The electrochemical actuation of covalent carbon materials, such as graphene, immersed in liquid electrolytes has shown immense promise for a myriad of applications. To realize this potential, an intimate understanding of the physics behind the actuation is essential. With the use of ab initio density functional calculations, it is shown that the strain induced in monolayer graphene by the formation of an electrostatic double-layer (DL) is the dominant actuation mechanism. The DL-induced strain (~1%) is found to exceed the quantum-mechanical strain (~0.2%) due to charge injection only, for charges and electric potentials of greater than -0.08 e/C-atom and 1 V, respectively. Various methods of calculating the graphene atomic charges based on first principle charge densities are compared and contrasted. The electrochemical charge-strain and potential-strain relationships for monolayer graphene are shown to be parabolic in nature. This study proves that the origin of the high electrochemical strains in covalent carbon materials is the electrostatic DL potential, and demonstrates the true viability of using monolayer graphene for nanoelectromechanical systems (NEMS) actuators.