  We describe and study an instantaneous definition of eccentricity to be
applied at the initial moment of full numerical simulations of binary black
holes. The method consists of evaluating the eccentricity at the moment of
maximum separation of the binary. We estimate it using up to third
post-Newtonian (3PN) order, and compare these results with those of evolving
(conservative) 3PN equations of motion for a full orbit and compute the
eccentricity $e_r$ from the radial turning points, finding excellent agreement.
We next include terms with spins up to 3.5PN, and then compare this method with
the corresponding estimates of the eccentricity $e_r^{NR}$ during full
numerical evolutions of spinning binary black holes, characterized invariantly
by a fractional factor $0\leq f\leq1$ of the initial tangential momenta. It is
found that our initial instantaneous definition is a very useful tool to
predict and characterize even highly eccentric full numerical simulations.
