Handheld Ground Penetrating Radar (GPR) is commonly employed for rebar detection; however, detecting damage remains challenging due to its low reflectance. This study introduces an algorithm designed to quantitatively estimate damage thickness from GPR-received waveforms. Simple methods to distinguish peaks in the time waveforms at the top and bottom of cracks are complicated by destructive interference and side lobes. Previous studies have confirmed that minor variations in damage thickness significantly affect the frequency properties. We propose an algorithm that estimates damage thickness through pattern matching with a theoretical amplitude spectrum, which considers multiple reflections. Initially, damage thickness is coarsely estimated by combining low-frequency spectrum centroids with spectrum amplitude. Following this initial estimate, further spectral pattern matching is performed within predefined gating and bandwidth ranges. This method enables the quantitative estimation of damage thickness ranging from 2 mm to 180 mm with millimeter-order accuracy, demonstrating substantial potential for practical application.