The spontaneous spin polarization of a quantum point contact (QPC) formed by the lateral confinement of a high-mobility two-dimensional electron gas in a GaAs/AlGaAs split gate heterostrucrure is investigated. Self consistent calculations of the electronic structure of the QPC are performed using the spin-polarized density functional formalism of Kohn and Sham. Spin polarization occurs at low electron densities and exchange interaction is found to be the dominant mechanism driving the local spin polarization within the QPC. The cascading scattering matrix approach is utilized to compute the conductance and a conductance anomaly at ∼ 0.5 (2e2/h) has been observed. In addition to this, the sheet density dependence of the 0.7 conduction anomaly is investigated.