We have studied monolayer Au islands on a Au(100) electrode in sulfuric acid solution using electrochemical scanning tunneling microscopy. We present quantitative studies of the equilibrium shape of Au islands on Au(100) electrodes and of island shape fluctuations. As was recently demonstrated for islands on metal surfaces under ultra-high vacuum, step and kink energies may be determined. Furthermore, we have measured the angle dependence of the step energy and the curvature of the quasi-straight island segments as a function of the electrode potential. We find that the step and the kink energies are potential dependent.