  Covariance matrices are a useful tool to investigate correlations and
entanglement in quantum systems. They are widely used in continuous variable
systems, but recently also for finite dimensional systems powerful entanglement
criteria in terms of covariance matrices have been derived. We show how these
results can be used for the quantification of entanglement in bipartite
systems. To that aim we introduce an entanglement parameter that quantifies the
violation of the covariance matrix criterion and can be used to give a lower
bounds on the concurrence. These lower bounds are easily computable and give
entanglement estimates for many weakly entangled states.
