Human-chosen passwords are the a dominant form of authentication systems. Passwords strength estimators are used to help users avoid picking weak passwords by predicting how many attempts a password cracker would need until it finds a given password. In this paper we propose a novel password strength estimator, called PESrank, which accurately models the behavior of a powerful password cracker. PESrank calculates the rank of a given password in an optimal descending order of likelihood. PESrank estimates a given password's rank in fractions of a second---without actually enumerating the passwords---so it is practical for online use. It also has a training time that is drastically shorter than previous methods. Moreover, PESrank is efficiently tweakable to allow model personalization in fractions of a second, without the need to retrain the model; and it is explainable: it is able to provide information on why the password has its calculated rank, and gives the user insight on how to pick a better password. Our idea is to cast the question of password rank estimation in a probabilistic framework used in side-channel cryptanalysis. We view each password as a point in a $d$-dimensional search space, and learn the probability distribution of each dimension separately. The dimensions represent the base word, plus a dimension for each possible transformation such as adding a suffix or using a capitalization pattern. Using this model, password strength estimation is analogous to side-channel rank estimation. We implemented PERrank in Python and conducted an extensive evaluation study of it. We also integrated it into the registration page of a course at our university. Even with a model based on 905 million passwords, the response time was well under 1 second, with up to a 1-bit accuracy margin between the upper bound and the lower bound on the rank.