Recent discoveries that astrocytes exert proactive regulatory effects on neural information processing and that they are deeply involved in normal brain development and disease pathology have stimulated broad interest in understanding astrocyte functional roles in brain circuit. Measuring astrocyte functional status is now technically feasible, due to recent advances in modern microscopy and ultrasensitive cell-type specific genetically encoded Ca2+ indicators for chronic imaging. However, there is a big gap between the capability of generating large dataset via calcium imaging and the availability of sophisticated analytical tools for decoding the astrocyte function. Current practice is essentially manual, which not only limits analysis throughput but also risks introducing bias and missing important information latent in complex, dynamic big data. Here, we report a suite of computational tools, called Functional AStrocyte Phenotyping (FASP), for automatically quantifying the functional status of astrocytes. Considering the complex nature of Ca2+ signaling in astrocytes and low signal to noise ratio, FASP is designed with data-driven and probabilistic principles, to flexibly account for various patterns and to perform robustly with noisy data. In particular, FASP explicitly models signal propagation, which rules out the applicability of tools designed for other types of data. We demonstrate the effectiveness of FASP using extensive synthetic and real data sets. The findings by FASP were verified by manual inspection. FASP also detected signals that were missed by purely manual analysis but could be confirmed by more careful manual examination under the guidance of automatic analysis. All algorithms and the analysis pipeline are packaged into a plugin for Fiji (ImageJ), with the source code freely available online at https://github.com/VTcbil/FASP.