A study of phase breaking of equilibrium and nonequilibrium electrons in a ballistic quantum dot is presented. Estimates for the phase breaking time are obtained from the magnitude of the weak-localization peak, observed in the conductance on sweeping either magnetic field or dc bias voltage. These investigations reveal that the phase breaking of equilibrium and nonequilibrium electrons exhibits the same functional dependence on energy. In particular, at sufficiently high energies the phase breaking time is found to vary as an inverse square law of energy, consistent with predictions for electron-electron scattering due to Coulomb interaction in quantum dots. At lower energies, however, a saturation in the phase breaking rate is observed, the onset of which is found to be well correlated to the average level spacing of the dot.