How many outliers are within an unlabeled and contaminated dataset? Despite a series of unsupervised outlier detection (UOD) approaches have been proposed, they cannot correctly answer this critical question, resulting in their performance instability across various real-world (varying contamination factor) scenarios. To address this problem, we propose FlexUOD, with a novel contamination factor estimation perspective. FlexUOD not only achieves its remarkable robustness but also is a general and plug-and-play framework, which can significantly improve the performance of existing UOD methods. Extensive experiments demonstrate that FlexUOD achieves state-of-the-art results as well as high efficacy on diverse evaluation benchmarks.