DNA molecules perform biological functions via large elastic deformations and conformational changes in their interactions with the cellular machinery. Accordingly, adequate characterization of DNA elasticity is instrumental to an in-depth understanding of DNA functions. Because of their profound complexity, however, nonlinear features inherent in DNA elasticity remains to be uncovered in a direct and full sense, and a unified and explicit characterization over the entire stretch range is still unavailable. This paper suggests that DNA elastic nonlinearities may be understood by combining linear springs with high compliance and high rigidity. This finding uncovers the inherent geometrical feature in profound nonlinearities of DNA elasticity, and leads to a unified and explicit force-extension formula up to breaking. This formula reveals for the first time a complete set of characteristic constants for DNA elasticity and is shown to provide a unified characterization for both double- and single-stranded DNA molecules. Results are presented in a straightforward and broad sense independent of any substructural details.