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Source-free unsupervised domain adaptation (SFUDA) aims to learn a target domain model using unlabeled target data and the knowledge of a well-trained source domain model. Most previous SFUDA works focus on inferring semantics of target data based on the source knowledge. Without measuring the transferability of the source knowledge, these methods insufficiently exploit the source knowledge, and fail to identify the reliability of the inferred target semantics. However, existing transferability measurements require either source data or target labels, which are infeasible in SFUDA. To this end, firstly, we propose a novel Uncertainty-induced Transferability Representation (UTR), which leverages uncertainty as the tool to analyse the channel-wise transferability of the source encoder in the absence of the source data and target labels. The domain-level UTR unravels how transferable the encoder channels are to the target domain and the instance-level UTR characterizes the reliability of the inferred target semantics. Secondly, based on the UTR, we propose a novel Calibrated Adaption Framework (CAF) for SFUDA, including i)the source knowledge calibration module that guides the target model to learn the transferable source knowledge and discard the non-transferable one, and ii)the target semantics calibration module that calibrates the unreliable semantics. With the help of the calibrated source knowledge and the target semantics, the model adapts to the target domain safely and ultimately better. We verified the effectiveness of our method using experimental results and demonstrated that the proposed method achieves state-of-the-art performances on the three SFUDA benchmarks. Code is available at https://github.com/SPIresearch/UTR.