pyTopoComplexity is a Python package designed for efficient and customizable quantification of topographic complexity using four advanced methods: two-dimensional continuous wavelet transform analysis, fractal dimension estimation, rugosity index, and terrain position index calculations. This package addresses the lack of open-source software for these advanced terrain analysis techniques essential for modern geomorphology and geohazard research, enhancing data comparison and reproducibility. By assessing topographic complexity across multiple spatial scales, pyTopoComplexity allows users to identify characteristic morphological scales of studied landforms. The software repository also includes a Jupyter Notebook that integrates components from the surface-process modeling platform Landlab (Hobley et al., 2017), facilitating the exploration of how terrestrial processes, such as hillslope diffusion and stream power incision, drive the evolution of topographic complexity over time. When these complexity metrics are calibrated with absolute age dating, they offer a means to estimate in situ hillslope diffusivity and fluvial erodibility, which are critical factors in determining the efficiency of landscape recovery after significant geomorphic disturbances such as landslides. By integrating these features, pyTopoComplexity expands the analytical toolkit for measuring and simulating the time-dependent persistence of geomorphic signatures against environmental and geological forces.