Cementitious concrete is a composite mixture of coarse and fine aggregates, and other additives cemented into a C-S-H matrix. Practically, its strength may be determined by performing compression and tensile tests to specimens with certain sizes and shapes. In order to understand and enhance its strength, it becomes natural to seek the quantitative connections between fractured concrete surfaces and the strength of concrete across the scales of coarse, fine aggregates, and the CSH matrix with nano-scale structures. A multiscale theory across from the size of a test specimen down to the nano-scale of the known C-S-H matrix is proposed here to explain the concrete strength in terms of several physical scales associated with the concrete constituents based on energy conservation principle and fractal characterization of fractured concrete surfaces. When examined against experimental observations and test results, the proposed theory yields satisfactory estimation on nano-level molecular bonding, showing its effectiveness and importance for advancing our understanding of concrete strength. Additionally, the size effect of the testing concrete strength is derived from the proposed theory without making extra physical assumptions.