We propose an empirical barrier distribution for a unified description of heavy-ion fusion and quasi-elastic scattering based on the Skyrme energy-density functional approach. The capture (fusion) cross sections and the quasi-elastic scattering cross sections of a large number of reactions can be well reproduced. Based on these systematic studies and the HIVAP calculations for the survival probability, the probability PCN of the compound-nucleus formation is extracted from the measured evaporation residue cross sections for “cold” and “hot” fusion reactions.