Materials based on Cu2O are potential p-type transparent semiconducting oxides. Developing an understanding of the mechanism leading to p-type behaviour is important. An accepted origin is the formation of Cu vacancies. However, the way in which this mechanism leads to p-type properties needs to be investigated. This paper presents a first principles analysis of the origin of p-type semiconducting behaviour in Cu2O with 1.5 and 3% Cu vacancy concentrations. Plane wave density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional is applied. In order to investigate the applicability of DFT, we firstly show that CuO, with 50% Cu vacancies cannot be described with DFT and in order to obtain a consistent description of CuO, the DFT + U approach is applied. The resulting electronic structure is consistent with experiment, with a spin moment of 0.64 mu(B) and an indirect band gap of 1.48 eV for U = 7 eV. However, for a 3% Cu vacancy concentration in Cu2O, the DFT and DFT+ U descriptions of Cu vacancies are similar, indicating that DFT is suitable for a small concentration of Cu vacancies; the formation energy of a Cu vacancy is no larger than 1.7 eV. Formation of Cu vacancies produces delocalised hole states with hole effective masses consistent with the semiconducting nature of Cu2O. These results demonstrate that the p-type semiconducting properties observed for Cu2O are explained by a small concentration of Cu vacancies.