Spin-resolved scanning tunneling microscopy is employed to quantitatively determine the spin polarization of the magnetic field-split Kondo state. Tunneling conductance spectra of a Kondo-screened magnetic atom are evaluated within a simple model taking into account inelastic tunneling due to spin excitations and two Kondo peaks positioned symmetrically around the Fermi energy. We fit the spin state of the Kondo-screened atom with a spin Hamiltonian independent of the Kondo effect and account for Zeeman splitting of the Kondo peak in the magnetic field. We find that the width and the height of the Kondo peaks scales with the Zeeman energy. Our observations are consistent with full spin polarization of the Kondo peaks, i.e., a majority spin peak below the Fermi energy and a minority spin peak above. The Kondo effect was discovered experimentally nearly one century ago and starting from the 1960s theory has been employed to unravel its origin and properties [1]. It arises from the screening of a localized magnetic moment by host electrons, which leads to a Fermi-level resonance in the density of states. Kondo physics in the absence of a magnetic field has been studied extensively [2,3], whereas the precise behavior of the Kondo state in a magnetic field is less studied [4][5][6][7][8]. The coupling of the localized spin to the environment sets the relevant energy scale which is typically referred to as Kondo temperature T K . For magnetic fields exceeding this energy the Kondo resonance splits. However, the spinresolved properties of this split Kondo state and, in particular, the amount of spin polarization of the two resulting peaks remains elusive [9,10]. While there is one spin-resolved measurement of a split Kondo state [11], the asymmetry of the peaks was not studied systematically and a comprehensive picture is missing.The Kondo effect of a single atom or molecule on a surface can be probed with scanning tunneling spectroscopy (STS) [3]. When the localized spin is only weakly coupled to the conduction electrons of the substrate a perturbative description can be used [12] and a logarithmic peak at the Fermi energy is detected [13]. For stronger hybridization the arising correlations lead to a change in the density of states [6], which is typically described by a Lorentzian or a Frota function [14]. An additional linear tunnel channel gives rise to interference between different paths, leading to an asymmetric, Fano-like, line shape [15,16]. Systems with a spin S > 1=2 can show the Kondo effect when the magnetocrystalline anisotropy leads to a degenerate m ¼ AE1=2 ground state [5]. Then the resonance at zero bias is accompanied by steps in the tunnel spectra due to inelastic electron tunneling that excites the spin at finite energy. Inelastic tunnel spectroscopy has been employed to investigate such spin excitations in single atoms, molecules, and small clusters on ultrathin insulating layers, semiconductors, and metals [5,[17][18][19][20][21].In this Letter we quantitatively determine the spin polarization of...