  The binding energy parameter $\lambda$ plays an important role in common
envelope (CE) evolution. Previous works have already pointed out that $\lambda$
varies throughout the stellar evolution, though it has been adopted as a
constant in most of the population synthesis calculations. We have
systematically calculated the binding energy parameter $\lambda$ for both
Population I and Population II stars of masses $1-20 M_{\sun}$, taking into
account the contribution from the internal energy of stellar matter. We present
fitting formulae for $\lambda$ that can be incorporated into future population
synthesis investigations. We also briefly discuss the possible applications of
the results in binary evolutions.
