This research presents a real-time adaptive phase correction technique for flexible phased array antennas on conformal surfaces of variable shapes. Previously reported pattern correctional methods for flexible phased array antennas require prior knowledge on the possible non-planar shapes in which the array may adapt for conformal applications. For the first time, this initial requirement of shape curvature knowledge is no longer needed and the instantaneous information on the relative location of array elements is used here for developing a geometrical model based on a set of B\'ezier curves. Specifically, by using an array of inclinometer sensors and an adaptive phase-correctional algorithm, it has been shown that the proposed geometrical model can successfully predict different conformal orientations of a 1–by–4 antenna array in real-time without the requirement of knowing the shape-changing characteristics of the surface the array is attached upon. Moreover, the phase correction technique is validated by determining the field patterns and broadside gain of the 1–by–4 antenna array on four different conformal surfaces with multiple points of curvatures. Throughout this work, measurements are shown to agree with the analytical solutions and full-wave simulations.