The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.