Synthetic Aperture Radar (SAR) experiments hae been performed over the last few years to measure ocean currents inferred from shifts in the Doppler spectral peak. Interpretations of aircraft SAR measurements, when compared with limited surface values, tend to underestimate the currents by about 25%. A theory is developed that modifies the classical Doppler expression showing that the radar measurements are dependent on the radar processor (system) bandwidth and the received signal bandwidth. Measured bandwidths give a correction that increases the inferred current values by about 25%, bringing the measurements into good agreement. This new correction lends credence to the theory and increases the potential for application of SAR systems to future ocean current measurements. SAR measurements should include the determination of processor and signal bandwidths such that this correction can be applied.