Determining the critical conditions of wear is crucial for accurately elucidating the wear mechanism. However, in previous studies, the elastic energy used to derive the critical conditions of wear was estimated. In this paper, the elastic energy stored in a single asperity was calculated accurately by using finite element method. Formulas for calculating the elastic energy in terms of the load, the size of asperities, and material parameters were provided. Subsequently, the critical wear conditions were determined by comparing the elastic energy with the fracture energy. Wear particles are formed only when the load and asperity size meet the given critical conditions. This outcome clarifies the existence of a normal load threshold for wear. It proves instrumental in comprehending the formation process of wear particles and establishing an accurate wear model. It provides theoretical references for wear problems in practical engineering.