It is well known that the kinetic energy formula of classical mechanics has a limited range of applicability. That formula breaks down when the mass of a moving body increases and the effects of relativity can no longer be ignored. More than a hundred years ago, Sommerfeld and Einstein defined relativistic kinetic energy as the difference between a body’s relativistic energy and its rest mass energy. This paper, however, derives a formula for relativistic kinetic energy that is not a definitional formula. The formula derived in this paper incorporates the phase velocity of a wave. It further finds that the phase velocity of the wave is an important physical quantity linking a body’s kinetic energy and momentum. In current standard physics, the de Broglie wave is not regarded as having physical reality. Nevertheless, this paper concludes that the phase velocity of a matter wave is an essential physical quantity.