  Understanding the quantitative relation between entanglement and Bell
nonlocality is a longstanding open problem of both fundamental and practical
interest. Here we provide a general approach to address this issue. Starting
with an observation that entanglement measures, while defined dramatically
different in mathematics, are basically the distances between the state of
interest and its closest separable state, we relate this minimal distance
between states with distance-based Bell nonlocality, namely, the minimal
distance between correlation of interest with respect to the set of classical
correlations. This establishes the quantitative relation between entanglement
and Bell nonlocality, leading to the bounds for entanglement in various
contexts. Our approach enjoys the merits of: (i) generality, it applies to any
Bell's scenario without requiring the information of devices and to many
entanglement measures, (ii) faithfulness, it gives a non-trivial entanglement
estimation from any nonlocal correlation.
