  We present exact formulas for the entanglement and R\'{e}nyi entropies
generated at a quantum point contact (QPC) in terms of the statistics of charge
fluctuations, which we illustrate with examples from both equilibrium and
non-equilibrium transport. The formulas are also applicable to groundstate
entanglement in systems described by non-interacting fermions in any dimension,
which in one dimension includes the critical spin-1/2 XX and Ising models where
conformal field theory predictions for the entanglement and R\'{e}nyi entropies
are reproduced from the full counting statistics. These results may play a
crucial role in the experimental detection of many-body entanglement in
mesoscopic structures and cold atoms in optical lattices.
