Differential privacy has become a popular privacy-preserving method in data analysis, query processing, and machine learning, which adds noise to the query result to avoid leaking privacy. Sensitivity, or the maximum impact of deleting or inserting a tuple on query results, determines the amount of noise added. Computing the sensitivity of some simple queries such as counting query is easy, however, computing the sensitivity of complex queries containing join operations is challenging. Global sensitivity of such a query is unboundedly large, which corrupts the accuracy of the query answer. Elastic sensitivity and residual sensitivity offer upper bounds of local sensitivity to reduce the noise, but they suffer from either low accuracy or high computational overhead. We propose two fast query sensitivity estimation methods based on sampling and sketch respectively, offering competitive accuracy and higher efficiency compared to the state-of-the-art methods.