and muon channels and an average integrated luminosity of 2350 pb-1 for the W mass analysis. The mass and width of the W boson is extracted by fitting to the transverse mass distribution, with the peak of the distribution being most sensitive to the mass and the tail of the distribution sensitive to the width. The W width measurement in the electron and muon channels is combined to give a final result of 2032 ± 73 MeV. The systematic uncertainty on the W mass from the recoil of the W boson against the initial state gluon radiation is discussed. A systematic study of the recoil in Z \rightarrow e+e- events where one electron is reconstructed in the central calorimeter and the other in the plug calorimeter and its effect on the W mass is presented for the first time in this thesis.