At a certain voltage E, equilibrium will attain and the forward and backward rates (v and v) will be equal. This is represented by the green curve in the above figure. The equilibrium rate constants will be written as k and k, and the equilibrium concentrations will be written c and c. The equilibrium currents (j and j) will be equal and are written as j, which is known as the exchange current density.
Note that the net current density at equilibrium will be zero. The equilibrium rate constants are then:
Solving the above for k and k in terms of the equilibrium concentrations c and c and the exchange current density j, the current density j as a function of applied potential E may now be written:
Assuming that equilibrium holds in the bulk solution, with concentrations  and , it follows that  and , and the above expression for the current density j is then the Butler–Volmer equation. Note that E-E is also known as &eta;, the activation overpotential.