  We present an approach to estimate the operational distinguishability between
an entangled state and any separable state directly from measuring an
entanglement witness. We show that this estimation also implies bounds on a
variety of other well-known entanglement quantifiers. This approach for
entanglement estimation is then extended to to both the
measurement-device-independent scenario and the fully device-independent
scenario, where we obtain non-trivial but sub-optimal bounds. The procedure
requires no numerical optimization and is easy to compute. It offers ways for
experimenters to not only detect, but also quantify, entanglement from the
standard entanglement witness procedure.
