We develop a simple coordinate transformation that can be employed to compensate for the nonlinearity introduced by a microwave kinetic inductance detector’s (MKID) homodyne readout scheme. This coordinate system is compared to the canonically used polar coordinates and is shown to improve the performance of the filtering method often used to estimate a photon’s energy. For a detector where the coordinate nonlinearity is primarily responsible for limiting its resolving power, this technique leads to increased dynamic range, which we show by applying the transformation to data from a hafnium MKID designed to be sensitive to photons with wavelengths in the 800- to 1300-nm range. The new coordinates allow the detector to resolve photons with wavelengths down to 400 nm, raising the resolving power at that wavelength from 6.8 to 17.