This study aims to characterize the size and shape dependent melting temperature of nanomaterials. Considering that surface atoms and interior atoms affect the melting of materials in different manners, we thus define an equivalent relationship between the contribution of surface atoms and interior atoms. Based on this definition, a criterion of melting is proposed through introducing a critical energy storage density of melting, the sum of the contribution of surface atoms and the interior atoms. According to the proposed criterion, a new theoretical model without any adjustable parameters is developed to characterize the size effect of melting temperatures of nanomaterials. The model predictions are in good agreement with the available experimental data or molecular dynamics simulations. This model uncovers the quantitative relationship between the melting temperature, size, atomic diameter and shape of nanomaterials. In addition, this model is extended to predict the size dependent glass transition temperatures of polymers. This study can help to better understand and characterize the size dependent melting temperatures of nanomaterials, as well as the size dependent glass transition temperatures of polymers.